A p-adaptive scheme for overcoming volumetric locking during plastic flow

Abstract

A feature of many classical plasticity yield functions is that they impose a volumetric constraint on plastic deformation. For low-order finite elements, this results in kinematic restraints on possible deformation modes of an element leading to an overly stiff response. The most robust procedure for overcoming volumetric locking is to use higher-order finite elements. However, low-order elements are popular for their efficiency and simplicity. To remedy volumetric locking in low-order elements, a p-adaptive scheme is proposed where through the partition of unity property of finite element shape functions, the underlying basis of low-order finite elements undergoing plastic flow is enhanced with higher-order polynomial functions. The computational result is extra degrees of freedom at existing nodes of elements undergoing plastic flow, while the rest of the nodes remain unaltered. The performance of the scheme is illustrated through two- and three-dimensional numerical examples.