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Subject: nonlinear elasticity × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    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.
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    Surface induced phase separation of a swelling hydrogel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Hennessy, Matthew G.; Münch, Andreas; Wagner, Barbara
    We present a formulation of the free boundary problem for a hydrogel that accounts for the interfacial free energy and finite strain due to the large deformation of the polymer network during solvent transport across the free boundary. For the geometry of an initially dry layer fixed at a rigid substrate, our model predicts a phase transition when a critical value of the solvent concentration has been reached near the free boundary. A one-dimensional case study shows that depending on the flux rate at the free boundary an initial saturation front is followed by spinodal decomposition of the hydrogel and the formation of an interfacial front that moves through the layer. Moreover, increasing the shear modulus of the elastic network delays or even suppresses phase separation.
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    Stochastic homogenization on perforated domains I: Extension operators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin
    This preprint is part of a major rewriting and substantial improvement of WIAS Preprint 2742. In this first part of a series of 3 papers, we set up a framework to study the existence of uniformly bounded extension and trace operators for W1,p-functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. We drop the classical assumption of minimaly smoothness and study stationary geometries which have no global John regularity. For such geometries, uniform extension operators can be defined only from W1,p to W1,r with the strict inequality r
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    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.