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Dual spaces of stresses and strains, with applications to Hencky plasticity. (English) Zbl 0532.73039
In this paper the authors formulate an optimality condition for the existence of a dual pairing between the stress field \(\sigma\) and the displacement field u, with regard to Hencky plasticity. These stress and displacement fields are extremals of a pair of dual convex variational problems and (\(\sigma\),u) can be considered a saddle-point for Hencky plasticity problems. The optimality condition (or ’saddle point’ condition) gives precisely the constitutive relationship between stress and strain. After some rigorous mathematical analysis, the authors prove the existence of an extremal displacement field under safe load conditions and also that any extremal stress and displacement fields are connected by an optimality condition which is equivalent to the constitutive relation between stress and strain for Hencky plasticity, provided the extremals are sufficiently regular. The paper is mathematical and requires a good knowledge of analysis to be understood clearly.
Reviewer: V.K.Arya

74C99 Plastic materials, materials of stress-rate and internal-variable type
49N15 Duality theory (optimization)
74S30 Other numerical methods in solid mechanics (MSC2010)
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