A two-field mixed formulation with scattered pressure node distribution in element-free Galerkin method for alleviating volumetric locking in hyperelastic materials

Abstract

Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models. Most of the hyperelastic materials are nearly incompressible, which poses challenges, i.e., volumetric locking during numerical modelling. There exist many formulations in the context of the finite element method, among which the mixed displacement-pressure formulation is robust. However, such a displacement-pressure formulation is less explored in meshfree methods, which mitigates the problem associated with mesh distortion during large deformation. This work addresses this issue of alleviating volumetric locking in the element-free Galerkin method (EFGM), which is one of the popular meshfree methods. A two-field mixed variational formulation using the perturbed Lagrangian approach within the EFGM framework is proposed for modelling nearly incompressible hyperelastic material models, such as Neo-Hookean and Mooney-Rivlin. Taking advantage of the meshless nature of the EFGM, this work introduces a unique approach by randomly distributing pressure nodes across the geometry, following specific guidelines. A wide spectrum of problems involving bending, tension, compression, and contact is solved using two approaches of the proposed displacement-pressure node formulation involving regular and irregular pressure node distribution. It is observed that both approaches give accurate results compared to the reference results, though the latter offers flexibility in the pressure nodal distribution.