Constructing convex limit surfaces in material mechanics

In our previous paper 3], a method of constructing convex surfaces in 6D space of symmetric second-rank tensors by means of deforming the unit sphere S⁵ into a conoidal surface has been considered. Now we extend this method to parabolic surfaces and to the case where the shape of the surfaces depends also on the third tensor invariant. The resulting equations can be utilized for specifying the limit surfaces in the mechanics of isotropic and anisotropic solids. Some examples on approximating data on the experimental strength are presented.Institute of Polymer Mechanics, Latvian Academy of Sciences. Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 339–349, May–June, 1996.