A NOVEL AUGMENTED FINITE ELEMENT METHOD FOR NONLINEAR FRACTURE IN ELASTOPLASTIC BARS

This paper presents a 1D elastoplastic augmented finite element method (A-FEM) that can deal with the nonlinear fracture in elastoplastic bars with significant plastic deformation. The new element employed the von Mises yield criterion and the linear isotropic hardening model for the pre-cracking elastoplastic deformation, and a cohesive law to account for the ensuing crack initiation and growth. Internal nodes were introduced to accommodate the discontinuous displacement field due to cohesive fracture but their degrees of freedom (DoFs) were eliminated via an efficient condensation procedure in each element. A mathematically exact element stiffness matrix in the piece-wise linear sense was thus derived, without any additional DoFs. An analytical elastoplastic solution based on the strength-of-material method has also been developed and employed to check the numerical efficiency and accuracy of the 1D elastoplastic A-FEM. Several numerical examples were conducted to demonstrate the correctness, efficiency and accuracy of the proposed elastoplastic A-FEM.