On Hill’s bipotential. (English) Zbl 1391.74034

Summary: A new formulation of the constitutive law of materials based on the concept of bipotential was introduced by de Saxcé. This concept is able to describe non-associated laws and to suggest robust numerical algorithms. Materials that admit a bipotential to model their behaviour constitute the class of Implicit Standard Materials (ISM). This class contains, as a sub-class, the Generalized Standard Materials (GSM). In this paper, we present a bipotential expressing the coaxiality of two tensors with preservation of the order of the eigenvalues. We call it Hill’s bipotential.
Editorial remark: See also [C. Vallée et al., in: New trends in continuum mechanics. Proceedings of the international conference, Constanţa, Romania, September 8–12, 2003. Bucharest: Theta. 339–351 (2005; Zbl 1177.74085)].


74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74M10 Friction in solid mechanics


Zbl 1177.74085
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