Modeling fracture in Mindlin–Reissner plates with the extended finite element method

A technique for the modeling of cracks and crack growth in plates using the extended finite element method (X-FEM) is presented. Beginning with a plate formulation which does not exhibit shear locking, the finite element approximation is enriched with both discontinuous and near-tip functions. This allows for the modeling of crack geometries which are independent of the finite element mesh topology, and greatly facilitates the simulation of crack growth. Guidelines for the construction of the enriched approximation and the numerical integration of the weak form in the X-FEM framework are reviewed. To obtain the mixed-mode stress intensity factors, we derive appropriate domain forms of an interaction integral in the context of Mindlin–Reissner plate theory. Several benchmark problems of through-the-thickness cracks in infinite and finite plates are solved to illustrate the accuracy and utility of the new formulation.