Treatment of near-incompressibility in meshfree and immersed-particle methods

Abstract

We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the $$\overline{\mathbf {B}}$$ and $$\overline{\mathbf {F}}$$ techniques as our point of departure, we develop projection methods for the conforming reproducing kernel method and the immersed-particle or material point-like methods. The methods are based on the projection of the dilatational part of the appropriate measure of deformation onto lower-dimensional approximation spaces, according to the traditional $$\overline{\mathbf {B}}$$ and $$\overline{\mathbf {F}}$$ approaches, but tailored to meshfree and particle methods. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.