A FINITE-ELEMENT METHOD FOR MICROSTRUCTURAL ANALYSIS

A new method is presented for the thermomechanical analysis of composite microstructures. The problem is defined on a unit cell of arbitrary geometry with the displacement field written in two parts: a slowly varying macroscopic part and a microscopic part for which periodic boundary conditions are imposed. The macroscopic stress field is then found by averaging the stress obtained from a finite element solution of the microscopic displacement field as a function of the macroscopic strains. Two- and three-dimensional microscopic analyses have been conducted for two different metal-matrix composites: unidirectional continuous boron fibers in an aluminum matrix and silicon carbide particles in an aluminum matrix. Theoretical elastic and yielding results are presented and compared with experimental tension, compression, and pure shear tests. The effects of the choice of microscopic geometry, reinforcement loading, finite element resolution, residual stresses and initial hardening are demonstrated.