Maier, Giulio; Novati, Giorgio Extremum theorems for finite-step backward-difference analysis of elastic-plastic nonlinearly hardening solids. (English) Zbl 0737.73049 Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 82, No. 4, 711-715 (1988). 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 Keywords:small strains; potential energy; complementary energy; yield function; sum of equivalent stress and yield limit; internal variables; material stability; hardening PDFBibTeX XMLCite \textit{G. Maier} and \textit{G. Novati}, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 82, No. 4, 711--715 (1988; Zbl 0737.73049)