Conforming finite elements with embedded strong discontinuities

Abstract

The possibility of embedding strong discontinuities into finite elements allowed the simulation of different problems, namely, brickwork masonry fracture, dynamic fracture, failure in finite strain problems and simulation of reinforcement concrete members. However, despite the significant contributions to this field, a general embedded formulation capable of dealing with strong discontinuities using conforming finite elements is still missing. Therefore a new conforming embedded formulation is herein proposed and compared with other relevant formulations, namely the Generalised Strong Discontinuity Approach (GSDA) [1] and the Generalised/Extended Finite Element Method (GFEM/XFEM) [2-5]. Academic and structural examples are given in order to illustrate the capabilities of the proposed approach in comparison with GSDA and GFEM/XFEM. In summary, the proposed formulation has the following properties: i) variational consistency; ii) no limitations on the choice of the parent finite element; iii) comprehensive kinematics of the discontinuity, including both rigid body motion and stretching; iv) fully compatible enhanced kinematic field; v) additional degrees of freedom located at the discontinuity; vi) continuity of both jumps and tractions across element boundaries; and vii) stress locking free.Structural EngineeringCivil Engineering and Geoscience