Computational plasticity and viscoplasticity for composite materials and structures

The paper extends a recently developed theory of mathematical homogenization with eigenstrains to account for viscous effects. A unified mathematical and numerical model of plasticity and viscoplasticity is employed within the framework of the power-law and the Bodner-Partom models. Introduction A typical aerospace composite component can be modeled on (at least) three different scales: (i) macroscale (structural level), (ii) mesoscale (laminate level), and (iii) microscale (the level of microconstituents). Additional scales can be introduced into the model. For example, the scale of material heterogeneity in each microphase, such as dislocations and grain boundaries, could be considered as another scale, not to mention the atomic and electronic scales as the smallest spatial scales. Computational models can be either deterministic or stochastic. Various deterministic approaches can be classified into the following three categories (i) the classical uncoupled ap- The uncoupled approach employs representative volume elements (RVE) at one level to produce averaged parameters for the use at the next level. The mathematical homogenization theory [12], [5] provides a theoretical framework for the uncoupled approach. For three or more spatial scales the mathematical homogenization theory has been employed in The primary objective of the present manuscript is to extend the recent formulation of the mathematical homogenization theory with eigenstrains developed by the authors in [4] to account for viscous effects. We focus on the uncoupled approach assuming solution peri