Unique existence of boundary value problems for certain models of anisotropic elastoplastic medium (Q1093407)

The author studies the mixed boundary problems of anisotropic elastoplasticity under proportional loading. She proves the theorem of uniqueness and existence of generalized solution of this problem. The tensor of deformations is linear. The constitutional law is \(\sigma_ i=\partial W/\partial e_ i\), \(i=1,...,6\) and \(\sigma_ i=C_{ij}\epsilon_ j+(\alpha_{ij}\epsilon_ j+\alpha_{i0})\omega (e_ u).\) A theorem of uniqueness and existence is proved under some conditions about functions and tensors by applying the theory of potential operators in a Hilbert space. A similar theorem is formulated for another constitutive law.