Numerical analysis of localization using a viscoplastic regularization: influence of stochastic material defects

The nite element reliability method is applied to evaluate the e ects of stochastic imperfections on the localization behaviour of elasto-viscoplastic softening solids. Material properties as the Youngʹs modulus, the softening modulus and the initial yield stress are considered to be random elds. Failure criteria are de ned for the peak load and the dissipated energy. Likely con gurations of imperfections which lead to failure are obtained and the nature and relative importance of the corresponding localization patterns are analyzed. Copyright