Recent progress in the mathematical analysis of variational models for the plastic deformation of crystals in a geometrically nonlinear setting is discussed. The focus lies on the first time-step and on situations where only one slip system is active, in two spatial dimensions. The interplay of invariance under finite rotations and plastic deformation leads to the emergence of microstructures, which can be analyzed in the framework of relaxation theory using the theory of quasiconvexity. A class of elastoplastic energies with one active slip system that converge asymptotically to a model with rigid elasticity is presented and the interplay between relaxation and asymptotics is investigated.

中文翻译：

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单滑弹塑性的最佳层压板

讨论了在几何非线性环境中对晶体塑性变形的变分模型进行数学分析的最新进展。重点放在第一个时间步上，以及在两个空间维度上只有一个滑移系统处于活动状态的情况。有限旋转和塑性变形下不变性的相互作用导致了微观结构的出现，可以在弛豫理论的框架内使用拟凸性理论对其进行分析。提出了一类具有一个主动滑移系统的弹塑性能量，该系统逐渐渐近收敛到具有刚性弹性的模型，并且研究了松弛和渐近之间的相互作用。