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New anisotropic crack-tip enrichment functions for the extended finite element method

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Abstract

In this paper, the extended finite element method (X-FEM) is implemented to analyze fracture mechanics problems in elastic materials that exhibit general anisotropy. In the X-FEM, crack modeling is addressed by adding discontinuous enrichment functions to the standard FE polynomial approximation within the framework of partition of unity. In particular, the crack interior is represented by the Heaviside function, whereas the crack-tip is modeled by the so-called crack-tip enrichment functions. These functions have previously been obtained in the literature for isotropic, orthotropic, piezoelectric and magnetoelectroelastic materials. In the present work, the crack-tip functions are determined by means of the Stroh’s formalism for fully anisotropic materials, thus providing a new set of enrichment functions in a concise and compact form. The proposed formulation is validated by comparing the obtained results with other analytical and numerical solutions. Convergence rates for both topological and geometrical enrichments are presented. Performance of the newly derived enrichment functions is studied, and comparisons are made to the well-known classical crack-tip functions for isotropic materials.

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Authors and Affiliations

  1. Department of Continuum Mechanics, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    G. Hattori, R. Rojas-Díaz & A. Sáez

  2. Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA, 95616, USA

    N. Sukumar

  3. Departamento de Ingeniería Civil, de Materiales y Fabricación, E.T.S. de Ingenieros Industriales, Universidad de Málaga, Doctor Ortiz Ramos, 29071, Malaga, Spain

    F. García-Sánchez

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  1. G. Hattori
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  2. R. Rojas-Díaz
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  3. A. Sáez
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  4. N. Sukumar
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  5. F. García-Sánchez
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Correspondence to R. Rojas-Díaz.

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Hattori, G., Rojas-Díaz, R., Sáez, A. et al. New anisotropic crack-tip enrichment functions for the extended finite element method. Comput Mech 50, 591–601 (2012). https://doi.org/10.1007/s00466-012-0691-0

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  • DOI: https://doi.org/10.1007/s00466-012-0691-0

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