The Initiation of Bifurcations and Localization in Damaging Materialsby M. K. Neilsen, Sandia Natl Lab, Albuquerque, United States,
H. L. Schreyer, Sandia Natl Lab, Albuquerque, United States,
Abstract: Criteria for diffuse and discontinuous bifurcations have previously been developed and used to investigate the initiation of necking and localization in elastic-plastic materials. In this study, the same bifurcation criteria are applied to elastic-damaging materials. Since the bifurcation criteria depend on the tangent stiffness tensor, the first step in this investigation was the derivation of the tangent stiffness tensor for a rather general continuum damage model. An eigenanalysis of the tangent stiffness tensor is shown to provide a significant amount of information about both diffuse and discontinuous bifurcations.
Subject Headings: Bifurcations | Elastic analysis | Stiffening | Strength of materials | Mathematical models | Professional societies
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