Stress resultants plasticity with general closest point projection

Abstract

In this paper, general closest point projection algorithm is derived for the elastoplastic behavior of a cross-section of a beam finite element. For given section deformations, the section forces (stress resultants) and the section tangent stiffness matrix are obtained as the response for the cross-section. Backward Euler time integration rule is used for the solution of the nonlinear evolution equations. The solution yields the general closest projection algorithm for stress resultants plasticity model. Algorithmic consistent tangent stiffness matrix for the section is derived. Numerical verification of the algorithms in a mixed formulation beam finite element proves the accuracy and robustness of the approach in simulating nonlinear behavior.