Simulating the propagation of displacement discontinuities in a regularized strain‐softening medium

A numerical model is developed which allows the inclusion of displacement discontinuities in a strain‐softening medium, independent of the finite element mesh structure. Inelastic deformations develop in the continuum and, when a critical threshold of inelastic deformation is reached, a displacement discontinuity is inserted. Discontinuities are introduced using the partition of unity concept which allows discontinuous functions to be added to the standard finite element basis. It is shown that the introduction of displacement discontinuities at the later stages of the failure process can lead to a failure mode that is fundamentally different than that using a continuum model only. This combined continuum‐discontinuous model is better able to describe the entire failure process than a continuum or a discrete model alone and treats mode‐I and mode‐II failure in a unified fashion.