For finite strain plasticity with both anisotropic yield functions and anisotropic hyperelasticity, we use the Kröner-Lee decomposition of the deformation gradient to obtain a differential-algebraic system (DAE) in the semi-implicit form and solve it by an implicit Richardson-extrapolated method based on intermediate substeps. The source is here the right Cauchy-Green tensor and the consistent Jacobian of the second Piola-Kirchhoff stress is determined with respect to this source. The system is composed by a smooth nonlinear first-order differential equation and a non-smooth algebraic equation. The development of a Richardson-extrapolated implicit integrator for any hyperelastic case and any yield function is the goal of this work. The integration makes use of a backward-Euler method for the flow law complemented by the solution of a yield constraint. The resulting system is solved by the Newton-Raphson method to obtain the plastic multiplier and the elastic right Cauchy-Green tensor ${\mathit{C}}_e$. To ensure power consistency, we make use of the elastic Mandel stress construction. Iso-error maps for three yield functions and three numerical examples are presented.

中文翻译：

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各向异性本构行为的外推和基于 Ce 的隐式积分

对于具有各向异性屈服函数和各向异性超弹性的有限应变塑性，我们使用变形梯度的 Kröner-Lee 分解来获得半隐式形式的微分代数系统 (DAE)，并通过隐式理查森外推法求解基于中间子步骤。此处的源是正确的柯西-格林张量，并且第二个 Piola-Kirchhoff 应力的一致雅可比矩阵是相对于该源确定的。该系统由一个光滑的非线性一阶微分方程和一个非光滑的代数方程组成。为任何超弹性情况和任何屈服函数开发理查森外推隐式积分器是这项工作的目标。积分使用后向欧拉法计算流动定律，并辅以产量约束的解法。所得系统通过 Newton-Raphson 方法求解，得到塑性乘子和弹性右柯西-格林张量${\mathit{C}}_{\mathrm{电子}}$. 为了确保功率的一致性，我们使用了弹性曼德尔应力结构。给出了三个屈服函数和三个数值示例的等误差图。