具有运动学硬化和塑性自旋的基于位错的率无关各向同性梯度塑性的存在性结果：具有对称局部背应力的情况
Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: The case with symmetric local backstress
摘要：
本文利用凸分析和变分不等式方法建立了一个具有随动硬化和塑性自旋的与率无关的无穷小梯度塑性模型的存在性结果，其中局部背应力张量保持对称.该模型具有缺陷的能量贡献，这是二次的位错密度张量卷曲p，引起非局部非对称运动硬化。利用最近建立的Korn型不等式的不相容张量场。非对称塑性变形的解空间自然是H（卷曲），以及塑性变形的适当切向边界条件。与其他模型的连接也建立起来了。
英文摘要：
In this paper we use convex analysis and variational inequality methods to establish an existence result for a model of infinitesimal rate-independent gradient plasticity with kinematic hardening and plastic spin, in which the local backstress tensor remains symmetric. The model features a defect energy contribution which is quadratic in the dislocation density tensor Curl p, giving rise to nonlocal non-symmetric kinematic hardening. Use is made of a recently established Korn's type inequality for incompatible tensor fields. The solution space for the non-symmetric plastic distortion is naturally H(Curl) together with suitable tangential boundary conditions on the plastic distortion. Connections to other models are established as well.
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