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Papers by Mahendra Kumar Pal

Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM fram... more Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM framework (HO-PDS-FEM) and applications in efficiently simulating cracks are presented in this paper. PDS is an approximation scheme which uses a conjugate domain tessellation pair like Voronoi and Delaunay in approximating a function and its derivatives. In approximating a function (or derivatives), HO-PDS first produces local polynomial approximations for the target function (or derivatives) within each element of respective tessellation. The approximations over the whole domain are then obtained by taking the union of those respective local approximations. These approximations are inherently discontinuous along the boundaries of the respective tessellation elements since the support of the local approximations is confined to the domain of respective tessellation elements and no continuity conditions are enforced. HO-PDS-FEM utilizes these inherent discontinuities in function approximation to efficiently model discontinuities such as cracks. Higher order PDS is implemented in FEM framework to solve boundary value problem of elastic solids, including mode-I crack problems. With several benchmark problems, it is shown that HO-PDS-FEM has higher expected accuracy and convergence rate. J-integral around a mode-I crack tip is calculated to demonstrate the improvement in the accuracy of the crack tip stress field. Further, it is shown that HO-PDS-FEM significantly improves the traction along the crack surfaces, compared to the zeroth-order PDS-FEM [Hori, M., Oguni, K. and Sakaguchi, H. [2005] “Proposal of FEM implemented with particle discretization scheme for analysis of failure phenomena,” J. Mech. Phys. Solids 53, 681–703].

Development of E-Simulator, which aims at reproducing the damage/collapse mechanism of soil, brid... more Development of E-Simulator, which aims at reproducing the damage/collapse mechanism of soil, bridge and building structures against strong earthquakes, is a project of E-Defense. Data measured in E-Defense shake table tests are used for validation of E-Simulator. As a research subject in the field of soil structures, we aim to simulate the large-scale experiment of soil and underground structures conducted at E-Defense in February 2012. In this study, we conduct elastic analysis by using detailed solid model of soil and underground structures. Our main objectives of this research are to determine the suitable mesh of analysis model and to identify appropriate technique to impose lateral boundary condition. Then, we clarify how the detailed solid model can simulate the experimental result and the limitation of the elastic analysis and identify the issues to be taken care of in the elasto-plastic analysis.

This paper presents implementation of higher order PDS (HO-PDS) in FEM framework (HO-PDS-FEM) to ... more This paper presents implementation of higher order PDS (HO-PDS) in FEM framework (HO-PDS-FEM) to solve a boundary value problems involving cracks in linear elastic bodies. Further, an alternative approach based on curl free restriction to extend the current PDS is also presented. This alternative curl-free implementation is scrutinized and compared with a former proposal for HO-PDS whose derivative is not guarantee to satisfy curl free condition. Analysis of traditional plate with a hole problem shows that curl free implementation does not have any specific advantage. Further, techniques for modeling cracks in HO-PDS-FEM are presented. Comparison of two formulations with mode-I crack problem indicates that former proposed HO-PDS-FEM is superior to the proposed curl free formulation, and there is a significant improvement compared to 0 th-order PDS-FEM.

This paper studies the extension of particle discretization scheme (PDS) in order to improve fini... more This paper studies the extension of particle discretization scheme (PDS) in order to improve finite element method implemented with this discretization scheme (PDS-FEM). Polynomials are included in the basis functions, while original PDS uses a characteristic function or zero-th order polynomial only. It is shown that including 1st order polynomials in PDS, the rate of the convergence reaches the value of 2 even for the derivative. 1st order polynomials are successfully included in PDS-FEM. A numerical experiment is carried out by applying 1st order PDS-FEM, and the improvement of the accuracy is discussed.

In this study we have presented two-scale Generalized Finite Element (GFEM) for fracture analysis... more In this study we have presented two-scale Generalized Finite Element (GFEM) for fracture analysis. GFEM is based on
the enrichment of the classical FEM approximation. These enrichment functions incorporate the discontinuity response
in the domain. A two-scale global local approach is used to get the enrichment function. Shape sensitivity analysis of an
elastic body with Generalized Finite Element (GFEM) has been illustrated as a numerical example. We have studied the
normalized Stress Intensity Factor (SIF) and J-integral sensitivity with respect to the crack length.

In this work multiscale failure modeling of composites is made using generalized finite element m... more In this work multiscale failure modeling of composites is made using generalized finite element method (GFEM). In this method the global approximation are constructed by combining the local basis with partition of unity functions. The enrichment functions for the GFEM approximation are computed using a proper orthogonal decomposition (POD) technique. The approximation is then used in a two scale Galerkin scheme for failure modeling of composites. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Conference Presentations by Mahendra Kumar Pal

Soil-structure interaction plays a vital role in evaluation of seismic performance of structure. ... more Soil-structure interaction plays a vital role in evaluation of seismic performance of structure. In this study, we present the systematic study of numerical and experimental results of large-scale experiment conducted at E-Defense. Suitability of mesh and adequacy of technique to impose lateral boundary conditions (i.e. modeling soil-container) are studied. This study also demonstrates the limitations of elastic analysis and provides the issues to be taken care in elasto-plastic analysis.

This paper presents the modelling and elasto-plastic analysis of E-Defense Shake Table test on so... more This paper presents the modelling and elasto-plastic analysis of E-Defense Shake Table test on soil-underground structure. Modified Cam-Clay model incorporating re-liquefaction phenomena by employing the concept of stress-anisotropy and superloading surface has been utilized for simulating soil-behaviour. Numerical results are compared with that of experiment in quantitative manner aiming to validate the numerical results of E-Simulator. Response histories of acceleration , displacement and strain at several critical locations namely soil-strata interface, vicinity of structural-joints and boundary of specimen are calculated and compared with experimental results. Comparison shows that responses have reasonable agreement with experimental results and do not possess any phase difference.

This paper presents the higher order extension of Particle Discretization Scheme (PDS) and its im... more This paper presents the higher order extension of Particle Discretization Scheme (PDS) and its implementation in FEM framework (PDS-FEM)[1, 2, 3] with the aim of simulating brittle cracks in linear elastic solids. PDS-FEM has several attractive features; has a numerically efficient failure treatment, no special treatments required for modeling crack branching, etc. The existing PDS and PDS-FEM are first-order accurate and the objective of this work is to develop a higher order extension while preserving the above mentioned attractive features. A unique property of PDS is the use of conjugate domain tessellations Voronoi and Delaunay to approximate functions and their derivatives, respectively. Let {Φ α } and {Ψ β } be sets of Voronoi and Delaunay tessellation elements of the analyzed domain. Further, let φ α (x) and ψ β (x) be the characteristic functions, and x α and y β be the mother points of elements Φ α and Ψ β , respectively. In higher order PDS, a function is approximated as f (x) ≈ f d (x) = α,n f αn P αn , where {P αn } = {1, x − x α ,. .. , (x − x α) r ,. . .}φ α (x) is a set of polynomial bases with the support of Φ α. The support of P αn 's being confined to the domain of each Φ α , f d (x) consists of discontinuities along Voronoi boundaries. Considering local polynomial approximations over Delaunay tessellation, {Ψ β }, which is the conjugate of Voronoi, PDS defines bounded derivatives for this discontinuous approximation f d (x). Higher order PDS approximates the derivative f, i = ∂f (x) /∂x i as f, i ≈ β,m g βm i Q βm , where {Q βm } = {1, x − x β ,. .. , (x − x β) r ,. . .}ψ β (x). Choosing a suitable sets of polynomial bases for {P αn } and {Q βm }, one can obtain higher order accurate approximations for a given function and its derivatives. The higher order PDS is implemented in the FEM framework to solve the boundary value problem of linear elastic solids. As above explained, PDS approximates a given function and its derivatives as the union of local polynomial expansions defined over the elements of conjugate tessellations. According to the authors' knowledge, this is the first time to use approximations based on local polynomial expansions to solve boundary value problems. With standard benchmark problems in linear elasticity, it is demonstrated that second order accuracy can be obtained by including polynomial bases of first order in {P αn }[3]. Further, exploiting the inherent discontinuities in f d (x), PDS-FEM proposes a numerically efficient treatment for modeling cracks. The efficient crack treatment of higher order PDS-FEM is verified with standard mode-I crack problems. References [1] Hori M, Oguni K, Sakaguchi H, Proposal of FEM implemented with particle discretization for analysis of failure phenomena, Journal of Mechanics and Physics of Solids. 2005; 53-3: 681-703. [2] M.L.L. Wijerathne, Kenji Oguni, Muneo Hori, Numerical analysis of growing crack problem using particle discretization scheme, Int.

We present the development a higher order extension of Particle Discretization Scheme (PDS) and i... more We present the development a higher order extension of Particle Discretization Scheme (PDS) and its implementation in FEM (PDS-FEM) for modeling 2D and 3D brittle elastic cracks. Numerically efficient treatment to model discontinuities is a salient feature of originally proposed PDS-FEM [1]. The higher order extension [2] brings two more attractive features; higher rate of convergence and increased accuracy of stress state in the vicinity of traction free crack surfaces. A peculiar property of PDS is the usage of conjugate domain tessellation schemes to approximate a given function and its derivatives; we use Voronoi and Delaunay tessellation pair for function and derivatives, respectively. A given function f (x x x) is approximated as f (x x x) ≈ f d (x x x) = ∑ α,n f α P αn (x x x)φ(x x x), where Φ α denotes the characteristic function of α th Voronoi element and P αn (x x x) denotes its n th polynomial base. Similarly, derivatives are approximated with a suitable set of base polynomials and characteristic functions, Ψ β 's, of Delaunay elements. The use of characteristic functions Φ α confines the support of the polynomial bases to the support of each tessellation element, making f d (x x x) discontinuous and giving rise to PDS's particle nature. Though f d (x x x) is discontinuous, PDS defines bounded approximations for derivatives, by approximating those with Delaunay tessellation which is the conjugate of Voronoi. The numerous discontinuities in f d (x) along Voronoi boundaries are utilized to efficiently model discontinuities when solving the boundary value problems. As an example, all it requires to introduce a crack along a Voronoi boundary is recalculating element stiffness matrix of relevant Delaunay element, ignoring the contribution from an infinitesimally thin neighbourhood of the Voronoi boundary to be broken. This surely is much lighter than competing methods in FEM. The proposed higher order extension is verified with several standard benchmark problems involving elastic deformation and mode-I cracks in 2D and 3D. While the benchmark problems without cracks produced the expected ideal convergence rate, those with mode-I cracks produced nearly ideal results. For the mode-I crack problems, higher order PDS-FEM with first order polynomial bases for approximating displacements produced the rate of convergence of 1.7 for J-integral; the ideally expected rate is 2. Further, it is demonstrated that the proposed higher order extension significantly improve the state of stress in the vicinity of traction free crack surfaces, compared to that of former 0 th order PDS-FEM[1]. References [1] M.L.L. Wijerathne, Kenji Oguni, Muneo Hori, Numerical analysis of growing crack problem using particle discretization scheme, Int.

We present a high fidelity numerical simulation technique to analyze the collapse behavior of a c... more We present a high fidelity numerical simulation technique to analyze the collapse behavior of a composite beam under cyclic loading. The analysis is performed by utilizing the in-house software package called E-Simulator [1], which is developed at Hyogo Earthquake Engineering Research Center (E-Defense) of National Institute of Earth Science and Disaster Prevention (NIED), Japan, with aim to replicate the seismic responses of building and civil structures. The E-simulator is incorporated with sophisticated material constitutive material model and damage/failure analysis. It uses the parallel FE-analysis software package: ADVENTURECluster [2], as platform to accomplish massive numerical computations. A heuristic and implicit approach with piecewise linear isotropic kinematic hardening law is used simulate the complex cyclic behavior of steel. The constitutive model is verified with simulation of a cantilever beam subjected to a cyclic forced displacement. Further, as a constitutive model for concrete, extended Drucker-Prager model has been employed and the parameters are identified so that compressive and tensile behavior of concrete can be reproduced. We are intended to improve the unloading behavior of composite beam, which was obtained in previous work [3] by including the compression failure of concrete into Drucker-Prager model. The effect of compression failure has been adopted by reducing the density of corresponding element, depending upon the plastic strain í µí¼̅ í µí± , which is controlled by parameter called cavity rate í µí± í µí±í µí±í µí±£í µí±. The cavity rate parameter is defined as í µí± í µí±í µí±í µí±£í µí± = 0.9 í µí¼̅ í µí± − í µí± 0 í µí± 1 − í µí± 0 where, í µí± 0 and í µí± 1 are the function of the first invariant of í µí°¼ í µí¼. A relation between the bending moment at the beam-to-column connection and the average deflection angle for composite beam has been analyzed and compared with experiment results, obtained in cycling loading test of full scale partial frame during E-Defense blind analysis contest. Numerical results are in good agreement with experiment results.