A generalized particle in cell method for explicit solid dynamics

Within the framework of the material point method, a generalized particle in cell method for explicit solid dynamics is presented. In this method, the solids are discretized by finite element meshes, and these meshes are embedded in a background Eulerian grid. The external and internal forces of the...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2020-11, Vol.371, p.113308, Article 113308
Main Authors: Nguyen, Vinh Phu, de Vaucorbeil, Alban, Nguyen-Thanh, Chi, Mandal, Tushar Kandal
Format: Article
Language:English
Subjects:
Boundary conditions
Configurations
Dirichlet problem
Elastic deformation
Explicit dynamics
Generalized particle in cell (GPIC)
Internal forces
Massive deformation
Material point method
Mathematical analysis
Meshless methods
Particle in cell technique
Plastic deformation
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Summary:Within the framework of the material point method, a generalized particle in cell method for explicit solid dynamics is presented. In this method, the solids are discretized by finite element meshes, and these meshes are embedded in a background Eulerian grid. The external and internal forces of the solids are calculated on their respective finite element meshes and are mapped to the background grid for solving the momentum equation. Two formulations for computing these forces are presented: one using the original configuration of the solids and the other employs the current configuration. Two and three dimensional numerical examples, covering massive tensile, compressive elastic and plastic deformation, demonstrate that the former formulation performs much better for extremely large deformation problems. Compared with previous material point methods, the proposed method offers these advantages: (i) better representation of solid boundaries, (ii) seamless enforcement of Dirichlet and Neumann boundary conditions, (iii) seamless treatment of material interfaces and (iv) higher efficiency. All of these are achieved with the introduction of a finite element mesh in a supposedly meshfree method.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2020.113308