Abstract
The macroscopic criterion of a porous material is investigated using the Gurson spherical model, but with a pressure-dependent matrix. Owing to the isotropy of the resultant macroscopic material, the problem is analyzed under axisymmetry assumption. In both statical and kinematical approaches, specific quadratic formulations were used for the stress and displacement velocity fields in the triangular finite elements. To improve the efficiency, analytical continuous fields, derived from the solution to the problem of a cavity under internal pressure, were superimposed on the fem fields. The final problems result in conic optimization, or linear programming after linearizing the criterion, so as to determine the “porous Coulomb” criterion. A fine iterative post-analysis strictly restores the admissibility of the statical and kinematical solutions. The comparison with a “translated modified Cam-clay” criterion shows that this criterion might be considered as a satisfactory approximation for some values of internal friction angle and porosity. Finally, a detailed comparison with the “porous Drucker-Prager” case is presented.
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Pastor, J., Thoré, P. (2009). Gurson Model for Porous Pressure Sensitive Materials. In: Dieter, W., Alan, P. (eds) Limit States of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9634-1_3
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DOI: https://doi.org/10.1007/978-1-4020-9634-1_3
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-1-4020-9634-1
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