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.


74C99 Plastic materials, materials of stress-rate and internal-variable type
39B62 Functional inequalities, including subadditivity, convexity, etc.
Full Text: DOI


[1] DOI: 10.1070/RM1980v035n05ABEH001928 · Zbl 0471.34045
[2] Mandel, Cours de Mecanique des Milieus Continus I (1976)
[3] DOI: 10.1007/978-3-642-66165-5
[4] DOI: 10.1016/0021-8928(85)90058-9 · Zbl 0604.73027
[5] DOI: 10.1002/cpa.3160230304
[6] Kuksin, Plasticity and Destruction of Solids (1988)
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