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A concise analytical treatment of elastic‐plastic bending of a strain hardening curved beam

Plane stress and plane strain analytical solutions to partially plastic deformation of a curved beam are presented. The beam has a narrow rectangular cross section and it is subjected to couples at its end sections prevailing pure bending conditions. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. The solutions are verified in comparison to the ones available in the literature. It is shown that plane stress and plane strain solutions agree well in the elastic and in the elastic‐plastic deformation stages. It is also observed that the changes in the dimensions of the beam as it deforms are negligibly small.