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On the extremal stress and displacement in Hencky plasticity. (English) Zbl 0548.73022
Some earlier studies have established the existence of an extremal displacement field $$\bar u$$ for an elasto-perfectly plastic material employing Hencky’s law. The construction of the extremal stress field $${\bar\sigma }$$ from $$\bar u$$ and duality between the spaces of stresses and strains have also been investigated. In the present paper, considering a pair of extremal fields $$\bar u$$, $${\bar\sigma }$$, it is proved that the singular density of the deformation $$\epsilon^ D(u)$$ is determined by the absolutely continuous tensor $${\bar\sigma }$$(D) via a relation stated in the paper. The proof has been presented with the help of several theorems and lemmas and requires a good knowledge of mathematical analysis.
Reviewer: V.K.Arya

##### MSC:
 74C99 Plastic materials, materials of stress-rate and internal-variable type 49J40 Variational inequalities 74S30 Other numerical methods in solid mechanics (MSC2010)
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##### References:
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