A Coupled Finite Element Material Point Method for Large Deformation Problems

In the dynamic analysis of mechanics, some of the large deformation problems such as contact and impact problems involve not only extreme deformations with material damage and separation but also finite and small deformations without material damage and separation. Consequently, it brings challenges to traditional finite element method in terms of element distortion and mesh entanglement due to extreme deformation and to advanced mesh-free methods in terms of low computational efficiency, especially when the size of finite/small deformation region is considerable. This chapter gives a state-of-the-art review of the coupled finite element material point (CFEMP) method, which takes both advantages of traditional finite element method (FEM) and a type of mesh-free methods, material point method (MPM), and avoids their disadvantages with the aim to overcome the challenges, and examples of its applications to the large deformation problems are also presented. The CFEMP method includes two variants, static CEMP based on a contact method and adaptive CFEMP further based on an element-to-particle conversion algorithm and alternative coupling method. In addition, MPM is also introduced in detail for completeness.