Starting from the exact solution of the heterogeneous linear viscoelastic Eshelby ellipsoidal inclusion problem obtained in the time domain for an ellipsoidal inclusion embedded in an isotropic matrix (Berbenni et al., 2015), a direct time-incremental homogenization Mori-Tanaka scheme for two-phase non linear elasto-viscoplastic materials is proposed. The extension to non-linear behavior is based on a “modified secant” formulation to obtain the linear comparison composite (LCC) properties. In contrast with more classic homogenization method based on the first moment of stresses (i.e. classic secant formulation), the present approach is based on the second-order moment of stresses making use of the Hill’s lemma. Hence, a modified secant viscoplastic compliance is considered for the matrix phase. The effective behavior as well as the evolution laws of the averaged strains and stresses per phase are directly solved in the time domain, without the need of Laplace-Carson transforms. The estimates provided by the present homogenization model are compared to full-field calculations from the literature for two-phase non linear particulate composites constituted of an isotropic elasto-viscoplastic matrix phase and isotropic elastic particles, and, for radial and non-radial loadings.

从对嵌入各向同性矩阵中的椭圆体夹杂物在时域中获得的异质线性粘弹性 Eshelby 椭圆体夹杂物问题的精确解（Berbenni 等人，2015 年）开始，直接时间增量均质化 Mori-Tanaka 方案用于两个-提出了相非线性弹粘塑性材料。非线性行为的扩展基于“修正割线”公式，以获得线性比较复合 (LCC) 属性。与基于应力一阶矩的更经典的均质化方法（即经典割线公式）相比，本方法基于利用希尔引理的二阶应力矩。因此，对于基体相考虑了改进的割线粘塑性柔顺性。有效行为以及每相平均应变和应力的演化规律在时域中直接求解，无需拉普拉斯-卡森变换。对于由各向同性弹-粘塑性基体相和各向同性弹性颗粒构成的两相非线性颗粒复合材料，以及径向和非径向载荷，将本均质模型提供的估计与文献中的全场计算进行比较。