On the Macroscopic Response and Field Statistics in Particulate Composites With Elasto-Plastic Phases and Random Microstructures

In this article, we carry out a theoretical investigation of the macroscopic response and field statistics in two-phase particulate composites with elasto-plastic constituents and random microstructures under cyclic loading conditions. To this end, we make use of the “incremental variational homogenization” (IVH) procedure of Agoras et al. (2016, “Incremental Variational Procedure for Elasto-Viscoplastic Composites and Application to Polymer- and Metal-Matrix Composites Reinforced by Spheroidal Elastic Particles,” Int. J. Solid Struct., 97–98, pp. 668–686) and corresponding unit cell finite element simulations. Results are obtained for statistically isotropic distributions of spherical particles and for “spheroidal distributions” of spheroidal particles. It is shown analytically that the IVH estimate of Agoras et al. and that of Lahellec and Suquet (2013, “Effective Response and Field Statistics in Elasto-Plastic and Elasto-Visco-Plastic Composites Under Radial and Non-Radial Loadings,” Int. J. Plasticity, 42, pp. 1–30) are equivalent. In addition, it is illustrated by means of specific numeral comparisons that the IVH estimate is also equivalent (to within numerical accuracy) to the corresponding estimates of Idiart and Lahellec (2016, “Estimates for the Overall Linear Properties of Pointwise Heterogeneous Solids With Application to Elasto-Viscoplasticity,” J. Mech. Phys. Solids, 97, pp. 317–332) and Lucchetta et al. (2019, “A Double Incremental Variational Procedure for Elastoplastic Composites With Combined Isotropic and Linear Kinematic Hardening,” Int. J. Solid Struct., 158, pp. 243–267). Furthermore, it is shown in the context of specific exact results for composite materials with lamellar microstructures that the elastic–plastic coupling and the Bauschinger effect are the macroscopic manifestations of the incompatibility of the local elastic strains. Local strain hardening is incorporate in the IVH model. The predictions of the IVH model for the macroscopic response of particulate composites are found to be in good agreement with the corresponding numerical results, in general. For the extreme cases of rigidly reinforced composites and porous materials, however, the IVH model fails to capture the elastic–plastic coupling and the Bauschinger effect. The underlying reasons for this shortcoming are discussed and a strategy toward the improvement of the IVH model is proposed.