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An adaptive finite element material point method and its application in extreme deformation problems

机译：自适应有限元材料点法及其在极端变形问题中的应用

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摘要

Taking advantages of both Lagrangian and Eulerian methods, material point method (MPM) is suitable for modeling problems with extreme deformation. However, MPM is less accurate and less efficient than finite element method (FEM) for small deformation problems due to particle quadrature and mappings between particles and background grid applied in MPM. To take advantages of both FEM and MPM, an adaptive finite element material point method is developed for modeling the dynamic behavior of material under extreme loading. Bodies are initially discretized by finite elements, and then the elements with large strain are adaptively converted into MPM particles based on their degree of distortion or plastic strain during the solution process. The interaction between the remaining finite elements and MPM particles is implemented based on the background grid in MPM framework. Several numerical examples are presented to validate the efficiency and accuracy of the proposed method, and the numerical results are in good agreement with experiments, while the efficiency of the method is higher than that of both MPM and FEM.
机译：利用拉格朗日方法和欧拉方法的优势，材料点方法（MPM）适用于建模具有极大变形的问题。但是，由于颗粒正交以及MPM中应用的颗粒与背景网格之间的映射，对于小变形问题，MPM的准确性和效率不如有限元方法（FEM）。为了同时利用FEM和MPM的优势，开发了一种自适应有限元材料点方法来模拟极端载荷下材料的动态行为。最初将实体离散化为有限元，然后根据固溶过程中变形或塑性应变的程度，将应变较大的元素自适应地转换为MPM粒子。其余有限元与MPM粒子之间的相互作用是基于MPM框架中的背景网格实现的。数值算例验证了所提方法的有效性和准确性，数值结果与实验结果吻合良好，但该方法的效率均高于MPM和FEM。

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