Numerical stability of implicit integration schemes in nonassociated viscoplasticity

Abstract

The analytical numerical stability of existing implicit integration schemes in nonassociated viscoplasticity when the finite element method is used as the discretization method is presented. This is done first by generalization of existing implicit numerical techniques to integrate the nonsymmetric system of equations obtained if nonassociated flow rules are used. Then the stability of the numerical process is analyzed for any smooth yield function and for both associated and nonassociated flow rules. The conclusions of the analytical stability study are verified using one numerical example and both associated and nonassociated flow rules. The Drucker-Prager yield function is used to study the stability behavior of the steady-state solution of a uniform strip footing on a weightless soil. Here both flow rules are used with varying degrees of nonassociativity. Both explicit and implicit numerical integration schemes are used. Two cases of implicit methods are specifically examined, which include the fully implicit and the trapezoidal methods.