论文标题
在消失的厚度和刚性弹性的极限的单滑晶体可塑性的渐近分析
Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
论文作者
论文摘要
我们通过$γ$ -Convergence进行单滑弹性体的2D-1D维度缩小分析。考虑了刚性塑料和弹性塑性状态。特别是，我们表明，即使受到与弹性刚性单滑状态相对应的最限制的约束，极限变形也可以自由弯曲。主要的挑战是在上边界中引起的，差异约束使任何弯曲都不产生额外的能源成本特别困难。我们通过合适的非平滑构造克服了这一障碍，并证明如果我们人为地将模型限制为平滑变形，就会发生Lavrentiev现象。如果差异约束适当地软化，则不存在此问题。
We perform via $Γ$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can essentially freely bend even if subjected to the most restrictive constraints corresponding to the elastically rigid single-slip regime. The primary challenge arises in the upper bound where the differential constraints render any bending without incurring an additional energy cost particularly difficult. We overcome this obstacle with suitable non-smooth constructions and prove that a Lavrentiev phenomenon occurs if we artificially restrict our model to smooth deformations. This issue is absent if the differential constraints are appropriately softened.
