Kinematic Limit Analysis of Nonassociated Perfectly Plastic Material by the Bipotential Approach and Finite Element Method

Limit analysis is one of the most fundamental methods of plasticity. For the nonstandard model, the concept of the bipotential, representing the dissipated plastic power, allowed us to extend limit analysis theorems to the nonassociated flow rules. In this work, the kinematic approach is used to find the limit load and its corresponding collapse mechanism. Because the bipotential contains in its expression the stress field of the limit state, the kinematic approach is coupled with the static one. For this reason, a solution of kinematic problem is obtained in two steps. In the first one, the stress field is assumed to be constant and a velocity field is computed by the use of the kinematic theorem. Then, the second step consists to compute the stress field by means of constitutive relations keeping the velocity field constant and equal to that of the previous step. A regularization method is used to overcome problems related to the nondifferentiability of the dissipation function. A successive approximation algorithm is used to treat the coupling question. A simple compression-traction of a nonassociated rigid perfectly plastic material and an application of punching by finite element method are presented in the end of the paper.