An explicit characterization of the quasiconvex envelope of the condensed energy in a model for finite elastoplasticity is presented, both in two and in three spatial dimensions. A variational formulation of plasticity, which is appropriate for the first time step in a time discrete formulation of the evolution problem, is used, and it is assumed that only one slip system is active. The model includes a nonlinear elastic energy, which is invariant under SO(n), and an effective plastic contribution which is quadratic in the slip parameter. The quasiconvex envelope arises via the formation of first-order laminates.

中文翻译：

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具有一个主动滑移系统和线性硬化的有限弹塑性模型的拟凸包络

在二维和三个空间维度上，给出了有限弹塑性模型中凝聚能量的拟凸包络线的显式表征。使用了适用于演化问题的时间离散公式中第一步骤的可塑性变化公式，并假定只有一个滑移系统有效。该模型包括一个非线性弹性能量（在SO（n）下不变），以及一个有效塑性贡献，其滑动参数为二次方。准凸包络线是通过形成一阶层压板而形成的。