ON THE CONVEXITY OF POTENTIAL OF NONLINEAR ELASTIC MEDIA MODEL WITH TENSOR DAMAGE PARAMETER

For solving problems of the theory elasticity using nonlinear models, question convexity potential used and proof uniqueness solution are decisive importance. The present work is devoted to determination conditions for local strict model, which ensure problem in a sufficiently small neighborhood desired solution. considered model generalization scalar rheological brittle solid deformation case tensor damage parameter, principal values describe reduction cross-sectional area material three orthogonal directions. An additional term second order elastic makes it possible dependence moduli on type stress-strain state, dilatancy under shear deformation, as well response even at low loads. introduced rank damage-induced anisotropy properties material. Conditions axes strain obtained this general misaligned tensors. To illustrate conditions, two special cases considered: transversely isotropic fractured medium with coaxial tensors, obliquely oriented fracturing. both cases, limiting parameter degree shown. It shown that weak anisotropy, give minorant estimate maximum allowable various types state. fracturing, dependences permissible angle inclination state plotted.