Numerical stability in quasi‐static elasto/visco‐plasticity

The numerical stability of simple marching schemes used in elasto/visco‐plasticity is investigated. An assumption of convexity renders possible the derivation of a theoretical stability criterion based on the identification of the numerical process with the integration of a non‐linear, first order, system of ordinary differential equations. Explicit stability criteria are obtained for commonly used visco‐plastic laws. Selected examples illustrate the necessity and effectiveness of the proposed stability criteria in actual computations.