Extended finite element method with cell-based smoothing for modeling frictional contact crack-induced acoustic nonlinearity involving distorted mesh

This study proposes a 2D cell-based smoothed extended finite element method (CS-XFEM) for accurate and efficient simulation of nonlinear ultrasonic wave propagation in solid structures, specifically addressing the effects of frictional contact in cracks. Traditional mesh discretization methods for cracks often suffer from mesh distortion and computational instability owing to their high aspect ratios. To overcome this, CS-XFEM integrates a cell-based smoothing technique into XFEM to model the frictional contact of a crack. A comprehensive numerical example demonstrates the advantages of CS-XFEM. The results show that CS-XFEM exhibits a higher convergence rate and enables a larger critical time increment than XFEM. Specifically, the critical time increment of CS-XFEM was found to be twice that of XFEM, leading to a 50% reduction in the total computational time. These findings confirm that CS-XFEM is an efficient, accurate, and robust numerical method for studying the acoustic nonlinearity induced by crack-induced frictional contact.