多乘法Maxwell流体的有效时间步进方法包含Mooney-Rivlin超弹性
Efficient time stepping for the multiplicative Maxwell fluid including the Mooney-Rivlin hyperelasticity
AI总结：
本文研究了基于变形梯度张量乘法分解的有限应变Maxwell流体模型，结合牛顿粘性和Mooney-Rivlin型超弹性，提出了一种简单、高效且稳健的隐式时间步进方法，该方法在无迭代、无条件稳定性和一阶精度下保持了不可逆不可压缩性、对称性、内部变量的正定性和w不变性，通过数值模拟验证了其在非比例加载和大应变增量下的应力计算精度，与改进的欧拉后向法和指数映射经典积分法等效，且因无迭代而更稳健和高效。
摘要：
本文考虑了一种流行的有限应变Maxwell流体版本，其基于变形梯度张量的乘法分解。该模型结合了牛顿粘性和Mooney-Rivlin型超弹性；它是Simo和Miehe（1992）提出的粘塑性模型的特殊情况。提出了一种简单、高效且稳健的隐式时间步进程序。该算法的拉格朗日和欧拉版本具有等效性质。数值方案无迭代、无条件稳定且一阶准确。它精确保持了不可逆不可压缩性、对称性、内部变量的正定性和w不变性。通过一系列涉及非比例加载和大应变增量的数值模拟测试了应力计算的准确性。在精度方面，所提算法等同于具有精确不可逆不可压缩性的改进欧拉后向法；所提方法也等同于基于指数映射的经典积分方法。由于新方法无迭代，因此更稳健且计算更高效。该算法被实现到MSC.MARC中，并解决了一系列初始边界值问题，以证明数值过程的实用性。
英文摘要：
A popular version of the finite strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of Mooney-Rivlin type; it is a special case of the viscoplasticty model proposed by Simo and Miehe (1992). A simple, efficient and robust implicit time stepping procedure is suggested. Lagrangian and Eulerian versions of the algorithm are available, with equivalent properties. The numerical scheme is iteration free, unconditionally stable and first order accurate. It exactly preserves the inelastic incompressibility, symmetry, positive definiteness of the internal variables, and w-invariance. The accuracy of the stress computations is tested using a series of numerical simulations involving a non-proportional loading and large strain increments. In terms of accuracy, the proposed algorithm is equivalent to the modified Euler backward method with exact inelastic incompressibility; the proposed method is also equivalent to the classical integration method based on exponential mapping. Since the new method is iteration free, it is more robust and computationally efficient. The algorithm is implemented into MSC.MARC and a series of initial boundary value problems is solved in order to demonstrate the usability of the numerical procedures.
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