For some polycrystalline materials such as austenitic stainless steel, magnesium, TATB, and HMX, twinning is a crucial deformation mechanism when the dislocation slip alone is not enough to accommodate the applied strain. To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solvers that couple the crystal plasticity material model with a phase field twining model such that the twinning nucleation and propagation can be captured via an implicit function. While a phase field order parameter is introduced to quantify the twinning induced shear strain and corresponding crystal reorientation, the evolution of the order parameter is driven by the resolved shear stress on the twinning system. To avoid introducing an additional set of slip systems for dislocation slip within the twinning region, we introduce a Lie algebra averaging technique to determine the Schmid tensor throughout the twinning transformation. Three different numerical schemes are proposed to solve the coupled problem, including a monolithic scheme, an alternating minimization scheme, and an operator splitting scheme. Three numerical examples are utilized to demonstrate the capability of the proposed model, as well as the accuracy and computational cost of the solvers.

中文翻译：

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带有单片和分裂解算器的多晶体耦合结晶可塑性和形变孪生的相场建模

对于某些多晶材料，例如奥氏体不锈钢，镁，TATB和HMX，当仅位错滑移不足以适应所施加的应变时，孪晶是至关重要的变形机制。为了预测晶体可塑性与形变孪生之间的耦合效应，我们引入了数学模型以及相应的整体和算子分裂求解器，将晶体可塑性材料模型与相场孪生模型耦合在一起，从而可以通过晶胞捕获孪晶的成核和传播。隐式函数。虽然引入了相位场阶参数来量化孪生引起的剪切应变和相应的晶体重新取向，但是阶参数的演变是由孪生系统上解析的剪切应力驱动的。为了避免在孪生区域内引入用于错位滑动的附加滑动系统集，我们引入了李代数平均技术来确定整个孪生转换中的Schmid张量。提出了三种不同的数值方案来解决耦合问题，包括整体方案，交替最小化方案和算子拆分方案。利用三个数值示例来证明所提出模型的功能以及求解器的准确性和计算成本。交替最小化方案和运算符拆分方案。利用三个数值示例来证明所提出模型的功能以及求解器的准确性和计算成本。交替最小化方案和运算符拆分方案。利用三个数值示例来证明所提出模型的功能以及求解器的准确性和计算成本。