New enrichments in XFEM to model dynamic crack response of 2-D elastic solids

Abstract In the present work, three different enrichment schemes are proposed in conjunction with XFEM to investigate the dynamic response of cracked structures. In the proposed enrichment schemes, only two additional degrees of freedom are added at each node of the crack tip element to reduce the matrix size. In the first enrichment scheme, only Heaviside function is used to model the crack tip. In the second enrichment scheme, the crack tip element is modeled by Heaviside function along with a linear ramp function whereas in third enrichment scheme, Heaviside function is combined with a cubic ramp function to model the crack tip. Newmark time integration scheme is adopted to obtain the dynamic response, and the values of dynamic stress intensity factor are computed by interaction integral approach. To check the accuracy and effectiveness of the enrichment schemes, several stationary and moving crack problems in homogeneous and bi-materials are solved. The numerical results obtained by XFEM are compared with available analytical results, and it is observed that the Heaviside function along with cubic ramp function provides slightly better results as compared to other enrichment schemes.

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