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

为了研究既具有各向同性又具有非线性的弹塑性复合材料的行为运动硬化，我们扩展了Lucchetta等人的双增量变分（DIV）公式。（2019），基于Lahellec和Suquet（2007）引入的增量变分原理以及Agoras等人提出的公式。（2016）。但是，阿姆斯特朗-弗雷德里克模型（阿姆斯特朗和弗雷德里克）通常用于描述非线性运动硬化并涉及非关联可塑性框架（Chaboche，1977），但不能在通用标准材料框架内进行处理。 DIV公式所依赖的增量变分原理所要求的。这就是为什么我们使用此模型的近似值，即修改后的Chaboche模型（Chaboche，1983年）。由于与此模型相关联的耗散潜力取决于内部变量，我们必须将Lahellec和Suquet的增量变分原理扩展到这种情况。然后，我们应用两次PonteCastañeda（1991）的变分程序，首先线性化局部行为，然后处理线性化步骤引起的热弹性线性比较复合材料（LCC）的相内不均匀性。通过经典的线性方案将得到的具有每相均质特性的热弹性LCC均质化。我们开发和实施这种新的增量变分程序，用于具有各向同性弹塑性基体的两相基体-夹杂物复合材料，该基体具有各向同性和非线性运动学强化组合。对于各种循环载荷，所提出的DIV公式的预测与基于Armstrong-Frederick模型的有限元模拟相比具有优势。