Overcoming Volumetric Locking in Three-Dimensional Material Point Analysis

Coombs, W.M.; Wang, L.; Augarde, C.E.

Abstract

The material point method is ideally suited to modelling large deformation problems in three dimensions, especially in cases where the finite element method struggles due to mesh distortion. However, when the method is used to analyse problems with near-incompressible material behaviour, such as in geotechnical engineering using models with isochoric plastic flow, it suffers from severe volumetric locking. This causes the method to over predict the forces for a given displacement and induces spurious stress oscillations through the problem domain. Several methods have been proposed in the finite element literature but few of these have been applied to the material point method. In this paper we present a way to avoid volumetric locking for three-dimensional material point analyses with simplex elements (linear tetrahedra) using an F bar patch approach. Not only does the technique avoid the over-stiff behaviour associated with volumetric locking but it also reduces the stress oscillations in the method, which are often attributed to cell-crossing instabilities. The formulation is validated against two three-dimensional benchmark problems.

Citation

Coombs, W., Wang, L., & Augarde, C. (2021, May). Overcoming Volumetric Locking in Three-Dimensional Material Point Analysis. Presented at IACMAG 2021

• Presentation Conference Type: Conference Paper (published)
• Conference Name: IACMAG 2021
• Start Date: May 5, 2021
• End Date: May 8, 2021
• Acceptance Date: Jan 24, 2020
• Online Publication Date: Jan 15, 2021
• Publication Date: Jan 15, 2021
• Deposit Date: Nov 8, 2022
• Publicly Available Date: Nov 9, 2022
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Pages: 772-778
• Series Title: Lecture Notes in Civil Engineering
• Series Number: 125
• Book Title: Challenges and Innovations in Geomechanics. IACMAG 2021.
• ISBN: 9783030645137
• DOI: https://doi.org/10.1007/978-3-030-64514-4_82
• Public URL: https://durham-repository.worktribe.com/output/1643653