Materials with more than one constituent phase exhibit behavior which is contingent on the configuration of the microstructure. Additional complexity is encountered when damage effects, such as plastic behavior, are considered. The local configuration of the composite microstructure dictates the location of stress concentrations which develop in the material. These stress concentrations then often determine the location and extent to which the material undergoes damage.

Homogenization techniques are a powerful tool used to describe composite materials in terms of effective material properties. Use of effective properties eliminates the need for an explicit model of the material microstructure in the analysis, significantly reducing computational cost. However, homogenization obscures local variations in the microstructure, which can be particularly critical in composite materials behaving inelastically. Meso-scale modeling is one approach to retaining some local descriptiveness, while at the same time removing some of the complexity inherent in the modeling problem.

There are three main objectives of this work. The first is to obtain material property estimates which are both localized and homogenized. These local properties include effective elastic behavior, and also a representation of the local evolution of plasticity in the material. A meso-scale modeling scheme is to be determined which accounts well for overall behavior when tested at the macro-scale. The second objective of this work is to characterize the accuracy of the meso-scale model. A benchmark single inclusion elasto-plastic problem is developed against which to compare the accuracy of the meso-scale model. Several metrics are used which include include stress concentrations in the material, strain energy, plastic dissipation energy, and a comparison of yielded areas. Thirdly, it will be shown that meso-scale homogenization techniques can be used as the basis for a simulation of material property fields in representing a random elasto-plastic composite microstructure using a two-dimensional, two-variable spectral representation simulation.