Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentials

标量 Hencky 塑性中的周期均匀化

Periodic homogenization in scalar Hencky plasticity

本文在Gamma-收敛框架下研究两相弹塑性材料的周期均匀化，建立与双尺度收敛的联系，但仅在1D情形确认均匀化能量的弹塑性特征。

弹性塑性板方程的均质化：消失硬化情况

Homogenization of elasto-plastic plate equations with vanishing hardening

本文研究薄异质弹性塑性板在线性化弹性塑性框架下的渐进行为，聚焦于板厚远快于材料周期微结构特征尺度消失的 regime。通过进化 Γ-收敛的维度约简方法，推导出具有等向和运动硬化特性的异质板模型，并通过双尺度均质化得到有效弹性完美塑性板模型，刻画了不同相界面的耗散势。

Stochastic homogenization of plasticity equations

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter $\eps>0$ denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit $\eps\to 0$. The homogenization limit is based on the needle-problem approach: We verify that the stochastic coefficients "allow averaging": …

Homogenization for dislocation based gradient visco-plasticit

In this work we study the homogenization for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening and general non-associative monotone plastic flows. The constitutive equations in the models we study are assumed to be only of monotone type. Based on the generalized version of Korn's inequality for incompatible tensor fields (the non-symmetric plastic distortion) due to Neff/Pauly/Witsch, we derive uniform estimates for the solutions of quasistatic initial-boundary value problems under consideration and then using an unfolding operator technique and a monoton…

有限塑性中的一个均匀化结果

A homogenization result in finite plasticity

针对带硬化的有限应变弹塑性非均质材料储能的积分泛函，在周期微观结构假设下，通过将$\textsf{SL}(3)$视为芬斯勒流形突破塑性变形约束障碍，建立了能量在周期趋于零时的$Γ$-收敛性。

Homogenization of layered materials with rigid components in single-slip finite crystal plasticity

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense that it admits only local rotations, the other one is softer featuring a single active slip system with linear self-hardening. As a main result, we obtain explicit homogenization formulas by means of Γ-convergence. Due to the anisotropic nature of the problem, the findings depend critically on the orientation of the slip direction relative to the layers, leadin…