Mesh independent modelling of cracks by using higher order shape functions

A mesh independent crack modelling approach based on displacement approximation with higher order shape functions is proposed. The Heaviside step function based local enrichment method, known as eXtended Finite Element Method, is modi ed by replacing the step function with a higher order shape functions approximation. Polynomial B-spline approximation functions are used in the present paper. An advantage of the proposed method is that its implementation only involves integration of the products of original shape functions and their derivatives and does not require modi cation of the integration domains. A volume integral based expression is proposed to calculate the e ective surface area of the crack modelled by using an approximate step function. It is shown to give the actual crack surface area in the limit of the approximate step function approaching the Heaviside function. The convergence and accuracy of the method is illustrated in examples of transverse and oblique (with respect to loading direction) crack problems in rectangular plates. Uniaxial tension of a unidirectional composite with an open hole is considered. Hoop stress relaxation due to longitudinal splitting is successfully modelled by the method proposed and compared to direct modelling by using ANSYS software