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.
Highlights
Failure of engineering structures is usually accompanied by cracking of solid materials, which is strongly affected by geometrical character istics and material properties of specimens as well as the loading con ditions
Additional advantages of material point method (MPM) in solving the crack propagation compared with Finite Element Method (FEM) include that the sharp discontinuities in the displacement field can be naturally treated, as the response is monitored at material points that move within a background Eulerian grid [35]
An implicit quasi-static formulation of MPM provides the computational platform for the deformation simulation, while the configurational force (CF) calculation and the crack propagation modelling are implemented through a post-processing procedure after obtaining convergence results for each load increment step
Summary
Failure of engineering structures is usually accompanied by cracking of solid materials, which is strongly affected by geometrical character istics and material properties of specimens as well as the loading con ditions. Unlike classical approaches incorpo rating partial derivatives, PD utilises integral expressions in the gov erning equations such that cracks and any other discontinuities in materials and structures can be treated naturally without special tech niques [28,29] This method is still in its infancy and several challenges remain, e.g. incorporating complex constitutive models and verification towards experimental results [30]. Additional advantages of MPM in solving the crack propagation compared with FEM include that the sharp discontinuities in the displacement field can be naturally treated, as the response is monitored at material points that move within a background Eulerian grid [35]. To the best of the authors’ knowledge, this is the first time that the configu rational force criterion has been combined with an MPM framework The combination of these two approaches provides a powerful frame work for modelling fracture in general materials. This paper is focused on linear elastic materials within a large deformation frame work to provide the essential basis for future extensions
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