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On classical solutions of the Prandtl-Reuss equations of perfect elastoplasticity. (English) Zbl 0861.73024

Summary: We study the elasticity domain for an antiplane deformation of a perfect elastoplastic medium, which is described by the Prandtl-Reuss equations. We prove that a boundary of this domain can be found by solving a system of nonlinear functional equations. In the simplest case of simple shear deformations, this system of equations is studied in detail.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
39B62 Functional inequalities, including subadditivity, convexity, etc.
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[2] Mandel, Cours de Mecanique des Milieus Continus I (1976)
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