A New Enriched Finite Element Method with Application to Static Fracture Problems with Internal Fluid Pressure

Abstract

A new enriched finite element technique, for modeling crack problems within the framework of the extended finite element method, is presented. In this method, crack nodes with displacement discontinuity degrees of freedom have been defined and used to explicitly describe the crack geometry and deformation. The crack deformation is represented by these displacement discontinuity degrees of freedom which are associated with the crack nodes distributed along the crack path, and the crack path is determined by the coordinates of the crack nodes which are solution dependent. This enables a direct and efficient description of the crack. Moreover, the corresponding work-conjugate variables allow for directly modeling the forces on the crack surfaces. In addition, this formulation provides a convenient way to calculate the internal fluid pressure within the crack and its contribution to the crack deformation as occurs in hydraulically driven fractures. Numerical experiments of several static fracture problems are provided to demonstrate the performance, utility and accuracy of the new enriched finite element technique by comparing the numerical results with analytical solutions available in the literature.