In this paper we discuss some issues in the computational testing of material samples with heterogeneous microstructure via the finite element method. The microstructures are irregular, and are generated by randomly dispersing particulate material throughout an otherwise homogeneous matrix material. Since every material sample generated during a testing process has a different microstructural morphology, and thus may require a different finite element mesh, an automated adaptive meshing scheme is developed to control the numerical error during material sample (microstructural) changes. Three dimensional numerical examples are given to illustrate the presented concepts
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