The Benefits of Using a Consistent Tangent Operator for Viscoelastoplastic Computations in Geodynamics
The Benefits of Using a Consistent Tangent Operator for Viscoelastoplastic Computations in Geodynamics
复制标题
在地球动力学中使用一致切线算子进行粘弹塑性计算的好处
DOI：
10.1029/2018gc007877
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发表时间：
2018
期刊：
影响因子：
3.7
通讯作者：
L. Le Pourhiet
中科院分区：
文献类型：
--
作者：
T. Duretz;A. Souche;R. Borst;L. Le Pourhiet
应变局部化在地球动力学中普遍存在，并在岩石圈内的所有尺度上发生。例如，岩石圈如何适应变形控制着造山带的结构和裂谷边缘的结构。因此，了解和预测应变局部化在地球动力学中具有重要意义。虽然岩石圈较深的部分有效地以粘性方式变形，但较浅的部分具有弹塑性流变行为的特征。在此，我们提出了一种基于时间离散化弹塑性关系的一致线性化和有限差分方法的弹塑性变形问题的快速而精确的求解方法。这些模型目前考虑了压力不敏感的冯·米塞斯和压力依赖的德鲁克-普拉格屈服标准。一致的线性化可以解决千米尺度上的应变局部化，同时提供最优的，即力剩余的二次收敛。我们通过与基于有限元方法的独立程序所获得的结果进行定性和定量的比较来验证我们的方法。我们还为粘弹塑性框架提供了一致的线性化，并展示了它在粘性、弹性和塑性应变分量之间提供精确划分的能力。研究的结果是完全可重现的，代码可以作为M2Di MatLab例程的子集使用。
Strain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere. How the lithosphere accommodates deformation controls, for example, the structure of orogenic belts and the architecture of rifted margins. Understanding and predicting strain localization is therefore of major importance in geodynamics. While the deeper parts of the lithosphere effectively deform in a viscous manner, shallower levels are characterized by an elastoplastic rheological behavior. Herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time‐discretized elastoplastic relation and the finite difference method. The models currently account for the pressure‐insensitive Von Mises and the pressure‐dependent Drucker‐Prager yield criteria. Consistent linearization allows for resolving strain localization at kilometer scale while providing optimal, that is, quadratic convergence of the force residual. We have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method. We also provide a consistent linearization for a viscoelastoplastic framework, and we demonstrate its ability to deliver exact partitioning between the viscous, the elastic, and the plastic strain components. The results of the study are fully reproducible, and the codes are available as a subset of M2Di MATLAB routines.