Numerical Investigation of the Multiscale Characteristics of Elastoplasticity in Microheterogeneous Continuum Media Using a Simple Hollow Sphere Model

In this paper, we investigate the fundamental characteristics of plasticity in microheterogeneous continuum materials. Plasticity in such materials is a multiscale phenomenon with contrasting characteristics at different scales. A hollow sphere model, including a matrix embedding an oblate spheroidal pore, is considered as a sample representative elementary volume (REV) of a microheterogeneous material where, at the local level (microscale), a simple Drucker–Prager plasticity model is assumed for the matrix obeying the classical continuum theory of plasticity. The plasticity model is Lode angle independent with associated plastic flow and no hardening. We perform finite element numerical simulations on the REV to investigate the characteristics of the homogenized plasticity of the REV. It is seen that the homogenized plasticity shows complex characteristics such as Lode angle dependency, presence of cap, hardening, and nonassociativity. Well-established as these aspects are in the literature, they are often presumed in the plasticity models of heterogeneous materials in an ad hoc form. In contrast, we present here a systematic and lucid way to capture these aspects as emergent phenomena of heterogeneous microstructures. This has crucial implications in guiding the theoretical constitutive developments for elastoplastic materials toward adopting a multiscale approach that properly considers the effect of microstructure and naturally captures these aspects without the need for ad hoc assumptions. A fundamental assumption in the classical theory of plasticity is the plastic flow rule postulate, which states that the direction of plastic strain increment is governed only by the current state variables, independent of the loading increment direction. We show, through a stress probing exercise in 3D principal stress space, that the flow rule, assumed for the microscale plasticity, is not valid for the macroscopic plasticity. Indeed, the homogenized plastic flow direction in heterogeneous materials is governed by the current state variables and loading increment direction. Finally, we show that the plastic response is also a function of the stress path taken prior to loading. As such, nonclassical characteristics are observed for the plasticity of microheterogeneous materials. These nonclassical characteristics for the simple REV considered in this work (the hollow sphere model) align with some of the results observed in experiments or only reported for microdiscrete materials; herein, we show they are also valid for a broader range of materials endowed with microstructure, i.e., microcontinuous materials, and, as such, the fundamental assumptions in the classical theory of plasticity require revision before being applicable to the plastic behavior of heterogeneous materials.