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

Powell-Sabin B-splines are employed to model progressive fracturing in afluid-saturated porous medium. These splines are defined on triangles and are C1-continuous throughout the domain, including the crack tips, so that crackinitiation can be evaluated directly at the tip. On one hand, the method capturesstresses and fluid fluxes more accurately than when using standard Lagrangeelements, enabling a direct assessment of the fracture criterion at the crack tipand ensuring local mass conservation. On the other hand, the method avoidslimitations for discrete crack analysis which adhere to isogeometric analysis.A crack is introduced directly in the physical domain. Due to the use of trian-gles, remeshing and crack path tracking are straightforward. During remeshingtransfer of state vectors (displacement, fluid pressure) is required from the oldto the new mesh. The transfer is done using a new approach which exploits aleast-squaresfitwiththeenergybalanceandconservationofmassasconstraints.The versatility and accuracy to simulate free crack propagation are assessed formode-I and mixed-mode fracture problems.