Analysis of progressive fracture in fluid-saturated porous medium using splines

Powell-Sabin B-splines are employed to model progressive fracturing in a fluid-saturated porous medium. These splines are defined on triangles and are $$ -continuous throughout the domain, including the crack tips, so that crack initiation can be evaluated directly at the tip. On one hand, the method captures stresses and fluid fluxes more accurately than when using standard Lagrange elements, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. On the other hand, the method avoids limitations for discrete crack analysis which adhere to isogeometric analysis. A crack is introduced directly in the physical domain. Due to the use of triangles, remeshing and crack path tracking are straightforward. During remeshing transfer of state vectors (displacement, fluid pressure) is required from the old to the new mesh. The transfer is done using a new approach which exploits a least-squares fit with the energy balance and conservation of mass as constraints. The versatility and accuracy to simulate free crack propagation are assessed for mode-I and mixed-mode fracture problems.