Stress‐hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids

A formulation of a quadrilateral finite element with embedded strong discontinuity, suitable for the material failure numerical analysis of plane stress solids, is presented. The kinematics of standard finite element is enhanced by displacement jumps that vary linearly along the embedded discontinuity line. They are described by four kinematic parameters that are related to four element separation modes. The modes are designed for no stress transfer over the discontinuity line at its fully softened (opened) state. As for the material, the bulk of the element is assumed to be elastic, and the softening plasticity, in terms of discontinuity tractions and displacement jumps, is assumed along the discontinuity line. The bulk stresses are described by the optimal five‐parameter interpolation. The combination of stress interpolation and enhanced kinematics yields simple form of the element stiffness matrix. To achieve efficient implementation, the stiffness matrix is statically condensed for both the enhanced kinematic parameters and the stress parameters. In a set of numerical examples, the performance of the derived element is illustrated. Obtained results are compared with some other representative embedded discontinuity quadrilateral elements (displacement‐based and enhanced assumed strain based). It turns out that the element performs very well. Copyright © 2013 John Wiley & Sons, Ltd.