A Finite Element-based Adaptive Energy Response Function Method for Curvilinear Progressive Fracture

An adaptive arbitrary-order curvilinear progressive 2D crack growth algorithm is presented. The method uses the ZFEM hypercomplex finite element program to compute arbitrary order derivatives of strain energy with respect to self-similar or perpendicular crack extensions, and then constructs a family of Taylor series functions of strain energy versus crack growth direction. An adaptive algorithm automatically selects the best high-degree polynomial to extrapolate a curvilinear crack path, and adjusts the length of the crack growth increment added during each simulation step to maintain the crack path and model energy within desired tolerances. The method is automated such that the full crack path from inception to failure is computed with multiple FE analyses. Numerical examples up to fifth order are presented and compared against experiments.