TM TM | University of Oxford (original) (raw)
Papers by TM TM
This article proposes the concept of anisotropy tailoring in multi-material lattices based on a m... more This article proposes the concept of anisotropy tailoring in multi-material lattices based on a mechanics-based bottom-up framework. It is widely known that isotropy in a mono-material lattice can be obtained when the microstructure has an isotropic geometry. For example, regular hexagonal lattices with a unit cell comprised of six equal members and equal internal angle of 120^o each, show isotropy in the elastic properties. Such limited microstructural configuration space for having isotropy severely restricts the scope of many multi-functional applications such as space filling in 3D printing. We first demonstrate that there are multiple structural geometries in mono-material lattices that could lead to isotropy. It is shown that the configuration space for isotropy can be expanded by multiple folds when more than one intrinsic material is introduced in the unit cell of a lattice. We explicitly demonstrate different degrees of anisotropy in regular geometrically isotropic lattices by introducing the multi-material architecture. The contours of achieving minimum anisotropy, maximum anisotropy and a fixed value of anisotropy are presented in the design space consisting of geometric and multi-material parameters. Proposition of such multi-material microstructures could essentially expand the multi-functional design scope significantly, offering a higher degree of flexibility to the designer in terms of choosing (or identifying) the most suitable microstructural geometry. An explicit theoretical characterization of the contours of anisotropy along with physical insights underpinning the configuration space of multi-material and geometric parameters will accelerate the process of its potential exploitation in various engineered multi-functional materials and structural systems across different length-scales with the demand of any specific degree of anisotropy but limitation in the micro-structural geometry.
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Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting mu... more Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting multi-functional properties. However, a single-layer of 2D materials may not have a certain property adequately , or multiple application-specic properties simultaneously to the desired and optimal level. For mitigating this lacuna, a new trend has emerged recently to develop nano-scale engineered heterostruc-tures by stacking multiple layers of dierent 2D materials, wherein each of the layers could also be twisted. The vast advantage of combining single layers of dierent 2D materials with dierent twisting angles has dramatically expanded this research eld well beyond the scope of considering a 2D material mono-layer, leading to a set of multifunctional physical properties corresponding to each possible combination of number of layers, dierent 2D materials therein, stacking sequence and the twisting angle of each layer. Eective mechanical properties such as Young's moduli are generally of utmost importance for analysing the viability of such engineered nano-heterostructures in various nanoelectromechanical applications. We have proposed efficient closed-form generic formulae for the eective Young's moduli of twisted multi-layer heterostructures. Based on this physics-based analytical approach, a wide range of insightful new results are presented for twisted heterostructures, covering mono-planar and multi-planar congurations with homogeneous and heterogeneous atomic distributions.
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Journal of Sandwich Structures and Materials, 2016
This paper presents a generic multivariate adaptive regression splines-based approach for dynamic... more This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C⁰ stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.
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Composites Part B Engineering, 2019
This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) p... more This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) plates subjected to free vibration and low-velocity impact to identify the most influential parameters in the respective analyses. A hybrid moment-independent sensitivity analysis is proposed coupled with the least angle regression based adaptive sparse polynomial chaos expansion. Here the surrogate model is integrated in the sensitivity analysis framework to achieve computational efficiency. The current paper is concentrated on the relative sensitivity of material properties in the free vibration (first three natural frequencies) and low-velocity impact responses of FGM plates. Typical functionally graded materials are made of two different components, where a continuous and inhomogeneous mixture of these materials is distributed across the thickness of the plate based on certain distribution laws. Thus, besides the overall sensitivity analysis of the material properties, a unique spatial sensitivity analysis is also presented here along the thickness of the plate to provide a comprehensive view. The results presented in this paper would help to identify the most important material properties along with their depth-wise spatial sensitivity for low-frequency vibration and low-velocity impact analysis of FGM plates. This is the first attempt to carry out an efficient adaptive sparse PCE based moment-independent sensitivity analysis (depth-wise and collectively) of FGM plates under the simultaneous susceptibility of vibration and impact. Such simultaneous multi-objective sensitivity analysis can identify the important system parameters and their relative degree of importance in advanced multi-functional structural systems.
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Thin-Walled Structures, 2019
This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwi... more This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwich plates with composite face sheets considering the effects of obliqueness in impact angle and twist in the plate geometry. The stochastic impact analysis is conducted by using finite element (FE) modelling based on an eight nodded isoparametric quadratic plate bending element coupled with multivariate adaptive regression spline (MARS) in order to achieve computational efficiency. The modified Hertzian contact law is employed to model contact force and other impact parameters. Newmark's time integration scheme is used to solve the time-dependent equations. Comprehensive deterministic as well as probabilistic results are presented by considering the effects of location of impact, ply orientation angle, impactor velocity, impact angle, face-sheet material property, twist angle, plate thickness and mass of impactor. The relative importance of various input parameters is determined by conducting a sensitivity analysis. The results presented in this paper reveal that the impact responses of sandwich plates are significantly affected by the effect of source-uncertainty that in turn establishes the importance of adopting an inclusive stochastic design approach for impact modelling in sandwich plates.
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Due to the absence of adequate control at different stages of complex manufacturing process, mate... more Due to the absence of adequate control at different stages of complex manufacturing process, material and geometric properties of composite structures are often uncertain. For a secure and safe design, tracking the impact of these uncertainties on the structural responses is of utmost significance. Composite materials, commonly adopted in various modern aerospace, marine, automobile and civil structures, are often susceptible to low-velocity impact caused by various external agents. Here, along with a critical review, we present machine learning based probabilistic and non-probabilistic (fuzzy) low-velocity impact analyses of composite laminates including a detailed deterministic characterization to systematically investigate the consequences of source-uncertainty. While probabilistic analysis can be performed only when complete statistical description about the input variables are available, the non-probabilistic analysis can be executed even in the presence of incomplete statistical input descriptions with sparse data. In this study, the stochastic effects of stacking sequence, twist angle, oblique impact, plate thickness, velocity of impactor and density of impactor are investigated on the crucial impact response parameters such as contact force, plate displacement, and impactor displacement. For efficient and accurate computation, a hybrid polynomial chaos based Kriging (PC-Kriging) approach is coupled with in-house finite element codes for uncertainty propagation in both the probabilistic and non-probabilistic analyses. The essence of this paper is a critical review on the hybrid machine learning algorithms followed by detailed numerical investigation in the probabilistic and non-probabilistic regimes to access the performance of such hybrid algorithms in comparison to individual algorithms from the viewpoint of accuracy and computational efficiency.
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A novel origami metamaterial with programmable multi-directional auxeticity is proposed by hybrid... more A novel origami metamaterial with programmable multi-directional auxeticity is proposed by hybridizing the concept of re-entrant honeycomb with the Miura pattern. Normal Miura-based origami metamaterials have been widely shown to exhibit negative in-plane Poisson's ratio. However, negative out-of-plane Poisson's ratio cannot be realized in these set of materials, essentially limiting their capability for prospective applications in many multi-functional devices and systems. Here we propose a hybrid Miura-based metamaterial that can show both in-plane and out-of-plane negative Poisson's ratios. More interestingly, we are able to program the Poisson's ratios to have mild to extreme auxeticity and map their mutual interaction as a function of the microstructural configuration. Besides the single-layer meta-sheets, we have shown that a class of multi-layer stacked metamaterial with uniform and graded configurations can be developed to achieve multi-objective functional goals. Theoretical and experimental analyses are combined in this paper to demonstrate the concepts of modulating multi-directional Poisson's ratios. The fundamental mechanics of the proposed origami based metamaterial being scale-independent, this novel class of deployable hybrid materials can be directly transferred for application in a range of milli-, micro-, and nanometer-size systems, essentially opening avenues for the design of energy absorbers, sensors, actuators, medical stents, catalysis, drug delivery systems, adaptive wings for next-generation of aircrafts and other deployable mechanical and electronic systems at multiple length-scales.
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An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependen... more An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependence of lattice material microstructures. Under a vibrating condition, effective elastic moduli of such microstructured materials can become negative for certain frequency values, leading to an unusual mechanical behaviour with a multitude of potential applications. We have derived the fundamental theoretical limits for the minimum frequency, beyond which the negative effective moduli of the materials could be obtained. An efficient dynamic stiffness matrix based approach is developed to obtain the closed-form limits, which can exactly capture the sub-wavelength scale dynamics. The limits turn out to be a fundamental property of the lattice materials and depend on certain material and geometric parameters of the lattice in a unique manner. An explicit characterization of the theoretical limits of negative elastic moduli along with adequate physical insights would accelerate the process of its potential exploitation in various engineered materials and structural systems under dynamic regime across the length-scales. Introduction.-The global mechanical properties can be engineered in lattice materials by intelligently identifying the material microstructures as the properties in these materials are often defined by their structural configuration along with the intrinsic material properties of the constituent members. This novel class of materials with tailorable application-specific mechanical properties (like equivalent elastic moduli, buckling, vibration and wave propagation characteristics with modulation features) have tremendous potential applications for future aerospace, civil, mechanical, electronics and medical applications across the length-scales. Naturally occurring materials cannot exhibit unprecedented and fascinating properties such as extremely lightweight, negative elastic moduli, negative mass density, pentamode material characteristics (meta-fluid), which can be achieved by an intelligent microstructural design [1, 2]. For example, the conventional positive value of Poisson's ratio in a hexagonal lattice metamaterial can be converted to a negative value [3] by making the cell angle θ in figure 1(b) negative. Other unusual and exciting properties can be realized in metamaterials under dynamic condition, such as negative bulk modulus induced by monopolar resonance [4], negative mass density induced by dipolar resonance [5], and negative shear modulus induced by quadrupolar resonance [6]. Elastic cloaks [7] and various other unprecedented dynamic behaviour of such materials have been widely reported in literature [8-14].
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Neural Computing and Applications
High-fidelity multi-scale design optimization of many real-life applications in structural engine... more High-fidelity multi-scale design optimization of many real-life applications in structural engineering still remains largely intractable due to the computationally intensive nature of numerical solvers like finite element method. Thus, in this paper, an alternate route of metamodel based design optimization methodology is proposed in multi-scale framework based on a symbolic regression implemented using genetic programming (GP) coupled with D-optimal design. This approach drastically cuts the computational costs by replacing the finite element module with appropriately constructed robust and efficient metamodels. Resulting models are compact, have good interpretability and assume a free-form expression capable of capturing the non-linearly, complexity and vastness of the design space. Two robust nature-inspired optimization algorithms, viz. multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), are used to generate Pareto optimal solutions for several test problems with varying complexity. TOPSIS, a multi-criteria decision-making approach is then applied to choose the best alternative among the Pareto optimal sets. Finally, the applicability of GP in efficiently tackling multi-scale optimization problems of composites is investigated, where a real-life scenario is explored by varying fractions of pertinent engineering materials to bring about property changes in the final composite structure across two different scales. The study reveals that a micro-scale optimization leads to better optimized solutions, demonstrating the advantage of carrying out a multi-scale optimization without any additional computational burden.
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ASCE, 2019
This article presents a concise overview on condition monitoring and retrofitting/ strengthening ... more This article presents a concise overview on condition monitoring and retrofitting/ strengthening of structures including a practical case study of strengthening for an existing historical building. Condition assessment of an existing structure is required mainly to check serviceability and safety requirements of the structure after short term events like earthquake or long term degradation of the structure with time. It is carried out to assess the ability of a structure to perform its intended operations under changed loading conditions with time or modification in its structural system as per newly imposed requirements. The condition assessment and strengthening may also be required for integrated extension of an existing structure. After assessing the condition of the structure, either it is retrofitted (or strengthened) or it is demolished according to the severity of the damage. In this article, such a critical condition assessment for an existing historical masonry building is presented and appropriate strengthening schemes are suggested by following two separate measures (concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative advantages and disadvantages of the strengthening measures are discussed from a practical engineering perspective. Aim of this article is not to propose any new method for condition assessment and strengthening of structures, rather we take a systematic approach to demonstrate our experience. Critical case studies on condition assessment and strengthening of historical buildings with adequate technical insights are very scarce to find in scientific literature. This article would serve as a valuable reference for the practicing engineers and the concerned scientific community.
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An insightful mechanics-based concept is developed for probing the frequency-dependence in in-pla... more An insightful mechanics-based concept is developed for probing the frequency-dependence in in-plane elastic moduli of microstructured lattice materials. Closed-form expressions for the complex elastic moduli are derived as a function of frequency by employing the dynamic stiffness matrix of beam elements, which can exactly capture the sub-wavelength scale dynamics. It is observed that the two Poisson's ratios are not dependent on the frequency of vibration, while the amplitude of two Young's moduli and shear modulus increase significantly with the increase of frequency. The variation of frequency-dependent phase of the complex elastic moduli is studied in terms of damping factors of the intrinsic material. The tunable frequency-dependent behaviour of elastic moduli in lattice materials could be exploited in the pseudo-static design of advanced engineering structures which are often operated in a vibrating environment. The generic concepts presented in this paper introduce new exploitable dimensions in the research of engineered materials for potential applications in various vibrating devices and structures across different length-scales.
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This article presents a concise overview on condition monitoring and retrofitting/ strengthening ... more This article presents a concise overview on condition monitoring and retrofitting/ strengthening of structures including a practical case study of strengthening for an existing historical building. Condition assessment of an existing structure is required mainly to check serviceability and safety requirements of the structure after short term events like earthquake or long term degradation of the structure with time. It is carried out to assess the ability of a structure to perform its intended operations under changed loading conditions with time or modification in its structural system as per newly imposed requirements. The condition assessment and strengthening may also be required for integrated extension of an existing structure. After assessing the condition of the structure, either it is retrofitted (or strengthened) or it is demolished according to the severity of the damage. In this article, such a critical condition assessment for an existing historical masonry building is presented and appropriate strengthening schemes are suggested by following two separate measures (concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative advantages and disadvantages of the strengthening measures are discussed from a practical engineering perspective. Aim of this article is not to propose any new method for condition assessment and strengthening of structures, rather we take a systematic approach to demonstrate our experience. Critical case studies on condition assessment and strengthening of historical buildings with adequate technical insights are very scarce to find in scientific literature. This article would serve as a valuable reference for the practicing engineers and the concerned scientific community.
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International Journal of Mechanical Sciences, 2019
The stochastic buckling behaviour of sandwich plates is presented considering uncertain system pa... more The stochastic buckling behaviour of sandwich plates is presented considering uncertain system parameters (material and geometric uncertainty). The higher-order-zigzag theory (HOZT) coupled with stochastic finite element model is employed to evaluate the random first three buckling loads. A cubic in-plane displacement variation is considered for both face sheets and core while quadratic transverse displacement is considered within the core and assumed constant in the faces beyond the core. The global stiffness matrix is stored in a single array by using skyline technique and stochastic buckling equation is solved by simultaneous iteration technique. The individual as well as compound stochastic effect of ply-orientation angle, core thickness, face sheets thickness and material properties (both core and laminate) of sandwich plates are considered in this study. A significant level of computational efficiency is achieved by using artificial neural network (ANN) based surrogate model coupled with the finite element approach. Statistical analyses are carried out to illustrate the results of stochastic buckling behaviour. Normally in case of various engineering applications, the critical buckling load with the least Eigen value is deemed to be useful. However, the results presented in this paper demonstrate the importance of considering higher order buckling modes in case of a realistic stochastic analysis. Besides that, the probabilistic results for global stability behaviour of sandwich structures show that a significant level of variation with respect to the deterministic values could occur due to the presence of inevitable source-uncertainty in the input parameters demonstrating the requirement of an inclusive design paradigm considering stochastic effects.
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This article presents a probabilistic framework to characterize the dynamic and stability paramet... more This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loève expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/ system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.
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This paper quantifies the compound effect of source-uncertainties on low-velocity impact of funct... more This paper quantifies the compound effect of source-uncertainties on low-velocity impact of functionally graded material (FGM) plates following a coupled surrogate based finite element simulation approach. The power law is employed to evaluate the material properties of FGM plate at different points, while the modified Hertzian contact law is implemented to determine the contact force and other parameters in a stochastic framework. The time dependent equations are solved by Newmark's time integration scheme. Insightful results are presented by investigating the effects of degree of stochasticity, oblique impact angle, thickness of plate, temperature, power law index, and initial velocity of impactor following both probabilistic and non-probabilistic approaches along with in-depth deterministic analyses. A detail probabilistic analysis leading to complete probabilistic characterization of the structural responses can be carried out when the statistical distribution of the stochastic input parameters are available. However, in many cases concerning FGM, these statistical distributions may remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based non-probabilistic approach could be appropriate to characterize the effect of uncertainty. A surrogate based approach based on artificial neural network coupled with the finite element model for low-velocity impact analysis of FGM plates is developed for achieving computational efficiency. The numerical results reveal that the low-velocity impact on FGM plates is significantly influenced by the effect of inevitable source-uncertainty associated with the stochastic system parameters, whereby the importance of adopting an inclusive design paradigm considering the effect of source-uncertainties in the impact analysis is established.
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This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framewo... more This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framework for studying the dynamic and stability characteristics of composite laminates with spatially varying system properties. Most of the studies concerning the uncertainty quantification of composites rely on probabilistic analyses, where the prerequisite is to have the statistical distribution of stochastic input parameters. In many engineering problems, these statistical distributions remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based approach could be appropriate to characterize the effect of uncertainty. A novel concept of fuzzy representative volume element (FRVE) is developed here for accounting the spatially varying non-probabilistic source-uncertainties at the input level. Such approach of uncertainty modelling is physically more relevant than the prevalent way of modelling non-probabilistic uncertainty without considering the ply-level spatial variability. An efficient radial basis function based stochastic algorithm coupled with the fuzzy finite element model of composites is developed for the multi-scale uncertainty propagation involving multi-synchronous triggering parameters. The concept of a fuzzy factor of safety (FFoS) is discussed in this paper for evaluation of safety factor in the non-probabilistic regime. The results reveal that the present physically relevant approach of modelling fuzzy uncertainty considering ply-level spatial variability obtains significantly lower fuzzy bounds of the global responses compared to the conventional approach of non-probabilistic modelling neglecting the spatially varying attributes.
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Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xe... more Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xenes (X= Si, Ge, Sn) has recently been reported to show promising electronic, optical and mechanical properties. This paper investigates the elastic moduli and crack propagation behaviour of single layer and bilayer stanene based on molecular dynamics simulations, which have been performed using Tersoff bond order potential (BOP). We have parameterized the interlayer van der Waals interaction for bilayer Lennard-Jones potential in case of the bilayer stanene. Density functional calculations are performed to fit the Lennard-Jones parameters for the properties which are not available from scientific literature. The effect of temperature and strain rate on mechanical properties of stanene is investigated for both single layer and bilayer stanene in the armchair and zigzag directions. The results reveal that both the fracture strength and strain of stanene decrease with increasing temperature, while at higher loading rate, the material is found to exhibit higher fracture strength and strain. The effect of chirality on elastic moduli of stanene is explained on the basis of a physics-based analytical approach, wherein the fundamental interaction between shear modulus and Young's modulus is elucidated. To provide a realistic perspective, we have investigated the compound effect of uncertainty on the elastic moduli of stanene based on an efficient analytical approach. Large-scale Monte Carlo simulations are carried out considering different degree of stochasticity. The in-depth results on mechanical properties presented in this article will further aid the adoption of stanene as a potential nano-electro-optical substitute with exciting features such as 2D topological insulating properties with large bandgap, capability to support enhanced thermoelectric performance, topological superconductivity and quantum anomalous Hall effect at near-room-temperature.
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The coupled effect of manufacturing uncertainty and a critical service-life damage condition (del... more The coupled effect of manufacturing uncertainty and a critical service-life damage condition (delamination) is investigated on the natural frequencies of laminated composite plates. In general, delamination is an unavoidable phenomenon in composite materials encountered often in real-life operating conditions. We have focused on the characterization of dynamic responses of composite plates considering source-uncertainty in the material and geometric properties along with various single and multiple delamination scenarios. A hybrid high dimensional model representation based uncertainty propagation algorithm coupled with layer-wise stochastic finite element model of composites is developed to achieve computational efficiency. The finite element formulation is based on Mindlin's theory considering transverse shear deformation. Numerical results are presented for the stochastic natural frequencies of delaminated composites along with a comprehensive deterministic analysis. Further, an inevitable effect of noise is induced in the surrogate based analysis to explore the effect of various errors and epistemic uncertainties involved with the system.
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This paper investigates the stochastic behaviour of hydrodynamic journal bearings by solving the ... more This paper investigates the stochastic behaviour of hydrodynamic journal bearings by solving the Reynolds equation with random parameters numerically based on finite difference method. The steady state and dynamic characteristics are quantified considering random variabilities in eccentricity and surface roughness that can closely simulate the uncertain service conditions and inevitable manufacturing imperfections. Based on efficient radial basis function, a Monte Carlo simulation (MCS) algorithm is developed in conjunction with the governing equations for quantifying stochastic characteristics of the crucial performance parameters concerning hydrodynamic bearings. Relative sensitivity to stochasticity for different performance parameters is analysed. Physically insightful new results are presented in a probabilistic framework, wherein it is observed that the stochasticity has pronounced influence on the performance of bearing.
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This article proposes the concept of anisotropy tailoring in multi-material lattices based on a m... more This article proposes the concept of anisotropy tailoring in multi-material lattices based on a mechanics-based bottom-up framework. It is widely known that isotropy in a mono-material lattice can be obtained when the microstructure has an isotropic geometry. For example, regular hexagonal lattices with a unit cell comprised of six equal members and equal internal angle of 120^o each, show isotropy in the elastic properties. Such limited microstructural configuration space for having isotropy severely restricts the scope of many multi-functional applications such as space filling in 3D printing. We first demonstrate that there are multiple structural geometries in mono-material lattices that could lead to isotropy. It is shown that the configuration space for isotropy can be expanded by multiple folds when more than one intrinsic material is introduced in the unit cell of a lattice. We explicitly demonstrate different degrees of anisotropy in regular geometrically isotropic lattices by introducing the multi-material architecture. The contours of achieving minimum anisotropy, maximum anisotropy and a fixed value of anisotropy are presented in the design space consisting of geometric and multi-material parameters. Proposition of such multi-material microstructures could essentially expand the multi-functional design scope significantly, offering a higher degree of flexibility to the designer in terms of choosing (or identifying) the most suitable microstructural geometry. An explicit theoretical characterization of the contours of anisotropy along with physical insights underpinning the configuration space of multi-material and geometric parameters will accelerate the process of its potential exploitation in various engineered multi-functional materials and structural systems across different length-scales with the demand of any specific degree of anisotropy but limitation in the micro-structural geometry.
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Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting mu... more Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting multi-functional properties. However, a single-layer of 2D materials may not have a certain property adequately , or multiple application-specic properties simultaneously to the desired and optimal level. For mitigating this lacuna, a new trend has emerged recently to develop nano-scale engineered heterostruc-tures by stacking multiple layers of dierent 2D materials, wherein each of the layers could also be twisted. The vast advantage of combining single layers of dierent 2D materials with dierent twisting angles has dramatically expanded this research eld well beyond the scope of considering a 2D material mono-layer, leading to a set of multifunctional physical properties corresponding to each possible combination of number of layers, dierent 2D materials therein, stacking sequence and the twisting angle of each layer. Eective mechanical properties such as Young's moduli are generally of utmost importance for analysing the viability of such engineered nano-heterostructures in various nanoelectromechanical applications. We have proposed efficient closed-form generic formulae for the eective Young's moduli of twisted multi-layer heterostructures. Based on this physics-based analytical approach, a wide range of insightful new results are presented for twisted heterostructures, covering mono-planar and multi-planar congurations with homogeneous and heterogeneous atomic distributions.
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Journal of Sandwich Structures and Materials, 2016
This paper presents a generic multivariate adaptive regression splines-based approach for dynamic... more This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C⁰ stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.
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Composites Part B Engineering, 2019
This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) p... more This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) plates subjected to free vibration and low-velocity impact to identify the most influential parameters in the respective analyses. A hybrid moment-independent sensitivity analysis is proposed coupled with the least angle regression based adaptive sparse polynomial chaos expansion. Here the surrogate model is integrated in the sensitivity analysis framework to achieve computational efficiency. The current paper is concentrated on the relative sensitivity of material properties in the free vibration (first three natural frequencies) and low-velocity impact responses of FGM plates. Typical functionally graded materials are made of two different components, where a continuous and inhomogeneous mixture of these materials is distributed across the thickness of the plate based on certain distribution laws. Thus, besides the overall sensitivity analysis of the material properties, a unique spatial sensitivity analysis is also presented here along the thickness of the plate to provide a comprehensive view. The results presented in this paper would help to identify the most important material properties along with their depth-wise spatial sensitivity for low-frequency vibration and low-velocity impact analysis of FGM plates. This is the first attempt to carry out an efficient adaptive sparse PCE based moment-independent sensitivity analysis (depth-wise and collectively) of FGM plates under the simultaneous susceptibility of vibration and impact. Such simultaneous multi-objective sensitivity analysis can identify the important system parameters and their relative degree of importance in advanced multi-functional structural systems.
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Thin-Walled Structures, 2019
This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwi... more This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwich plates with composite face sheets considering the effects of obliqueness in impact angle and twist in the plate geometry. The stochastic impact analysis is conducted by using finite element (FE) modelling based on an eight nodded isoparametric quadratic plate bending element coupled with multivariate adaptive regression spline (MARS) in order to achieve computational efficiency. The modified Hertzian contact law is employed to model contact force and other impact parameters. Newmark's time integration scheme is used to solve the time-dependent equations. Comprehensive deterministic as well as probabilistic results are presented by considering the effects of location of impact, ply orientation angle, impactor velocity, impact angle, face-sheet material property, twist angle, plate thickness and mass of impactor. The relative importance of various input parameters is determined by conducting a sensitivity analysis. The results presented in this paper reveal that the impact responses of sandwich plates are significantly affected by the effect of source-uncertainty that in turn establishes the importance of adopting an inclusive stochastic design approach for impact modelling in sandwich plates.
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Due to the absence of adequate control at different stages of complex manufacturing process, mate... more Due to the absence of adequate control at different stages of complex manufacturing process, material and geometric properties of composite structures are often uncertain. For a secure and safe design, tracking the impact of these uncertainties on the structural responses is of utmost significance. Composite materials, commonly adopted in various modern aerospace, marine, automobile and civil structures, are often susceptible to low-velocity impact caused by various external agents. Here, along with a critical review, we present machine learning based probabilistic and non-probabilistic (fuzzy) low-velocity impact analyses of composite laminates including a detailed deterministic characterization to systematically investigate the consequences of source-uncertainty. While probabilistic analysis can be performed only when complete statistical description about the input variables are available, the non-probabilistic analysis can be executed even in the presence of incomplete statistical input descriptions with sparse data. In this study, the stochastic effects of stacking sequence, twist angle, oblique impact, plate thickness, velocity of impactor and density of impactor are investigated on the crucial impact response parameters such as contact force, plate displacement, and impactor displacement. For efficient and accurate computation, a hybrid polynomial chaos based Kriging (PC-Kriging) approach is coupled with in-house finite element codes for uncertainty propagation in both the probabilistic and non-probabilistic analyses. The essence of this paper is a critical review on the hybrid machine learning algorithms followed by detailed numerical investigation in the probabilistic and non-probabilistic regimes to access the performance of such hybrid algorithms in comparison to individual algorithms from the viewpoint of accuracy and computational efficiency.
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A novel origami metamaterial with programmable multi-directional auxeticity is proposed by hybrid... more A novel origami metamaterial with programmable multi-directional auxeticity is proposed by hybridizing the concept of re-entrant honeycomb with the Miura pattern. Normal Miura-based origami metamaterials have been widely shown to exhibit negative in-plane Poisson's ratio. However, negative out-of-plane Poisson's ratio cannot be realized in these set of materials, essentially limiting their capability for prospective applications in many multi-functional devices and systems. Here we propose a hybrid Miura-based metamaterial that can show both in-plane and out-of-plane negative Poisson's ratios. More interestingly, we are able to program the Poisson's ratios to have mild to extreme auxeticity and map their mutual interaction as a function of the microstructural configuration. Besides the single-layer meta-sheets, we have shown that a class of multi-layer stacked metamaterial with uniform and graded configurations can be developed to achieve multi-objective functional goals. Theoretical and experimental analyses are combined in this paper to demonstrate the concepts of modulating multi-directional Poisson's ratios. The fundamental mechanics of the proposed origami based metamaterial being scale-independent, this novel class of deployable hybrid materials can be directly transferred for application in a range of milli-, micro-, and nanometer-size systems, essentially opening avenues for the design of energy absorbers, sensors, actuators, medical stents, catalysis, drug delivery systems, adaptive wings for next-generation of aircrafts and other deployable mechanical and electronic systems at multiple length-scales.
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An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependen... more An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependence of lattice material microstructures. Under a vibrating condition, effective elastic moduli of such microstructured materials can become negative for certain frequency values, leading to an unusual mechanical behaviour with a multitude of potential applications. We have derived the fundamental theoretical limits for the minimum frequency, beyond which the negative effective moduli of the materials could be obtained. An efficient dynamic stiffness matrix based approach is developed to obtain the closed-form limits, which can exactly capture the sub-wavelength scale dynamics. The limits turn out to be a fundamental property of the lattice materials and depend on certain material and geometric parameters of the lattice in a unique manner. An explicit characterization of the theoretical limits of negative elastic moduli along with adequate physical insights would accelerate the process of its potential exploitation in various engineered materials and structural systems under dynamic regime across the length-scales. Introduction.-The global mechanical properties can be engineered in lattice materials by intelligently identifying the material microstructures as the properties in these materials are often defined by their structural configuration along with the intrinsic material properties of the constituent members. This novel class of materials with tailorable application-specific mechanical properties (like equivalent elastic moduli, buckling, vibration and wave propagation characteristics with modulation features) have tremendous potential applications for future aerospace, civil, mechanical, electronics and medical applications across the length-scales. Naturally occurring materials cannot exhibit unprecedented and fascinating properties such as extremely lightweight, negative elastic moduli, negative mass density, pentamode material characteristics (meta-fluid), which can be achieved by an intelligent microstructural design [1, 2]. For example, the conventional positive value of Poisson's ratio in a hexagonal lattice metamaterial can be converted to a negative value [3] by making the cell angle θ in figure 1(b) negative. Other unusual and exciting properties can be realized in metamaterials under dynamic condition, such as negative bulk modulus induced by monopolar resonance [4], negative mass density induced by dipolar resonance [5], and negative shear modulus induced by quadrupolar resonance [6]. Elastic cloaks [7] and various other unprecedented dynamic behaviour of such materials have been widely reported in literature [8-14].
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Neural Computing and Applications
High-fidelity multi-scale design optimization of many real-life applications in structural engine... more High-fidelity multi-scale design optimization of many real-life applications in structural engineering still remains largely intractable due to the computationally intensive nature of numerical solvers like finite element method. Thus, in this paper, an alternate route of metamodel based design optimization methodology is proposed in multi-scale framework based on a symbolic regression implemented using genetic programming (GP) coupled with D-optimal design. This approach drastically cuts the computational costs by replacing the finite element module with appropriately constructed robust and efficient metamodels. Resulting models are compact, have good interpretability and assume a free-form expression capable of capturing the non-linearly, complexity and vastness of the design space. Two robust nature-inspired optimization algorithms, viz. multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), are used to generate Pareto optimal solutions for several test problems with varying complexity. TOPSIS, a multi-criteria decision-making approach is then applied to choose the best alternative among the Pareto optimal sets. Finally, the applicability of GP in efficiently tackling multi-scale optimization problems of composites is investigated, where a real-life scenario is explored by varying fractions of pertinent engineering materials to bring about property changes in the final composite structure across two different scales. The study reveals that a micro-scale optimization leads to better optimized solutions, demonstrating the advantage of carrying out a multi-scale optimization without any additional computational burden.
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ASCE, 2019
This article presents a concise overview on condition monitoring and retrofitting/ strengthening ... more This article presents a concise overview on condition monitoring and retrofitting/ strengthening of structures including a practical case study of strengthening for an existing historical building. Condition assessment of an existing structure is required mainly to check serviceability and safety requirements of the structure after short term events like earthquake or long term degradation of the structure with time. It is carried out to assess the ability of a structure to perform its intended operations under changed loading conditions with time or modification in its structural system as per newly imposed requirements. The condition assessment and strengthening may also be required for integrated extension of an existing structure. After assessing the condition of the structure, either it is retrofitted (or strengthened) or it is demolished according to the severity of the damage. In this article, such a critical condition assessment for an existing historical masonry building is presented and appropriate strengthening schemes are suggested by following two separate measures (concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative advantages and disadvantages of the strengthening measures are discussed from a practical engineering perspective. Aim of this article is not to propose any new method for condition assessment and strengthening of structures, rather we take a systematic approach to demonstrate our experience. Critical case studies on condition assessment and strengthening of historical buildings with adequate technical insights are very scarce to find in scientific literature. This article would serve as a valuable reference for the practicing engineers and the concerned scientific community.
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An insightful mechanics-based concept is developed for probing the frequency-dependence in in-pla... more An insightful mechanics-based concept is developed for probing the frequency-dependence in in-plane elastic moduli of microstructured lattice materials. Closed-form expressions for the complex elastic moduli are derived as a function of frequency by employing the dynamic stiffness matrix of beam elements, which can exactly capture the sub-wavelength scale dynamics. It is observed that the two Poisson's ratios are not dependent on the frequency of vibration, while the amplitude of two Young's moduli and shear modulus increase significantly with the increase of frequency. The variation of frequency-dependent phase of the complex elastic moduli is studied in terms of damping factors of the intrinsic material. The tunable frequency-dependent behaviour of elastic moduli in lattice materials could be exploited in the pseudo-static design of advanced engineering structures which are often operated in a vibrating environment. The generic concepts presented in this paper introduce new exploitable dimensions in the research of engineered materials for potential applications in various vibrating devices and structures across different length-scales.
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This article presents a concise overview on condition monitoring and retrofitting/ strengthening ... more This article presents a concise overview on condition monitoring and retrofitting/ strengthening of structures including a practical case study of strengthening for an existing historical building. Condition assessment of an existing structure is required mainly to check serviceability and safety requirements of the structure after short term events like earthquake or long term degradation of the structure with time. It is carried out to assess the ability of a structure to perform its intended operations under changed loading conditions with time or modification in its structural system as per newly imposed requirements. The condition assessment and strengthening may also be required for integrated extension of an existing structure. After assessing the condition of the structure, either it is retrofitted (or strengthened) or it is demolished according to the severity of the damage. In this article, such a critical condition assessment for an existing historical masonry building is presented and appropriate strengthening schemes are suggested by following two separate measures (concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative advantages and disadvantages of the strengthening measures are discussed from a practical engineering perspective. Aim of this article is not to propose any new method for condition assessment and strengthening of structures, rather we take a systematic approach to demonstrate our experience. Critical case studies on condition assessment and strengthening of historical buildings with adequate technical insights are very scarce to find in scientific literature. This article would serve as a valuable reference for the practicing engineers and the concerned scientific community.
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International Journal of Mechanical Sciences, 2019
The stochastic buckling behaviour of sandwich plates is presented considering uncertain system pa... more The stochastic buckling behaviour of sandwich plates is presented considering uncertain system parameters (material and geometric uncertainty). The higher-order-zigzag theory (HOZT) coupled with stochastic finite element model is employed to evaluate the random first three buckling loads. A cubic in-plane displacement variation is considered for both face sheets and core while quadratic transverse displacement is considered within the core and assumed constant in the faces beyond the core. The global stiffness matrix is stored in a single array by using skyline technique and stochastic buckling equation is solved by simultaneous iteration technique. The individual as well as compound stochastic effect of ply-orientation angle, core thickness, face sheets thickness and material properties (both core and laminate) of sandwich plates are considered in this study. A significant level of computational efficiency is achieved by using artificial neural network (ANN) based surrogate model coupled with the finite element approach. Statistical analyses are carried out to illustrate the results of stochastic buckling behaviour. Normally in case of various engineering applications, the critical buckling load with the least Eigen value is deemed to be useful. However, the results presented in this paper demonstrate the importance of considering higher order buckling modes in case of a realistic stochastic analysis. Besides that, the probabilistic results for global stability behaviour of sandwich structures show that a significant level of variation with respect to the deterministic values could occur due to the presence of inevitable source-uncertainty in the input parameters demonstrating the requirement of an inclusive design paradigm considering stochastic effects.
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This article presents a probabilistic framework to characterize the dynamic and stability paramet... more This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loève expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/ system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.
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This paper quantifies the compound effect of source-uncertainties on low-velocity impact of funct... more This paper quantifies the compound effect of source-uncertainties on low-velocity impact of functionally graded material (FGM) plates following a coupled surrogate based finite element simulation approach. The power law is employed to evaluate the material properties of FGM plate at different points, while the modified Hertzian contact law is implemented to determine the contact force and other parameters in a stochastic framework. The time dependent equations are solved by Newmark's time integration scheme. Insightful results are presented by investigating the effects of degree of stochasticity, oblique impact angle, thickness of plate, temperature, power law index, and initial velocity of impactor following both probabilistic and non-probabilistic approaches along with in-depth deterministic analyses. A detail probabilistic analysis leading to complete probabilistic characterization of the structural responses can be carried out when the statistical distribution of the stochastic input parameters are available. However, in many cases concerning FGM, these statistical distributions may remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based non-probabilistic approach could be appropriate to characterize the effect of uncertainty. A surrogate based approach based on artificial neural network coupled with the finite element model for low-velocity impact analysis of FGM plates is developed for achieving computational efficiency. The numerical results reveal that the low-velocity impact on FGM plates is significantly influenced by the effect of inevitable source-uncertainty associated with the stochastic system parameters, whereby the importance of adopting an inclusive design paradigm considering the effect of source-uncertainties in the impact analysis is established.
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This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framewo... more This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framework for studying the dynamic and stability characteristics of composite laminates with spatially varying system properties. Most of the studies concerning the uncertainty quantification of composites rely on probabilistic analyses, where the prerequisite is to have the statistical distribution of stochastic input parameters. In many engineering problems, these statistical distributions remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based approach could be appropriate to characterize the effect of uncertainty. A novel concept of fuzzy representative volume element (FRVE) is developed here for accounting the spatially varying non-probabilistic source-uncertainties at the input level. Such approach of uncertainty modelling is physically more relevant than the prevalent way of modelling non-probabilistic uncertainty without considering the ply-level spatial variability. An efficient radial basis function based stochastic algorithm coupled with the fuzzy finite element model of composites is developed for the multi-scale uncertainty propagation involving multi-synchronous triggering parameters. The concept of a fuzzy factor of safety (FFoS) is discussed in this paper for evaluation of safety factor in the non-probabilistic regime. The results reveal that the present physically relevant approach of modelling fuzzy uncertainty considering ply-level spatial variability obtains significantly lower fuzzy bounds of the global responses compared to the conventional approach of non-probabilistic modelling neglecting the spatially varying attributes.
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Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xe... more Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xenes (X= Si, Ge, Sn) has recently been reported to show promising electronic, optical and mechanical properties. This paper investigates the elastic moduli and crack propagation behaviour of single layer and bilayer stanene based on molecular dynamics simulations, which have been performed using Tersoff bond order potential (BOP). We have parameterized the interlayer van der Waals interaction for bilayer Lennard-Jones potential in case of the bilayer stanene. Density functional calculations are performed to fit the Lennard-Jones parameters for the properties which are not available from scientific literature. The effect of temperature and strain rate on mechanical properties of stanene is investigated for both single layer and bilayer stanene in the armchair and zigzag directions. The results reveal that both the fracture strength and strain of stanene decrease with increasing temperature, while at higher loading rate, the material is found to exhibit higher fracture strength and strain. The effect of chirality on elastic moduli of stanene is explained on the basis of a physics-based analytical approach, wherein the fundamental interaction between shear modulus and Young's modulus is elucidated. To provide a realistic perspective, we have investigated the compound effect of uncertainty on the elastic moduli of stanene based on an efficient analytical approach. Large-scale Monte Carlo simulations are carried out considering different degree of stochasticity. The in-depth results on mechanical properties presented in this article will further aid the adoption of stanene as a potential nano-electro-optical substitute with exciting features such as 2D topological insulating properties with large bandgap, capability to support enhanced thermoelectric performance, topological superconductivity and quantum anomalous Hall effect at near-room-temperature.
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The coupled effect of manufacturing uncertainty and a critical service-life damage condition (del... more The coupled effect of manufacturing uncertainty and a critical service-life damage condition (delamination) is investigated on the natural frequencies of laminated composite plates. In general, delamination is an unavoidable phenomenon in composite materials encountered often in real-life operating conditions. We have focused on the characterization of dynamic responses of composite plates considering source-uncertainty in the material and geometric properties along with various single and multiple delamination scenarios. A hybrid high dimensional model representation based uncertainty propagation algorithm coupled with layer-wise stochastic finite element model of composites is developed to achieve computational efficiency. The finite element formulation is based on Mindlin's theory considering transverse shear deformation. Numerical results are presented for the stochastic natural frequencies of delaminated composites along with a comprehensive deterministic analysis. Further, an inevitable effect of noise is induced in the surrogate based analysis to explore the effect of various errors and epistemic uncertainties involved with the system.
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This paper investigates the stochastic behaviour of hydrodynamic journal bearings by solving the ... more This paper investigates the stochastic behaviour of hydrodynamic journal bearings by solving the Reynolds equation with random parameters numerically based on finite difference method. The steady state and dynamic characteristics are quantified considering random variabilities in eccentricity and surface roughness that can closely simulate the uncertain service conditions and inevitable manufacturing imperfections. Based on efficient radial basis function, a Monte Carlo simulation (MCS) algorithm is developed in conjunction with the governing equations for quantifying stochastic characteristics of the crucial performance parameters concerning hydrodynamic bearings. Relative sensitivity to stochasticity for different performance parameters is analysed. Physically insightful new results are presented in a probabilistic framework, wherein it is observed that the stochasticity has pronounced influence on the performance of bearing.
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