On isotropic rank 1 convex functions. (English) Zbl 0945.26018
The main topic of this paper is to establish necessary and sufficient conditions for the rank 1 convexity of a rationally invariant function defined on the set of all tensors with positive determinant on an \(n\)-dimensional vector space. The author gets his results using the representation of such a function received through the singular values. He also proves that the rank 1 convexity is equivalent to a restricted ordinary convexity when the function is expressed in terms of signed invariants of the deformation.
MSC:
| 26B25 | Convexity of real functions of several variables, generalizations |
| 74B20 | Nonlinear elasticity |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
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