Structural softening, mesh dependence, and regularisation in non‐associated plastic flow

Abstract

Summary A severe dependence of numerical simulations on the mesh density is usually attributed to the presence of strain softening in the constitutive relation. However, other material instabilities, like non‐associated plastic flow, can also cause mesh sensitivity. Indeed, loss of ellipticity in quasi‐static analyses is the fundamental cause of the observed mesh dependence. It has been known since long that non‐associated plastic flow can cause loss of ellipticity, but the consequence for mesh sensitivity, and subsequently, for the difficulty of the equilibrium‐finding iterative procedure to converge have remained largely unnoticed. We first demonstrate at the hand of a biaxial test structural softening and a marked mesh dependence for an ideally plastic material equipped with a non‐associated flow rule. The phenomena are then analysed in depth using an infinitely long shear layer. Finally, it is shown that the mesh effect disappears when the standard continuum model is replaced by a Cosserat continuum, a well‐known regularisation method for strain‐softening constitutive relations.