Hill’s biopotential. (English) Zbl 1177.74085

Mihăilescu-Suliciu, Mihaela (ed.), New trends in continuum mechanics. Proceedings of the international conference, Constanţa, Romania, September 8–12, 2003. Bucharest: Theta (ISBN 973-85432-5-8). Theta Series in Advanced Mathematics 3, 339-351 (2005).
De Saxcé [G. De Saxcé and Z.-Q. Feng, Math. Comput. Modelling 28, No. 4–8, 225–245 (1998; Zbl 1126.74341)] proposed a new formulation of the constitutive law of materials based on the concept of bipotential. 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. This class contains, as a sub-class, the generalized standard materials.
The authors introduce the notion of Hill’s bipotential, which is a bipotential expressing the coaxiality of two tensors with preservation of the order of the eigenvalues.
For the entire collection see [Zbl 1108.74005].


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


Zbl 1126.74341