Blurred maximal cyclically monotone sets and bipotentials

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 $\phi \in \Gamma_{0}(X)$ for that the differential inclusion $y \in \bar{B}(\epsilon) + \partial \phi(x)$ can be put in the form $y \in \partial b(\cdot, y)(x)$, with $b$ a bipotential.Comment: Revised version, corrections in theorem 6.

A variational formulation for constitutive laws described by bipotentials

Inspired by the algorithm of Berga and de Saxce for solving the discretisation in time of the evolution problem for an implicit standard material, we propose a general variational formulation in terms of bipotentials

Blurred constitutive laws and bipotential convex covers

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

The brezis-ekeland-nayroles minimization principle with mixed finite element method for elastoplastic dynamic problems

We propose a modification of the Hamiltonian formalism which can be used for dissipative systems, the Brezis-Ekeland-Nayroles principle. The formalism is specialized to the standard plasticity in small strains and dynamics. We apply it to solve the classical problem of a thin tube in plane strain subjected to an internal pressure. The continuum is discretized with mixed finite elements

Combined sticking: a new approach for finite-amplitude Coulomb frictional contact

Engineering-level accuracy of discretization methods for frictional contact originates from precise representation of discontinuous frictional and normal interaction laws and precise discrete contact techniques. In terms of discontinuous behavior in the quasi-static case, two themes are of concern: the normal interaction (i.e. impact) and the jumps in tangential directions arising from high frictional values. In terms of normal behavior, we use a smoothed complementarity relation. For the tangential behavior, we propose a simple and effective algorithm, which is based a stick predictor followed by corrections to the tangential velocity. This allows problems with impact and stick-slip behavior to be solved with an implicit code based on Newton–Raphson iterations. Three worked examples are shown with comparisons with published results. An extension to node-to-face form in 3D is also presented

3D Revolute Joint with Clearance in Multibody Systems

International audienceThe aim of this paper is to understand the influence of radial and axial clearance in the revolute joints on the overall performance of a circuit breaker. A circuit breaker mechanism is made of seven links, seven revolute joints with clearance in both radial and axial direction, four unilateral contacts with friction, and it has forty-two degrees of freedom. The Moreau-Jean nonsmooth contact dynamics (NSCD) numerical method is used to perform the simulations. The numerical results are validated by careful comparisons with experimental data

Heat partition and surface temperature in sliding contact systems of rough surfaces

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