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Extremum theorems for finite-step backward-difference analysis of elastic-plastic nonlinearly hardening solids. (English) Zbl 0737.73049

Summary: For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of “material stability” are assumed. This communiction anticipates results to be presented elsewhere in an extended version. Therefore, proofs of the statements and various comments are omitted.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74S20 Finite difference methods applied to problems in solid mechanics
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