Constitutive inequalities in general static and dynamic theory of elastic shells undergoing finite deformation are discussed. Constitutive inequalities are well known in continuum mechanics. They express physical or mathematical restrictions for constitutive equations of 3D elastic materials. In this paper we discuss the analogs of the strong ellipticity, Hadamard and Coleman‐Noll (GCN‐condition) inequalities for nonlinear elastic shells. It is shown that the GCN‐condition implies the strong elipticity for shell theory whereas the strong ellipticity is equivalent to the existence conditions of acceleration waves in shell.
The theory of line defects (dislocations and disclinations) in elastic bodies has been revisited. A consistent application of the formal limiting passage from isolated defects to the continuous distribution of these allows one to obtain a complete system of equations describing internal stresses in a body with distributed defects. Special emphasis is placed on disclinations in planar systems like graphene which very often demonstrate nonlinear elastic response. As a specific example an exact solution has been found for the problem of the eigenstresses in a disc of nonlinear elastic material due to a given density of continuously distributed disclinations.
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