Treatment of near-incompressibility and volumetric locking in higher order material point methods

TL;DR

This paper introduces a new projection technique for higher order material point methods to effectively address near-incompressibility and volumetric locking, improving accuracy in elasticity and plasticity simulations.

Contribution

It develops a novel projection approach based on Bbar and Fbar methods tailored for higher order material point methods, reducing locking and stress oscillations.

Findings

Reduced stress oscillations in numerical examples

Elimination of volumetric locking and hourglassing

Effective in both small- and large-deformation scenarios

Abstract

We propose a novel projection method to treat near-incompressibility and volumetric locking in small- and large-deformation elasticity and plasticity within the context of higher order material point methods. The material point method is well known to exhibit volumetric locking due to the presence of large numbers of material points per element that are used to decrease the quadrature error. Although there has been considerable research on the treatment of near-incompressibility in the traditional material point method, the issue has not been studied in depth for higher order material point methods. Using the Bbar and Fbar methods as our point of departure we develop an appropriate projection technique for material point methods that use higher order shape functions for the background discretization. The approach is based on the projection of the dilatational part of the appropriate strain rate measure onto a lower dimensional approximation space, according to the traditional Bbar and Fbar techniques, but tailored to the material point method. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.