A configurational force-based material point method for crack propagation modelling in 2D

Abstract The modelling of fracture initiation and propagation is a nontrivial problem in computational mechanics. However, it is an area that is extremely important in engineering applications, requiring accurate and robust numerical methods that can be applied to a variety of materials. This paper presents the development of a new numerical modelling approach, which combines material, or configurational, forces and the material point method (MPM), for finite deformation crack modelling of linear elastic solids in two dimensions. The combination of these numerical methods offers a number of advantages relating to the flexibility of the MPM in terms of decoupling the material deformation from the computational grid and the general nature of configurational force theory in terms of being applicable across different material behaviour. In the method presented in this paper, the MPM forms the basis of the mechanical response of the underlying material, while the configurational force theory provides a fracture criterion for crack modelling through a post-processing procedure. The developed modelling framework is applied to a number of benchmark problems for linear elastic solids in 2D. All simulations show good agreement with the results in the literature, which demonstrates that the combined configuration force-material point framework is a promising numerical tool for fracture modelling.