Computation of the Effective Properties of Materials with Microstructure

Abstract

Effective material properties are computed for materials with microstructure. Two types of materials are considered. The first type of material studied is a discontinuously reinforced composite material. This type of material has a microstructure that consists of stiff,brittle particles surrounded by a compliant matrix. A micromechanical model is utilized to estimate the elastic-plastic deformation characteristics of these composite materials. The models consist of an elastic-plastic matrix material reinforced with a dilute concentration of axisymmetric elastic inclusions. The model is based on the dilute approximation which models the composite material as sn inclusion of the finite size embedded in an infinite material. The matrix material is assumed to obey the J2 flow theory with isotropic hardening. The finite element method is utilized to solve the nonlinear boundary value problem. Results are presented which illustrate the effect of reinforcement shape on the evolution of the local matrix state variables. A volume averaging scheme is then employed to obtain dilute estimates for the macroscopic response. Results showing the effect of reinforcement shape and volume fraction on the predicted stress-strain response of the composite are presented. It is shown that the reinforcement shape can have a significant effect on the effective properties of the composite material. The second type of material studied is a material which has a granular and/or fiberous microstructure. The microstructures of these types of materials are often modeled by a latticelike arrangement of load carrying members. Within the framework of the finite element method, a general technique is presented to compute the effective properties of materials which are modeled by these latticelike microstructures. The equivalency between the continuum and microstructural stiffness matrices is utilized to produce an over-determined system of equations which is solved using the Moore-Penrose generalized inverse procedure. Although the resulting solution is not exact, it is unique in the least squares sense. The effective properties are reported in the form of a continuum constitutive matrix which approximates the behavior of the latticelike microstructure. Several specific examples are given to demonstrate the effectiveness and accuracy of the method.