On Hill’s bipotential. (English) Zbl 1391.74034

Ban, M.; Vallée, C.; Lerintiu, C.

PAMM, Proc. Appl. Math. Mech. 5, 288-289 (2005).

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)].

MSC:

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

Citations:

Zbl 1177.74085