Incremental variational homogenization of elastoplastic composites with isotropic and Armstrong-Frederick type nonlinear kinematic hardening

In order to investigate the behavior of elastoplastic composites exhibiting both isotropic and nonlinear kinematic hardening, we extend Double Incremental Variational (DIV) formulation Lucchetta et al. (2019), based on incremental variational principles introduced by Lahellec Suquet (2007) proposed Agoras (2016). However, Armstrong-Frederick model (Armstrong Frederick), which is very often used describe hardening refers framework non-associated plasticity (Chaboche, 1977), cannot be handled within generalized standard materials as required DIV relies. That why work with an approximation this model, namely modified Chaboche 1983). As dissipation potential associated depends internal variables, have such a situation. Then, apply twice procedure Ponte Castañeda (1991), first linearize local then deal intraphase heterogeneity thermoelastic Linear Comparison Composite (LCC) induced linearisation step. The resulting LCC per-phase homogeneous properties homogenized classical linear schemes. We develop implement new for two-phase matrix-inclusions matrix combined hardening. For various cyclic loadings, predictions compare favorably Finite Element simulations model.