This paper discusses the homogenization method to determine the effective average elastic constants of linear elasticity of general composite materials by considering their microstructure. After giving a brief theory of the homogenization method, a finite element approximation is introduced with convergence study and corresponding error estimate. Applying these, computer programs PREMAT and POSTMAT are developed for preprocessing and postprocessing of material characterization of composite materials. Using these programs, the homogenized elastic constants for macroscopic stress analysis are obtained for typical composite materials to show their capability. Finally, the adaptive finite element method is introduced to improve the accuracy of the finite element approximation.

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Mathematical Theory of Elastic and Elasto Plastic Bodies: An Introduction

Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

Basic error estimates for elliptic problems

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering

Weak and Measure-Valued Solutions to Evolutionary PDEs

Numerical methods for unilateral problems in solid mechanics

This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.

/pdf/mathematical-models-in-contact-mechanics-15zb50eyyq.pdf

Mathematical Theory of Elastic and Elasto Plastic Bodies: An Introduction

Citations

Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

Basic error estimates for elliptic problems

Weak and Measure-Valued Solutions to Evolutionary PDEs

Numerical methods for unilateral problems in solid mechanics

Mathematical Models in Contact Mechanics

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