A new enrichment scheme in XFEM to model crack growth behavior in ductile materials

Abstract

In this paper, a new enrichment scheme is employed in conjunction with XFEM for the stable crack growth analysis in ductile materials. In the proposed enrichment scheme, only Heaviside enrichment function is used with the ramp function to model the entire crack. The objective of ramp function is to terminate the effect of Heaviside enrichment function exactly at the crack tip in the crack tip element. It also reduces the stiffness matrix size of the crack tip element as compared to standard XFEM. The nonlinear equations obtained as a result of material nonlinearity are solved using Newton-Raphson iterative method. J-R criterion is used to model the stable crack growth in ductile materials. To check the accuracy and effectiveness of the proposed enrichment scheme, four standard fracture mechanics problems of homogenous and bi-materials are considered for the simulations. The numerical results obtained through proposed enrichment scheme are compared with available literature results and are found in good agreement.