Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finite-deformation response of anisotropic elastic–inelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as Rij, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations, Rij are equal to the negative of the components of the rate of Nye-Kröner’s dislocation density tensor. In contrast to these small strain components, each Rij is invariant under superposed rigid body motions such that it can be used independently in the constitutive equations to describe the material behavior. Specifically, in this work, Rij provide a size-dependent enhancement to hardening that can increase or decrease during loading history, modeling the generation and annihilation of densities of geometrically necessary dislocations in metal plasticity. The application to the finite-deformation cyclic torsion of thin wires demonstrates the potential of this approach and the importance of the constitutive equation for the plastic spin rate both on the rotations of the microstructural vectors and on the predicted size-effect.

中文翻译：

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应用于有限扭转中尺寸相关硬化的弹性不相容性欧拉率


弹性不相容率的测量是在各向异性弹性-非弹性材料的有限变形响应的欧拉框架内开发的。这样的框架依赖于微观结构向量的进化。需要强调的是，不相容率（此处表示为 Rij）取决于不弹性率的本构方程。对于小应变和旋转，Rij 等于 Nye-Kröner 位错密度张量速率分量的负值。与这些小的应变分量相反，每个 Rij 在叠加的刚体运动下都是不变的，因此它可以在本构方程中独立使用来描述材料行为。具体来说，在这项工作中，Rij 为硬化提供了一种尺寸依赖性的增强，可以在加载历史中增加或减少，模拟金属塑性中几何必要位错的密度的产生和湮灭。在细线的有限变形循环扭转中的应用证明了这种方法的潜力以及塑性自旋速率的本构方程对微结构矢量的旋转和预测的尺寸效应的重要性。