Mahmood Ettehad - Academia.edu (original) (raw)
Papers by Mahmood Ettehad
A communication network can be modeled as a directed connected graph with edge weights that chara... more A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is not known. In particular, temporal correlations between path metrics have been used to infer composite weights on the subpath formed by the path intersection. We call these subpath weights the Path Correlation Data. In this manuscript we ask the following question: when can the underlying weighted graph be recovered knowing only the boundary vertices and the Path Correlation Data? We establish necessary and sufficient conditions for a graph to be reconstructible from this information, and describe an algorithm to perform the reconstruction. Subject to fairly general conditions which will be elaborated in next Section, the results applies...
Applied Mathematics and Computation, 2020
This study presents a novel, linear superposition method (LSM) to compute the stress tensor field... more This study presents a novel, linear superposition method (LSM) to compute the stress tensor field and displacement vector field in a homogeneous elastic medium with an unlimited (but finite) number of circular cylindrical holes. The displacement field and the associated stress concentrations are due to a far-field stress. The method allows for the holecenters to occur in arbitrary locations, and the hole-radii may vary over a wide range (but holes may not overlap). The holes may also induce additional elastic displacement due to internal pressure loading that will affect the local stress field, which is fully accounted for in the method. Each hole may be loaded by either equal or individual pressure loads. The underlying algorithms and solution methodology are explained and examples are given for a variety of cases. Selected case study examples show excellent matches with results obtained via independent methods (photo-elastics, complex analysis, and discrete volume solution methods). The LSM provides several advantages over alternative methods: (1) Being closed-form solutions, infinite resolution is preserved throughout, (2) Being grid-less, no time is lost on gridding, and (3) fast computation times. The specific examples of LSM applications to the multi-hole problem developed here, allow for an unlimited number of holes, with either equal or varying radii, in arbitrary constellations. The solutions further account for variable combinations of far-field stress and pressure loads on individual holes. The method can be applied for either plane strain or plane stress boundary conditions. A constitutive equation for linear elasticity controls the stress field solutions, which can be scaled for the full range of Poisson's ratios and Young moduli possible in linear elastic materials.
Applied Mathematics and Computation, 2019
This study demonstrates how analytical solutions for displacement field potentials of deformation... more This study demonstrates how analytical solutions for displacement field potentials of deformation in elastic media can be obtained from known vector field solutions for analog fluid flow problems. The theoretical basis is outlined and a geomechanical application is elaborated. In particular, closed-form solutions for deformation gradients in elastic media are found by transforming velocity field potentials of fluid flow problems, using similarity principles. Once an appropriate displacement gradient potential is identified, solutions for the principal displacements, elastic strains, stress magnitudes and stress trajectories can be computed. An application is included using the displacement gradient due to the internal pressure-loading of single and multiple wellbores. The analytical results give perfect matches with results obtained with an independent discrete element modeling method.
This thesis is devoted to the numerical investigation of mechanical behavior of Dual phase (DP) s... more This thesis is devoted to the numerical investigation of mechanical behavior of Dual phase (DP) steels. Such grade of advanced high strength steels (AHSS) is favorable to the automotive industry due the unique properties such as high strength and ductility with low finished cost. Many experimental and numerical studies have been done to achieve the optimized behavior of DP steels by controlling their microstructure. Experiments are costly and time consuming so in recent years numerical tools are utilized to help the metallurgist before doing experiments. Most of the numerical studies are based on classical (local) constitutive models where no material length scale parameters are incorporated in the model. Although these models are proved to be very effective in modeling the material behavior in the large scales but they fail to address some critical phenomena which are important for our goals. First, they fail to address the size effect phenomena which materials show at microstructural scale. This means that materials show stronger behavior at small scales compared to large scales. Another issue with classical models is the mesh size dependency in modeling the softening behavior of materials. This means that in the finite element context (FEM) the results will be mesh size dependent and no converged solution exist upon mesh refinement. Thereby by applying the classical (local) models one my loose the accuracy on measuring the strength and ductility of DP steels. Among the non-classical (nonlocal) models, gradient-enhanced plasticity models which consider the effect of neighboring point on the behavior of one specific point are proved to be numerically effective and versatile tools to accomplish the two concerns mentioned above. So in this thesis a gradient-enhanced plasticity model which incorporates both the energetic and dissipative material length scales is derived based on the laws of thermodynamics. This model also has a consistent yield-like function for the interface which is an essential part of the higher-order gradient theories. The main issue with utilizing these theories is the implementation which limits the application of these theories for modeling the real problems. Here a straightforward implementation method based on the classical FEM and Meshless method will be proposed which due to its simplicity it can be applied for many problems. The application of the developed model and implementation will be shown on removing the mesh size dependency and capturing the size effect in microstructure level of dual phase steels
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011
There are numerous experimental results that indicate a size-dependent mechanical behavior of mat... more There are numerous experimental results that indicate a size-dependent mechanical behavior of materials at the micron or submicron scales, in the sense that “smaller is stronger”. As no material length scale exits in the conventional (local) constitutive theories, they fail to capture this size dependency of material behavior at small length scales. A number of theories for generalizing the classical plasticity theories in order to account for the observed size effects have been proposed and still motivates researchers in this area. Among them the nonlocal continuum theories of either integral or gradient type have been introduced to model material behavior size dependency in a computationally effective way [1, 2]. The concept behind these theories is that; plastic strain gradients lead to the enhancement in the density of geometrically necessary dislocations (GNDs) and thereby to an elevation in the material’s strength [3]. Higher-order gradient dependent plasticity theory which enforces microscopic boundary conditions at interfaces and free surfaces has been introduced to improve first-order gradient theories as they fail to predict size effects. Recently, micro/nano compression tests have attracted several researchers to investigate the small-scale mechanical behavior of micro/nano-pillars with sizes range from few micrometers down to a few hundred of nanometers (see [4, 5] and reference quoted therein). Typically focused ion beam (FIB) machining from a thin film or a bulk specimen is used to produce columnar structure which then subjected to compression using a nanoindenter outfitted with a flat punch indenter (e.g. [4, 5]). Usually extrinsic defects like high initial dislocation density in the order of 15 2 10 /m , vacancy clusters, intermetallic components, and near surface amorphous layers are formed at a layer adjacent to the milled surface [5, 6]. Deformation in micro/nano-pillar’s compression is macroscopically uniform, so one may doubt how gradient enhanced theories could be able to capture size effect as gradient terms have minor effects. However, the authors believe that higher-order gradient plasticity theories can capture this size effect even for macroscopically uniform deformation as higher-order boundary conditions play an important role once the size of specimen decreases [7, 10]. For example, initial defects or amorphous layers or surface roughness at external surfaces of the micro/nanopillars may increase the level of surface energy for embedding dislocation annihilation through the surface [10]. Moreover, as mentioned above, the fabrication process of these pillars cause initial GNDs formation within the specimen with higher density at milled surfaces so one may claim that this causes initial plastic strain distribution which is related to the initial GND density distribution. In the current paper, different initial effective plastic strain distributions that correspond to constant plastic strain gradients within a micropillar sample have been assumed and the ability of gradient enhanced plasticity theory to capture size effect for different pillar sizes is presented.
Finite Elements in Analysis and Design, 2015
ABSTRACT The higher-order gradient plasticity theory is successful in explaining the size effects... more ABSTRACT The higher-order gradient plasticity theory is successful in explaining the size effects encountered at the micron and submicron length scale. Due to the incorporation of spatial gradients of one or more internal variables in these theories and the associated non-classical boundary conditions, special types of elements in the finite element method maybe necessary. This makes the numerical implementation of this higher-order theory not straightforward. In this paper, a robust but straightforward numerical implementation of higher-order gradient-dependent plasticity theories is presented. The novelty of this paper is in (1) the application of the meshless methods, particularly the moving weighted least square method, combined with the finite element method for the numerical computation of plastic strain gradients, and (2) the numerical implementation of different types of higher-order microscopic boundary conditions at internal/external surfaces, interfaces, and moving elastic–plastic boundaries. The proposed numerical implementation algorithms can be easily adapted in the implementation of any form of higher-order gradient-dependent constitutive models. Examples of applying the current numerical approach is demonstrated for capturing mesh-objective shear band formation and size effect and boundary layer formation in thin films on elastic substrates and metal matrix composites with embedded elastic inclusions through the consideration of stiff, intermediate, and soft interfaces.
International Journal of Material Forming, 2009
Sandwich structures are gaining increase application in aeronautical, marine, automotive and civi... more Sandwich structures are gaining increase application in aeronautical, marine, automotive and civil engineering. Since such sheet can be subjected to stamping processes and their deformation limited by various defects, knowing beforehand the limiting amount of deformation is very important. For achieving this goal, sandwich sheet of Al 3105/Polymer/Al 3105 were prepared using thin film hot melt adheres. FLD of sandwich
Materials & Design, 2010
The most prominent feature of sheet material forming process is an elastic recovery phenomenon du... more The most prominent feature of sheet material forming process is an elastic recovery phenomenon during unloading which leads to spring back and side wall curl. Metal–polymer laminate sheets are emerging materials that have many potential applications. Therefore evaluation of spring back is mandatory for production of precise products from these new sheet materials. In this paper, the results of spring
Journal of Engineering Materials and Technology, 2013
Sandwich sheet structures are gaining a wide array of applications in the aeronautical, marine, a... more Sandwich sheet structures are gaining a wide array of applications in the aeronautical, marine, automotive, and civil engineering fields. Since such sheets can be subjected to forming/stamping processes, it is crucial to characterize their limiting amount of deformation before trying out any forming/stamping process. To achieve this goal, sandwich sheets of Al 3105/polymer/Al 3105 were prepared using thin film hot melt adheres. Through an experimental effort, forming limit diagrams (FLDs) of the prepared sandwich sheets were evaluated. In addition, simulation efforts were conducted to predict the FLDs of the sandwich sheets using finite element analysis (FEA) by considering the Gurson–Tvergaard–Needleman (GTN) damage model. The agreement among the experimental results and simulated predictions was promising. The effects of different parameters such as polymer core thickness, aluminum face sheet thickness, and shape constraints were investigated on the FLDs.
Journal of Engineering Materials and Technology, 2010
Sandwich structures are gaining wide applications in aeronautical, marine, automotive, and civil ... more Sandwich structures are gaining wide applications in aeronautical, marine, automotive, and civil engineering. Since such sheets can be subjected to stamping processes, it is crucial to characterize their forming behavior before trying out any conventional forming process. To achieve this goal, sandwich sheets of Al 3105/polymer/Al 3105 were prepared using thin film hot melt adheres. Different sandwich specimens with different thickness ratios (of polymer core to aluminum face sheet) were prepared. Throughout an experimental effort, the limiting drawing ratios (LDRs) of the sandwich sheets were determined. Besides, the LDR of the sandwich sheets were predicted using finite element analysis simulations by considering Gurson–Tvergaard–Needleman damage model. The results show the capability of the damage model to predict the LDR and the location of damaged zone in a workpiece during a forming operation.
Journal of Engineering Materials and Technology, 2011
Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, ... more Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedl...
Proceedings of the 5th International Congress on Computational Mechanics and Simulation, 2014
Shortest path graph distances are widely used in data science and machine learning, since they ca... more Shortest path graph distances are widely used in data science and machine learning, since they can approximate the underlying geodesic distance on the data manifold. However, the shortest path distance is highly sensitive to the addition of corrupted edges in the graph, either through noise or an adversarial perturbation. In this paper we study a family of Hamilton-Jacobi equations on graphs that we call the p-eikonal equation. We show that the p-eikonal equation with p = 1 is a provably robust distance-type function on a graph, and the p→∞ limit recovers shortest path distances. While the p-eikonal equation does not correspond to a shortest-path graph distance, we nonetheless show that the continuum limit of the p-eikonal equation on a random geometric graph recovers a geodesic density weighted distance in the continuum. We consider applications of the p-eikonal equation to data depth and semi-supervised learning, and use the continuum limit to prove asymptotic consistency results ...
This article considers the problem of optimally recovering stable linear time-invariant systems o... more This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal-recovery results relative to such approximability models, we construct some optimal algorithms and characterize the optimal performance for the identification and evaluation of transfer functions in the framework of the Hardy Hilbert space and of the disc algebra. In particular, we determine explicitly the optimal recovery performance for frequency measurements taken at equispaced points on an inner circle or on the torus.
Studies in Applied Mathematics
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describ... more We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is shown to be self-adjoint. In the special case of planar frames, the operator decomposes into a direct sum of two operators, one coupling out-of-plane displacement to angular (torsional) displacement and the other coupling in-plane displacement with axial displacement (compression). Detailed analysis of two examples is presented. We actively exploit the symmetry present in the examples and decompose the operator by restricting it onto reducing subspaces corresponding to irreducible representations of the symmetry group. These "quotient" operators are shown to capture particular oscillation modes of the frame.
When attempting to recover functions from observational data, one naturally seeks to do so in an ... more When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal Recovery. The distinctive twists here are the consideration of inaccurate data through some boundedness models and the emphasis on computational realizability. Several scenarios are unraveled through the efficient constructions of optimal recovery maps: local optimality under linearly or semidefinitely describable models, global optimality for the estimation of linear functionals under approximability models, and global near-optimality under approximability models in the space of continuous functions.
ArXiv, 2019
A communication network can be modeled as a directed connected graph with edge weights that chara... more A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is not known. Recent work has established conditions under which the underlying directed graph can be recovered exactly the pairwise Path Correlation Data, namely, the set of weights of intersection of each pair of directed paths to and from each endpoint. Algorithmically, this enables us to consistently fused tree-based view of the set of network paths to and from each endpoint to reconstruct the underlying network. However, in practice the PCD is not consistently determined by path measurements. Statistical fluctuations give rise to inconsistent inferred weight of edges from measurement based on different endpoints, as do operational cons...
We present full description of spectra for elastic beam Hamiltonian defined on periodic hexagonal... more We present full description of spectra for elastic beam Hamiltonian defined on periodic hexagonal lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar valued self-adjoint fourth-order operator equipped with a real periodic symmetric potential. Compared to the Schrödinger operator commonly applied in quantum graph literature, here vertex matching conditions encode geometry of the graph by their dependence on angles at which edges are met. We show that for a special equal-angle lattice, known as graphene, dispersion relation has a similar structure as reported for Schrödinger operator on periodic hexagonal lattices. This property is then further utilized to prove existence of singular Dirac points. We next discuss the role of the potential on reducibility of Fermi surface at uncountably many low-energy levels for this special lattice. Applying perturbation analysis, the developed theory is extended to derive dispersion relation for angle-per...
A communication network can be modeled as a directed connected graph with edge weights that chara... more A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is not known. In particular, temporal correlations between path metrics have been used to infer composite weights on the subpath formed by the path intersection. We call these subpath weights the Path Correlation Data. In this manuscript we ask the following question: when can the underlying weighted graph be recovered knowing only the boundary vertices and the Path Correlation Data? We establish necessary and sufficient conditions for a graph to be reconstructible from this information, and describe an algorithm to perform the reconstruction. Subject to fairly general conditions which will be elaborated in next Section, the results applies...
Applied Mathematics and Computation, 2020
This study presents a novel, linear superposition method (LSM) to compute the stress tensor field... more This study presents a novel, linear superposition method (LSM) to compute the stress tensor field and displacement vector field in a homogeneous elastic medium with an unlimited (but finite) number of circular cylindrical holes. The displacement field and the associated stress concentrations are due to a far-field stress. The method allows for the holecenters to occur in arbitrary locations, and the hole-radii may vary over a wide range (but holes may not overlap). The holes may also induce additional elastic displacement due to internal pressure loading that will affect the local stress field, which is fully accounted for in the method. Each hole may be loaded by either equal or individual pressure loads. The underlying algorithms and solution methodology are explained and examples are given for a variety of cases. Selected case study examples show excellent matches with results obtained via independent methods (photo-elastics, complex analysis, and discrete volume solution methods). The LSM provides several advantages over alternative methods: (1) Being closed-form solutions, infinite resolution is preserved throughout, (2) Being grid-less, no time is lost on gridding, and (3) fast computation times. The specific examples of LSM applications to the multi-hole problem developed here, allow for an unlimited number of holes, with either equal or varying radii, in arbitrary constellations. The solutions further account for variable combinations of far-field stress and pressure loads on individual holes. The method can be applied for either plane strain or plane stress boundary conditions. A constitutive equation for linear elasticity controls the stress field solutions, which can be scaled for the full range of Poisson's ratios and Young moduli possible in linear elastic materials.
Applied Mathematics and Computation, 2019
This study demonstrates how analytical solutions for displacement field potentials of deformation... more This study demonstrates how analytical solutions for displacement field potentials of deformation in elastic media can be obtained from known vector field solutions for analog fluid flow problems. The theoretical basis is outlined and a geomechanical application is elaborated. In particular, closed-form solutions for deformation gradients in elastic media are found by transforming velocity field potentials of fluid flow problems, using similarity principles. Once an appropriate displacement gradient potential is identified, solutions for the principal displacements, elastic strains, stress magnitudes and stress trajectories can be computed. An application is included using the displacement gradient due to the internal pressure-loading of single and multiple wellbores. The analytical results give perfect matches with results obtained with an independent discrete element modeling method.
This thesis is devoted to the numerical investigation of mechanical behavior of Dual phase (DP) s... more This thesis is devoted to the numerical investigation of mechanical behavior of Dual phase (DP) steels. Such grade of advanced high strength steels (AHSS) is favorable to the automotive industry due the unique properties such as high strength and ductility with low finished cost. Many experimental and numerical studies have been done to achieve the optimized behavior of DP steels by controlling their microstructure. Experiments are costly and time consuming so in recent years numerical tools are utilized to help the metallurgist before doing experiments. Most of the numerical studies are based on classical (local) constitutive models where no material length scale parameters are incorporated in the model. Although these models are proved to be very effective in modeling the material behavior in the large scales but they fail to address some critical phenomena which are important for our goals. First, they fail to address the size effect phenomena which materials show at microstructural scale. This means that materials show stronger behavior at small scales compared to large scales. Another issue with classical models is the mesh size dependency in modeling the softening behavior of materials. This means that in the finite element context (FEM) the results will be mesh size dependent and no converged solution exist upon mesh refinement. Thereby by applying the classical (local) models one my loose the accuracy on measuring the strength and ductility of DP steels. Among the non-classical (nonlocal) models, gradient-enhanced plasticity models which consider the effect of neighboring point on the behavior of one specific point are proved to be numerically effective and versatile tools to accomplish the two concerns mentioned above. So in this thesis a gradient-enhanced plasticity model which incorporates both the energetic and dissipative material length scales is derived based on the laws of thermodynamics. This model also has a consistent yield-like function for the interface which is an essential part of the higher-order gradient theories. The main issue with utilizing these theories is the implementation which limits the application of these theories for modeling the real problems. Here a straightforward implementation method based on the classical FEM and Meshless method will be proposed which due to its simplicity it can be applied for many problems. The application of the developed model and implementation will be shown on removing the mesh size dependency and capturing the size effect in microstructure level of dual phase steels
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011
There are numerous experimental results that indicate a size-dependent mechanical behavior of mat... more There are numerous experimental results that indicate a size-dependent mechanical behavior of materials at the micron or submicron scales, in the sense that “smaller is stronger”. As no material length scale exits in the conventional (local) constitutive theories, they fail to capture this size dependency of material behavior at small length scales. A number of theories for generalizing the classical plasticity theories in order to account for the observed size effects have been proposed and still motivates researchers in this area. Among them the nonlocal continuum theories of either integral or gradient type have been introduced to model material behavior size dependency in a computationally effective way [1, 2]. The concept behind these theories is that; plastic strain gradients lead to the enhancement in the density of geometrically necessary dislocations (GNDs) and thereby to an elevation in the material’s strength [3]. Higher-order gradient dependent plasticity theory which enforces microscopic boundary conditions at interfaces and free surfaces has been introduced to improve first-order gradient theories as they fail to predict size effects. Recently, micro/nano compression tests have attracted several researchers to investigate the small-scale mechanical behavior of micro/nano-pillars with sizes range from few micrometers down to a few hundred of nanometers (see [4, 5] and reference quoted therein). Typically focused ion beam (FIB) machining from a thin film or a bulk specimen is used to produce columnar structure which then subjected to compression using a nanoindenter outfitted with a flat punch indenter (e.g. [4, 5]). Usually extrinsic defects like high initial dislocation density in the order of 15 2 10 /m , vacancy clusters, intermetallic components, and near surface amorphous layers are formed at a layer adjacent to the milled surface [5, 6]. Deformation in micro/nano-pillar’s compression is macroscopically uniform, so one may doubt how gradient enhanced theories could be able to capture size effect as gradient terms have minor effects. However, the authors believe that higher-order gradient plasticity theories can capture this size effect even for macroscopically uniform deformation as higher-order boundary conditions play an important role once the size of specimen decreases [7, 10]. For example, initial defects or amorphous layers or surface roughness at external surfaces of the micro/nanopillars may increase the level of surface energy for embedding dislocation annihilation through the surface [10]. Moreover, as mentioned above, the fabrication process of these pillars cause initial GNDs formation within the specimen with higher density at milled surfaces so one may claim that this causes initial plastic strain distribution which is related to the initial GND density distribution. In the current paper, different initial effective plastic strain distributions that correspond to constant plastic strain gradients within a micropillar sample have been assumed and the ability of gradient enhanced plasticity theory to capture size effect for different pillar sizes is presented.
Finite Elements in Analysis and Design, 2015
ABSTRACT The higher-order gradient plasticity theory is successful in explaining the size effects... more ABSTRACT The higher-order gradient plasticity theory is successful in explaining the size effects encountered at the micron and submicron length scale. Due to the incorporation of spatial gradients of one or more internal variables in these theories and the associated non-classical boundary conditions, special types of elements in the finite element method maybe necessary. This makes the numerical implementation of this higher-order theory not straightforward. In this paper, a robust but straightforward numerical implementation of higher-order gradient-dependent plasticity theories is presented. The novelty of this paper is in (1) the application of the meshless methods, particularly the moving weighted least square method, combined with the finite element method for the numerical computation of plastic strain gradients, and (2) the numerical implementation of different types of higher-order microscopic boundary conditions at internal/external surfaces, interfaces, and moving elastic–plastic boundaries. The proposed numerical implementation algorithms can be easily adapted in the implementation of any form of higher-order gradient-dependent constitutive models. Examples of applying the current numerical approach is demonstrated for capturing mesh-objective shear band formation and size effect and boundary layer formation in thin films on elastic substrates and metal matrix composites with embedded elastic inclusions through the consideration of stiff, intermediate, and soft interfaces.
International Journal of Material Forming, 2009
Sandwich structures are gaining increase application in aeronautical, marine, automotive and civi... more Sandwich structures are gaining increase application in aeronautical, marine, automotive and civil engineering. Since such sheet can be subjected to stamping processes and their deformation limited by various defects, knowing beforehand the limiting amount of deformation is very important. For achieving this goal, sandwich sheet of Al 3105/Polymer/Al 3105 were prepared using thin film hot melt adheres. FLD of sandwich
Materials & Design, 2010
The most prominent feature of sheet material forming process is an elastic recovery phenomenon du... more The most prominent feature of sheet material forming process is an elastic recovery phenomenon during unloading which leads to spring back and side wall curl. Metal–polymer laminate sheets are emerging materials that have many potential applications. Therefore evaluation of spring back is mandatory for production of precise products from these new sheet materials. In this paper, the results of spring
Journal of Engineering Materials and Technology, 2013
Sandwich sheet structures are gaining a wide array of applications in the aeronautical, marine, a... more Sandwich sheet structures are gaining a wide array of applications in the aeronautical, marine, automotive, and civil engineering fields. Since such sheets can be subjected to forming/stamping processes, it is crucial to characterize their limiting amount of deformation before trying out any forming/stamping process. To achieve this goal, sandwich sheets of Al 3105/polymer/Al 3105 were prepared using thin film hot melt adheres. Through an experimental effort, forming limit diagrams (FLDs) of the prepared sandwich sheets were evaluated. In addition, simulation efforts were conducted to predict the FLDs of the sandwich sheets using finite element analysis (FEA) by considering the Gurson–Tvergaard–Needleman (GTN) damage model. The agreement among the experimental results and simulated predictions was promising. The effects of different parameters such as polymer core thickness, aluminum face sheet thickness, and shape constraints were investigated on the FLDs.
Journal of Engineering Materials and Technology, 2010
Sandwich structures are gaining wide applications in aeronautical, marine, automotive, and civil ... more Sandwich structures are gaining wide applications in aeronautical, marine, automotive, and civil engineering. Since such sheets can be subjected to stamping processes, it is crucial to characterize their forming behavior before trying out any conventional forming process. To achieve this goal, sandwich sheets of Al 3105/polymer/Al 3105 were prepared using thin film hot melt adheres. Different sandwich specimens with different thickness ratios (of polymer core to aluminum face sheet) were prepared. Throughout an experimental effort, the limiting drawing ratios (LDRs) of the sandwich sheets were determined. Besides, the LDR of the sandwich sheets were predicted using finite element analysis simulations by considering Gurson–Tvergaard–Needleman damage model. The results show the capability of the damage model to predict the LDR and the location of damaged zone in a workpiece during a forming operation.
Journal of Engineering Materials and Technology, 2011
Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, ... more Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedl...
Proceedings of the 5th International Congress on Computational Mechanics and Simulation, 2014
Shortest path graph distances are widely used in data science and machine learning, since they ca... more Shortest path graph distances are widely used in data science and machine learning, since they can approximate the underlying geodesic distance on the data manifold. However, the shortest path distance is highly sensitive to the addition of corrupted edges in the graph, either through noise or an adversarial perturbation. In this paper we study a family of Hamilton-Jacobi equations on graphs that we call the p-eikonal equation. We show that the p-eikonal equation with p = 1 is a provably robust distance-type function on a graph, and the p→∞ limit recovers shortest path distances. While the p-eikonal equation does not correspond to a shortest-path graph distance, we nonetheless show that the continuum limit of the p-eikonal equation on a random geometric graph recovers a geodesic density weighted distance in the continuum. We consider applications of the p-eikonal equation to data depth and semi-supervised learning, and use the continuum limit to prove asymptotic consistency results ...
This article considers the problem of optimally recovering stable linear time-invariant systems o... more This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal-recovery results relative to such approximability models, we construct some optimal algorithms and characterize the optimal performance for the identification and evaluation of transfer functions in the framework of the Hardy Hilbert space and of the disc algebra. In particular, we determine explicitly the optimal recovery performance for frequency measurements taken at equispaced points on an inner circle or on the torus.
Studies in Applied Mathematics
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describ... more We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is shown to be self-adjoint. In the special case of planar frames, the operator decomposes into a direct sum of two operators, one coupling out-of-plane displacement to angular (torsional) displacement and the other coupling in-plane displacement with axial displacement (compression). Detailed analysis of two examples is presented. We actively exploit the symmetry present in the examples and decompose the operator by restricting it onto reducing subspaces corresponding to irreducible representations of the symmetry group. These "quotient" operators are shown to capture particular oscillation modes of the frame.
When attempting to recover functions from observational data, one naturally seeks to do so in an ... more When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal Recovery. The distinctive twists here are the consideration of inaccurate data through some boundedness models and the emphasis on computational realizability. Several scenarios are unraveled through the efficient constructions of optimal recovery maps: local optimality under linearly or semidefinitely describable models, global optimality for the estimation of linear functionals under approximability models, and global near-optimality under approximability models in the space of continuous functions.
ArXiv, 2019
A communication network can be modeled as a directed connected graph with edge weights that chara... more A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is not known. Recent work has established conditions under which the underlying directed graph can be recovered exactly the pairwise Path Correlation Data, namely, the set of weights of intersection of each pair of directed paths to and from each endpoint. Algorithmically, this enables us to consistently fused tree-based view of the set of network paths to and from each endpoint to reconstruct the underlying network. However, in practice the PCD is not consistently determined by path measurements. Statistical fluctuations give rise to inconsistent inferred weight of edges from measurement based on different endpoints, as do operational cons...
We present full description of spectra for elastic beam Hamiltonian defined on periodic hexagonal... more We present full description of spectra for elastic beam Hamiltonian defined on periodic hexagonal lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar valued self-adjoint fourth-order operator equipped with a real periodic symmetric potential. Compared to the Schrödinger operator commonly applied in quantum graph literature, here vertex matching conditions encode geometry of the graph by their dependence on angles at which edges are met. We show that for a special equal-angle lattice, known as graphene, dispersion relation has a similar structure as reported for Schrödinger operator on periodic hexagonal lattices. This property is then further utilized to prove existence of singular Dirac points. We next discuss the role of the potential on reducibility of Fermi surface at uncountably many low-energy levels for this special lattice. Applying perturbation analysis, the developed theory is extended to derive dispersion relation for angle-per...