Thomas Roche

Publications (3) View all

• Article: Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence

  Matthias Liero, Thomas Roche
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  ABSTRACT: This paper deals with dimension reduction in linearized elastoplasticity in the rate-independent case. The reference configuration of the elastoplastic body is given by a two-dimensional middle surface and a small but positive thickness. We derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations which are coupled via plastic strains. The convergence analysis is based on an abstract Γ-convergence theory for rate-independent evolution formulated in the framework of energetic solutions. This concept is based on an energy-storage functional and a dissipation functional, such that the notion of solution is phrased in terms of a stability condition and an energy balance.
  Nonlinear Differential Equations and Applications NoDEA 10/2011; · 0.54 Impact Factor
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  Available from: Thomas Roche

  Article: Lipschitz continuous data dependence of sweeping processes in BV spaces

  Pavel Krejčí, Thomas Roche
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  ABSTRACT: For a rate independent sweeping process with a time dependent smooth convex constraint, we prove that the Kurzweil solution for possibly discontinuous inputs depends locally Lipschitz continuously on the data in terms of the BV-norm.
  Discrete and Continuous Dynamical Systems - Series B. 01/2010;
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  Article: Uniqueness of a quasivariational sweeping process on functions of bounded variation

  Thomas Roche
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  ABSTRACT: We prove existence and uniqueness of a quasivariational sweeping process on functions of bounded variation thereby generalizing earlier results for absolutely continuous functions. It turns out that the size of the discontinuities plays a crucial role: In case they are small enough we prove existence and uniqueness. For large jumps we present a counterexample to the uniqueness of the solution. Finally we show that the condition on the jump size can be replaced by suitable conditions on the convex set.
  ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE. 01/2010;