Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids

• Novel embedded finite elements with continuous displacement jumps are proposed.
• The enriched discontinuity modes satisfy a priori the traction continuity condition.
• General relative stretching modes are identified with no limit of a vanishing Poisson’s ratio.
• The model is intrinsically stress locking free, numerically stable and of high coarse mesh resolution.
• Boundary conditions and linear equation constraints can be trivially imposed on the displacement jumps.

This paper addresses novel extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids. On one hand, based upon the unified multiscale kinematics of strong discontinuities, standard finite elements at the coarse scale are enriched with fine scale kinematics in which non-uniform discontinuity modes are incorporated. On the other hand, the traction continuity condition across the discontinuity is enforced in the statically optimal form as the fine scale statics. The admissible discontinuity modes satisfying a priori the traction continuity condition are derived. In addition to the relative rigid body motions (translations and rotations), more general relative stretching modes that induce discontinuous strain/stress fields in the bulk, are obtained with no limit of a vanishing Poisson’s ratio. The proposed model then particularizes to 2D quadrilateral elements. The displacement jumps at the discontinuity nodes are selected as the enrichment parameters and regarded as global variables shared by neighboring elements. The resulting model not only is intrinsically stress locking free for a fully softened discontinuity, but also automatically guarantees global continuity of the displacement jumps. Another benefit is that the numerical instability suffered under the unfavorable element/discontinuity configuration can be easily circumvented. Furthermore, the vanishing displacement jumps at the discontinuity tip can be enforced trivially as conventional essential boundary conditions and those complex strategies introduced in existing models are avoided. Together with the failure criterion related to the element average stress and the propagation orientation based on a simplified nonlocal stress, a local crack tracking algorithm is adopted to guarantee global continuity of the discontinuity path. Representative numerical simulations of element and structure benchmark tests are presented to verify the performance of the proposed approach in the modeling of arbitrary discontinuity propagation in solids.