考虑Burgers矢量的各向同性硬化和塑性自旋的几何线性各向同性梯度塑性正则率无关模型
A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector
摘要：
本文提出了一个与率无关的唯象几何线性梯度塑性问题的正则变分框架。该模型结合了添加剂分解的总变形为非对称的弹性和塑性变形，与缺陷能量的贡献，考虑到伯格斯矢量通过只依赖于位错密度张量卷曲（p）引起的非对称非局部背应力，和各向同性硬化响应仅取决于累积的等效塑性应变。该模型是完全各向同性的，并满足线性化规范不变条件，即，只有真实的状态变量才会出现。该模型还满足最大耗散的原则，允许显示存在的弱制定。对于这个结果，最近引入的Korn不等式的不相容张量场是必要的。在强解类中证明了唯一性。当能量长度尺度为零时，模型退化为具有对称塑性应变sym（p）和标准各向同性硬化的经典弹塑性模型。
英文摘要：
In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl(p) giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain sym(p) and standard isotropic hardening.
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