Iaconeta Ilaria, Larese Antonia, Rossi Riccardo, Guo Zhiming
International Center for Numerical Methods in Engineering (CIMNE), Edificio C1, Campus Norte, Jordi Girona 1-3, 08034 Barcelona, Spain.
Department of Civil and Environmental Engineering (DECA), Technical University of Catalonia (UPC), Edificio C1, Campus Norte, Jordi Girona 1-3, 08034 Barcelona, Spain.
Materials (Basel). 2017 Sep 30;10(10):1150. doi: 10.3390/ma10101150.
The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from "standard" Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.
在几个工程领域中，涉及复杂的与历史相关的本构定律的大变形问题模拟至关重要。必须特别注意选择合适的数值技术，以便能够获得可靠的结果。本文提出了一种物质点法（MPM）和一种伽辽金无网格法（GMM），并针对固体力学中的经典基准进行了验证。目的是证明这些方法在模拟粘性摩擦材料时，在静态和动态状态以及处理大变形问题时的良好性能。文献中绝大多数的MPM技术基于某种显式时间积分。相反，当前工作中提出的技术基于隐式方法，其也可以很容易地适用于静态情况的模拟。介绍这两种方法是为了突出它们与有限元（FE）社区常用的“标准”更新拉格朗日（UL）方法的相似之处而非差异。尽管这两种方法都能够给出良好的预测，但可以观察到，在介质非常大的变形情况下，由于其无网格性质，GMM缺乏鲁棒性，这使得无网格形状函数的定义比MPM更困难且成本更高。另一方面，基于网格的MPM在极端大变形情况下被证明更稳健可靠。
