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Based on an extension of Fenchel inequality, bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Given the graph M ⊂ X × Y of a multivalued law T : X → 2 Y , we state a simple necessary and sufficient… (More)
A recent paper has described a new functional method, the symmetrical centre of rotation (SCoRE), for locating joint centre position [Ehrig, R.M., Taylor, W.R., Duda, G.N., Heller, M.O., 2006. A survey of formal methods for determining the centre of rotation of ball joints. Journal of Biomechanics 39 (15), 2798-2809]. For in vitro analyses, the SCoRE method… (More)
This is a survey of recent results about bipotentials representing multival-ued operators. The notion of bipotential is based on an extension of Fenchel's inequality, with several interesting applications related to non associated con-stitutive laws in non smooth mechanics, such as Coulomb frictional contact or non-associated Drücker-Prager model in… (More)
Let X be a reflexive Banach space and Y its dual. In this paper we find necessary and sufficient conditions for the existence of a bipotential for a blurred maximal cyclically monotone graph. Equivalently, we find a necessary and sufficient condition on φ ∈ Γ0(X) for that the differential inclusion y ∈ ¯ B(ε) + ∂φ(x) can be put in the form y ∈ ∂b(·, y)(x),… (More)
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property 13 of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators 15 that can be approximated by operators of finite rank and having a countable family of… (More)
In many practical situations, incertitudes affect the mechanical behaviour that is given by a family of graphs instead of a single one. In this paper, we show how the bipotential method is able to capture such blurred constitutive laws, using bipotential convex covers.
We show a surprising connexion between a property of the inf convolutions of a family of convex lower semicontinuous functions and the fact that intersections of maximal cyclically monotone graphs are the critical set of a bipotential. We then extend the results from  to bipotentials convex covers, generalizing the notion of a bi-implicitly convex… (More)