标题： 关于层状复合材料晶体塑性中的静态和演化均质化 显示英文标题

标题： On static and evolutionary homogenization in crystal plasticity for stratified composites

摘要： 这项工作的起点是一个高对比度层状材料在单滑移有限晶体塑性中的静态宏观模型，该模型在[Christowiak & Kreisbeck, Calc. Var. PDE (2017)]中被识别为通过{\Gamma }-收敛的均质极限。首先，我们分析了这个极限模型的极小值，解决了唯一性问题并推导了必要条件。特别是，结果表明，在能量最优变形的定义量中，即旋转和剪切变量，至少有一个是唯一确定的，并且我们确定了在刚体运动意义上导致平凡材料响应的条件。第二部分涉及将静态均质化扩展到特定情况下的演化{\Gamma }-收敛型结果，即在某些关于滑移系统的假设和能量的适当正则化下，能量和耗散效应在极限中分离。有趣的是，当滑移方向与层状微观结构对齐时，极限系统是纯能量的，这可以解释为通过均质化失去耗散。 显示英文摘要

摘要： The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via {\Gamma}-convergence. First, we analyze the minimizers of this limit model, addressing the question of uniqueness and deriving necessary conditions. In particular, it turns out that at least one of the defining quantities of an energetically optimal deformation, namely the rotation and the shear variable, is uniquely determined, and we identify conditions that give rise to a trivial material response in the sense of rigid-body motions. The second part is concerned with extending the static homogenization to an evolutionary {\Gamma}- convergence-type result for rate-independent systems in specific scenarios, that is, under certain assumptions on the slip systems and suitable regularizations of the energies, where energetic and dissipative effects decouple in the limit. Interestingly, when the slip direction is aligned with the layered microstructure, the limiting system is purely energetic, which can be interpreted as a loss of dissipation through homogenization.