Limit analysis of hollow spheres or spheroids with Hill orthotropic matrix

作者：Pastor Franck; Pastor Joseph; Kondo Djimedo^*

来源：Comptes Rendus Mecanique, 2012, 340(3): 120-129.

DOI：10.1016/j.crme.2011.11.011

• Porous media
• Anisotropy
• Hill matrix
• Gurson approach
• Hollow spheroid model
• Limit analysis
• 3D-FEM
• Conic optimization

Recent theoretical studies of the literature are concerned by the hollow sphere or spheroid (confocal) problems with orthotropic Hill type matrix. They have been developed in the framework of the limit analysis kinematical approach by using very simple trial velocity fields. The present Note provides, through numerical upper and lower bounds, a rigorous assessment of the approximate criteria derived in these theoretical works. To this end, existing static 3D codes for a von Mises matrix have been easily extended to the orthotropic case. Conversely, instead of the non-obvious extension of the existing kinematic codes, a new original mixed approach has been elaborated on the basis of the plane strain structure formulation earlier developed by F. Pastor (2007). Indeed, such a formulation does not need the expressions of the unit dissipated powers. Interestingly, it delivers a numerical code better conditioned and notably more rapid than the previous one, while preserving the rigorous upper bound character of the corresponding numerical results. The efficiency of the whole approach is first demonstrated through comparisons of the results to the analytical upper bounds of Benzerga and Besson (2001) or Monchiet et al. (2008) in the case of spherical voids in the Hill matrix. Moreover, we provide upper and lower bounds results for the hollow spheroid with the Hill matrix which are compared to those of Monchiet et al. (2008).

• 出版日期2012-3