Filters

2006 - 20082

More filters

20192
Reset filters

Settings

End date: 2009 × Start date: 2000 × DDC: 510 × Type: Text × Version: publishedVersion × Subject: existence × Subject: nonlinear elasticity ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Existence results for a contact problem with varying friction coefficient and nonlinear forces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Schmid, Florian; Mielke, Alexander
    We consider the rate-independent problem of a particle moving in a three - dimensional half space subject to a time-dependent nonlinear restoring force having a convex potential and to Coulomb friction along the flat boundary of the half space, where the friction coefficient may vary along the boundary. Our existence result allows for solutions that may switch arbitrarily often between unconstrained motion in the interior and contact where the solutions may switch between sticking and frictional sliding. However, our existence result is local and guarantees continuous solutions only as long as the convexity of the potential is strong enough to compensate the variation of the friction coefficient times the contact pressure. By simple examples we show that our sufficient conditions are also necessary. Our method is based on the energetic formulation of rate-independent systems as developed by Mielke and co-workers. We generalize the time-incremental minimization procedure of Mielke and Rossi for the present situation of a non-associative flow rule.
  • Thumbnail Image
    Item
    Quasi-static contact problem with finitely many degrees of freedom and dry friction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Schmid, Florian
    A quasi-static contact problem is considered for a non-linear elastic system with finitely many degrees of freedom. Coulomb's law is used to model friction and the friction coefficient may be anisotropic and may vary along the surface of the rigid obstacle. Existence is established following a time-incremental minimization problem. Friction is artificially decreased to resolve the discontinuity arising from making and losing contact.