On the development of a material point method compatible arc length solver for large deformation solid mechanics

Gavin, N.D.; Coombs, W.M.; Brigham, J.C.; Augarde, C.E.

Abstract

The Material Point Method is a versatile technique, however, it may be unable to provide a valid solution if there is a snap-through or snap-back response in the equilibrium path. One approach of overcoming this issue is the use of path following techniques and one example is the arc-length method. This technique is well established in finite element analysis but not in any Material Point Method formulation. This paper details the modifications made to the standard arc-length scheme for use within the Material Point Method. A numerical example is presented to demonstrate the implementation of the Material Point-Based Arc-length scheme in tracking a snap-through response.

Citation

Gavin, N., Coombs, W., Brigham, J., & Augarde, C. (2023). On the development of a material point method compatible arc length solver for large deformation solid mechanics.

• Conference Name: UKACM 2023
• Conference Location: Coventry, UK
• Start Date: Apr 19, 2023
• End Date: Apr 21, 2023
• Publication Date: 2023
• Deposit Date: Jul 5, 2023
• Publicly Available Date: Jul 5, 2023
• Public URL: https://durham-repository.worktribe.com/output/1133638
• Publisher URL: https://sites.google.com/view/ukacm2023conference