Determination of the limit states of elastoplastic bodies (Q2713962)

The authors consider the equations of quasistatic deformation of elastoplastic bodies in a geometrically linear formulation. After the spatial discretization of equations by the finite element method, the problem of determining equilibrium configurations reduces to the integration of a system of nonlinear ordinary differential equations. In the limiting state of an ideally elastoplastic body, the matrix of the system degenerates and the problem becomes singular. The authors propose a regularization algorithm for determining solutions in the limiting state of bodies. Numerical solutions are given for test problems to confirm the reliability of the regularization algorithm.