Effective spatial resolution control for complex stress field in cracked orthotropic material by Galerkin-based multiresolution wavelet approximation

A Galerkin-based fixed grid modeling with multiresolution (MR) wavelet functions is presented to effectively control spatial resolution of a complex stress field in cracked orthotropic material. The B-spline wavelet bases are employed and the MR property is utilized. The square root singularity and Heaviside enrichment functions are also employed for the efficient fracture modeling. The local enrichment of the MR wavelet function and the singularity function properly captures the complicated orthotropic characteristics and the stress gradients around the crack tip. The fracture mechanics parameters are constructively approximated using the interaction integral method. The cracked orthotropic materials are presented using several examples and the validity of the modeling is carefully examined comparing to the existing solutions of the analytical/numerical approaches.