Nonlinear kinematics Reissner's beam with combined hardening/softening elastoplasticity

In this work, we present geometrically non-linear beam finite element with embedded discontinuity which can represent elastoplastic constitutive behavior with both hardening and softening response. The constitutive equations are presented in rate form by using the multiplicative decomposition of deformation gradient. Formulation of elastoplastic response is presented in terms of stress resultants including the interaction between axial force, shear force and bending moment appropriate for metallic materials. The softening response is used to model the failure in connections, introducing displacement field discontinuity or a rotational hinge. The hinges or displacement discontinuity are presented in the framework of incompatible modes that can handle three different failure modes dealing with bending, shearing or axial deformation. With several numerical simulations, the FEM implementation is proven very robust for solving the problems of practical interest, such as push-over analysis.