Abstract
Elastic plastic fracture mechanics relies on the finite element method both as an engineering tool to evaluate residual strength of a damaged structure and to implement research theories that cannot be evaluated analytically. One common formulation assumes that the crack plane is flat and that the structure is symmetric about the crack plane. This situation arises for typical laboratory coupons such as the compact tension and middle crack tension specimens. Crack growth is modeled by monitoring analysis results for a critical fracture criterion, extending the crack, and resuming the analysis. When a symmetry plane corresponds to the crack-plane, an efficient crack growth procedure called nodal release can be used. A typical implementation reduces to the simultaneous solution of a set of linear equations, each of which corresponds to a displacement in the body being modeled. The system of equations is symmetric positive definite and sparse. This paper presents scalable sparse matrix factorization and update techniques required for efficient crack extension using nodal release.
This work has been funded in part by the National Aeronautics and Space Agency through grant NAG-1-01085 and by the National Science Foundation through grants NSF CCR-981334 and NSF ACI-0102537 and through the Maria Goeppert Mayer Award from the Department of Energy and the Argonne National Labs. This work was performed by Dr. James when he was an NRC Research Associate at NASA Langley Research Center, Hampton, VA 23681.
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Raghavan, P., James, M.A., Newman, J.C., Seshadri, B.R. (2002). Scalable Sparse Matrix Techniques for Modeling Crack Growth. In: Fagerholm, J., Haataja, J., Järvinen, J., Lyly, M., Råback, P., Savolainen, V. (eds) Applied Parallel Computing. PARA 2002. Lecture Notes in Computer Science, vol 2367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48051-X_58
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DOI: https://doi.org/10.1007/3-540-48051-X_58
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