SUMMARYThe initiation and evolution of transverse matrix cracks and delaminations are predicted within a meshindependent cracking (MIC) framework. MIC is a regularized extended finite element method (x-FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra-ply MIC opening is implemented by using a mixed-mode cohesive formulation in a fully three-dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates without a priori knowledge of damage location or initiation. Good agreement with conventional

SUMMARYA 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 modiÿed 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 modiÿcation 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.

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