The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t)=F L(X,t)F P(X,t), an initial stress-free polycrystal is constructed by imposing F L to be a piecewise constant rotation field R 0(X), and F P=R 0(X)T, thereby having F(X,0)=I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

中文翻译：

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扩散界面多晶可塑性：将晶界表示为几何上必要的位错

在多晶中建模可塑性的标准方法是对每个晶粒中的单晶使用晶体可塑性模型，并在晶粒边界上施加适当的牵引力和滑移边界条件。以这种方式，将系统建模为具有匹配边界条件的边界值问题的集合。在本文中，我们开发了一种用于多晶材料的扩散界面晶体可塑性模型，该模型会导致以单晶为参考构型的单边界值问题。使用变形梯度的乘法分解成格子和塑性部分，即F（X，t）= F L（X，t）F P（X，t），通过将F L设为分段恒定旋转场R 0（X）且F P = R 0（X）T来构造初始无应力多晶，从而使F（X，0）= I，并且弹性应变为零。该模型是具有晶界能量和演化的高阶晶体可塑性模型的先驱。