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A geometric nonlinear triangular finite element with an embedded discontinuity for the simulation of quasi-brittle fracture

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Abstract

This paper is aimed to model the appearance and evolution of discrete cracks in quasi-brittle materials using triangular finite elements with an embedded interface in a geometric nonlinear setting. The kinematics for the discontinuous displacement field is presented and the standard variational formulation with respect to the reference configuration is extended to a body with an internal discontinuity. Special attention is paid to the algorithmic treatment. The discontinuity is modeled by additional global degrees of freedom and the continuity of the displacements across the element boundaries is enforced. Finally, representative numerical examples for mode-I and mixed-mode fracture, namely a tension test, different three-point bending tests and a single edge notched beam with structured and unstructured finite element meshes are discussed to study the evolving crack pattern and to show the ability of the model.

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  1. Institut für Mechanik, FB Bauwissenschaften, Universität Duisburg-Essen, Campus Essen , D-45117 Essen, Universitätsstr. 15, Germany

    J. Schröder & J. Löblien

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  1. J. Schröder
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  2. J. Löblien
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Schröder, J., Löblien, J. A geometric nonlinear triangular finite element with an embedded discontinuity for the simulation of quasi-brittle fracture. Comput Mech 36, 139–157 (2005). https://doi.org/10.1007/s00466-004-0648-z

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  • DOI: https://doi.org/10.1007/s00466-004-0648-z

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