Somnath Ghosh

Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method

Abstract This paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with Voronoi cell (VCFEM) for microstructural modeling. The Voronoi cell finite element model originates from Dirichlet tessellation of a representative material element or a base cell in the microstructure. Homogenized material coefficients for a global displacement finite element model are generated by VCFEM analysis using periodic boundary conditions on the base cell. Following the macroscopic analysis, the local VCFEM analysis is implemented to depict the true evolution of microstructural stresses and strains. Various numerical examples are executed for validating the effectiveness of VCFEM macro-micro modeling of elastic materials. The effect of size, shape, orientation and distribution of heterogeneities on the local and global response are examined.

Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model

In this paper, a multiple scale finite element model (VCFEM-HOMO) has been developed for elastic-plastic analysis of heterogeneous (porous and composite) materials by combining asymptotic homogenization theory with the Voronoi Cell finite element model (VCFEM). VCFEM for microstructural modeling originates from Dirichlet tessellation of representative material elements at sampling points in the structure. Structural modeling is done by the general purpose finite element code ABAQUS, and interfacing with the microscale VCFEM analysis is done through the user subroutine in ABAQUS for material constitutive relation, UMAT. Asymptotic homogenization in UMAT generates macroscopic material parameters for ABAQUS. Following the macroscopic analysis, a local VCFEM analysis is invoked to depict the true evolution of microstructural state variables. Various numerical examples are executed for validating the effectiveness of VCFEM-HOMO, and the effect of size, shape and distribution of heterogeneities on local and global response is examined.

Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method

Abstract In this paper, a Voronoi Cell finite element method is developed to solve small deformation elastic-plasticity problems for arbitrary heterogenous materials. Dirichlet Tessellation of microstructural representative materials results in a network of arbitrary-sided polygons called Voronoi cells. Each Voronoi cell encompasses one second phase heterogeneity at most. These are natural elements for the microstructure, representing the basic structural elements of the material. In this paper, formulations are developed for directly considering Voronoi cells as elements in a finite element model without any further dissection. Furthermore, a composite Voronoi Cell finite element method is developed to account for the presence of the second phase within each polygonal element. Various numerical elastic-plastic examples are executed for validating the effectiveness of this formulation. Finally, studies are conducted to understand the effect of size, shape and distribution of second phase on the averaged and true local responses of representative material elements.

Deformation and creep modeling in polycrystalline Ti-6Al alloys

Abstract This paper develops an experimentally validated computational model for titanium alloys accounting for plastic anisotropy and time-dependent plasticity for analyzing creep and dwell phenomena. A time-dependent crystal plasticity formulation is developed for hcp crystalline structure, with the inclusion of microstructural crystallographic orientation distribution. A multi-variable optimization method is developed to calibrate crystal plasticity parameters from experimental results of single crystals of α-Ti–6Al. Statistically equivalent orientation distributions of orientation imaging microscopy data are used in constructing the polycrystalline aggregate model. The model is used to study global and local response of the polycrystalline model for constant strain rate, creep, dwell and cyclic tests. Effects of stress localization and load shedding with orientation mismatch are also studied for potential crack initiation.

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids

Abstract Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.

Three dimensional characterization and modeling of particle reinforced metal matrix composites: part I Quantitative description of microstructural morphology

In this first of a two part sequence of papers, 3-D microstructures of Si particle reinforced aluminum matrix composites are computationally constructed by assembling digitally acquired micrographs obtained by serial sectioning. The material samples considered vary in volume fraction and in particle size. Furthermore, equivalent microstructures with actual particles replaced by ellipses (in 2-D) or ellipsoids (in 3-D) are computationally simulated for efficiency. The equivalent microstructures are tessellated by a particle surface based algorithm into a mesh of Voronoi cells. Various 3-D characterization functions are developed to identify particle size, shape, orientation and spatial distribution in the actual materials and to compare with 2-D micrographs. Through this analysis, differences between 2- and 3-D characterization are established. Results indicate that it may not be sufficient to use 2-D section information for characterizing detailed microstructural features like particle shapes, orientations and near-neighbor distances. The second part of this sequence of papers will describe the important relationship of these features to damage evolution in these same materials. This sequence of papers is perhaps one of the first on 3-D physical characterization of the phase and damage structure for this class of materials.

Statistically Equivalent Representative Volume Elements for Unidirectional Composite Microstructures: Part I - Without Damage

The representative volume element (RVE) of a material microstructure plays an important role in the analysis of heterogeneous materials, such as composites. Effective material properties in a composite material depend on the microstructural concentration and dispersion of different phases in the RVE. In this study, a combination of statistical and computational tools are proposed for identifying the statistically equivalent RVE (SERVE) for an elastic composite with nonuniform dispersion of inclusions. Numerical tests are conducted with various statistical functions of geometry, stresses, and strains to examine the validity of potential alternative definitions of the SERVE. In the first of this two-part article, methods are addressed for undamaged composite microstructures with continuous interfaces between the fiber and the matrix. The sequel article deals with the evolution of SERVE caused by damage due to interfacial debonding.

Interfacial debonding analysis in multiple fiber reinforced composites

Decohesion at multiple fiber interfaces of elastic fiber reinforced composites is modeled by the Voronoi cell finite element model (VCFEM) in this paper. Interfacial debonding is accommodated by cohesive zone models, in which normal and tangential springs tractions are expressed in terms of interfacial separation. Model simulations are compared with results from experiments using cruciform specimens, of single and multiple fiber polymer-matrix composites. An inverse problem is solved to calibrate the cohesive zone parameters. Debonding at fiber-matrix interfaces is simulated for different architectures, volume fractions and boundary conditions, to understand the influence of microstructural morphology and boundary conditions on the decohesion process.

Particle fracture simulation in non-uniform microstructures of metal–matrix composites

This paper deals with the evolution of damage in microstructures of reinforced ductile-matrix composites, by particle cracking and splitting. A small deformation Voronoi Cell finite element model is developed, in which each element may consist of a matrix phase, an inclusion phase and a crack phase. Brittle inclusions may be of arbitrary shapes and sizes, and may be dispersed non-uniformly in the matrix. Damage initiation of inclusions is assumed to follow a maximum principal stress theory. Complete particle cracking or splitting is assumed at the onset of damage. The model is validated by a few comparison studies. Various geometric patterns are studied to test the effectiveness of the model, as well as to understand the effect of morphology on damage evolution. Actual microstructures from optical micrographs of Al-Si-Mg composite systems are analyzed and compared with experimentally observed results. Quantitative characterization and statistical analysis is conducted to correlate morphological parameters with mechanical response.

A material based finite element analysis of heterogeneous media involving Dirichlet tessellations

Abstract In this paper, a new finite element formulation has been developed for analysis of heterogeneous media, in which the second phase is randomly dispersed within the matrix. It introduces a tessellation based mesh generation technique to account for the arbitrariness in location, shape and size of the second phase. An assumed stress hybrid formulation has been implemented to utilize the resulting Voronoi polygons as elements in a finite element model. The effect of the second phase has been accounted for by introducing a transformation strain based constitutive formulation. Numerical examples have been conducted to validate the model.