Limit analysis and Gursonʹs model

The yield criterion of a porous material using Gursonʹs model [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth – Part I: Yield criteria and flow rules for porous ductile media. ASME J. Engrg. Mater. Technol. 99, 2–15] is investigated herein. Both methods of Limit Analysis are applied using linear and conic programming codes for solving resulting non-linear optimization problems. First, the results obtained for a porous media with cylindrical cavities [Francescato, P., Pastor, J., Riveill-Reydet, B., 2004. Ductile failure of cylindrically porous materials. Part 1: Plane stress problem and experimental results. Eur. J. Mech. A Solids 23, 181–190; Pastor, J., Francescato, P., Trillat, M., Loute, E., Rousselier, G., 2004. Ductile failure of cylindrically porous materials. Part 2: Other cases of symmetry. Eur. J. Mech. A Solids 23, 191–201] are summarized, showing that the Gurson expression is too restrictive in this case. Then the hollow sphere problem is investigated, in the axisymmetrical and in the three-dimensional (3D) cases. A plane mesh of discontinuous triangular elements is used to model the hollow sphere as RVE in the axisymmetrical example. This first model does not provide a very precise yield criterion. Then a full 3D model is applied (using discontinuous tetrahedral elements), thus solving nearly exactly the general three-dimensional problem. Several examples of loadings are investigated in order to test the final criterion in a variety of situations. As a result, the Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches.