A blended variationally consistent phase field material point method for material fragmentation problems
Journal
Engineering with Computers
Journal Volume
41
Journal Issue
3
Start Page
1575
End Page
1596
ISSN
14355663
01770667
Date Issued
2025
Author(s)
Abstract
The material point method (MPM) can effectively address material fragmentation issues over mesh-based methods due to its meshfree nature, but faces numerical inaccuracies such as cell-crossing instability and Galerkin inexactness inherent in its numerical framework. The utilization of previously developed variational consistent (VC) corrections with smooth reproducing kernel (RK) approximations has proven effective, albeit limited to continuum bodies. In this study, we present a blended variationally consistent phase field material point method for modeling the material fragmentation process. The phase field damage method is integrated into MPM to facilitate the tracking of damage/cracks during the fragmentation process. The incorporation of the VC correction alongside smooth RK approximation offers benefits not only for non-oscillatory stress modes but also for robust phase field evolution. To address the complexities of VC in handling domain boundary tracking during fragmentation, we introduce a deformation-driven blending scheme to seamlessly blend non-VC for fragmented regions and VC for continuous domains with a smooth transition zone in the Galerkin MPM. This approach enhances the stability and robustness of the formulation for simulating fragmentation problems. Benchmark examples involving extreme deformation scenarios illustrate the effectiveness of the proposed MPM framework, confirming its consistency and stability.
Subjects
Blending Approach
Fragmentation Modeling
Material Point Method
Phase Field Method
Reproducing Kernel Approximation
Variationally Consistent Integration
Benchmarking
Continuum Damage Mechanics
Galerkin Methods
Variational Techniques
Blending Approach
Consistent Integrations
Fragmentation Models
Kernel Approximation
Material Point Methods
Phase Field Methods
Phase Fields
Reproducing Kernel
Reproducing Kernel Approximation
Variationally Consistent Integration
Mesh Generation
Publisher
Springer Science and Business Media Deutschland GmbH
Type
journal article