Abstract
In his famous 1977-paper, Gurson used the kinematic approach of Limit Analysis (LA) about the hollow sphere model with a von Mises solid matrix. The computation led to a macroscopic yield function of the “Porous von Mises”-type materials. Several extensions have been further proposed in the literature, such as those accounting for void shape effects by Gologanu et al. (J. Eng. Mater. Technol. 116:290–297, 1994; Continuum Micromechanics, Springer, Berlin, 1997), among others. To obtain pertinent lower and upper bounds to the exact solutions in terms of LA, we have revisited our existing kinematic and static 3D-FEM codes for spherical cavities to take into account the model with confocal spheroid cavity and boundary. In both cases, the optimized formulations have allowed to obtain an excellent efficiency of the resulting codes. A first comparison with the Gurson criterion does not only show an improvement of the previous results but points out that the real solution to the hollow sphere model problem depends on the third invariant of the stress tensor. A second series of tests is presented for oblate cavities, in order to analyze the above-mentioned works in terms of bound and efficiency.
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Pastor, F., Thoré, P., Kondo, D., Pastor, J. (2013). Limit Analysis and Conic Programming for Gurson-Type Spheroid Problems. In: de Saxcé, G., Oueslati, A., Charkaluk, E., Tritsch, JB. (eds) Limit State of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5425-6_12
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DOI: https://doi.org/10.1007/978-94-007-5425-6_12
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