Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions

The effective mechanical behavior of an elasto-plastic matrix reinforced with a random and homogeneous distribution of aligned elastic ellipsoids was obtained by the finite element simulation of a representative volume element (RVE) of the microstructure and by homogenization methods. In the latter, the composite behavior was modeled by linearization of the local behavior through the use of the tangent or secant stiffness tensors of the phases. ‘‘Quasi-exact’’ results for the tensile deformation were attained by averaging of the stress-strain curves coming from the numerical simulation of RVEs containing a few dozens of ellipsoids. These results were used as benchmarks to assess the accuracy of the homogenization models. The best approximations to the reference numerical results were provided by the incremental and the second-order secant methods, while the classical or first-order secant approach overestimated the composite flow stress, particularly when the composite was deformed in the longitudinal direction. The discrepancies among the homogenization models and the numerical results were assessed from the analysis of the stress and strain microfields provided by the numerical simulations, which demonstrated the dominant effect of the localization of the plastic strain in the matrix on the accuracy of the homogenization models.