Monolithic coupling of the implicit material point method with the finite element method. (15th July 2019)

• Record Type: Journal Article
• Authors: Aulisa, Eugenio; Capodaglio, Giacomo
• Is Part Of: Computers & structures. Volume 219(2019)
• Page Start: 1
• Page End: 15
• Publication Date: 2019-07-15
• Subjects: Implicit material point method -- Finite element method -- Monolithic coupling -- Automatic differentiation -- MPM-FEM coupling; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2019.04.006
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: The paper describes a novel approach for the coupling of the material point method (MPM) with the finite element method (FEM). The most widely used approach in the literature consists of treating the MPM body and the FEM body as two separate entities, handling the contact detection and description with appropriate algorithms. We propose an alternative approach, where the two bodies are treated as a single continuum in a monolithic fashion inspired by fluid-structure interaction problems. In this way, the interface between the bodies is automatically tracked and the contact can be accurately described with a simple algorithm. Abstract: A monolithic coupling between the material point method (MPM) and the finite element method (FEM) is presented. The MPM formulation described is implicit, and the exchange of information between particles and background grid is minimized. The reduced information transfer from the particles to the grid improves the stability of the method. Once the residual is assembled, the system matrix is obtained by means of automatic differentiation. In such a way, no explicit computation is required and the implementation is considerably simplified. When MPM is coupled with FEM, the MPM background grid is attached to the FEM body and the coupling is monolithic. With this strategy, no MPM particle can penetrate a FEM element, and the need for computationally expensive contact search algorithms used by existing coupling procedures is eliminated. The coupled system can be assembled with a single assembly procedure carried out element by element in a FEM fashion. Numerical results are reported to display the performances and advantages of the methods here discussed.