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Author: Thomas, Marita × End date: 2019 × Start date: 2010 ×

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Now showing 1 - 10 of 22
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    Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics
    (Bristol : IOP Publ., 2016) Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica
    This note deals with the analysis of a model for partial damage, where the rate- independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading.
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    From an adhesive to a brittle delamination model in thermo-visco-elsticity
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Rossi, Riccarda; Thomas, Marita
    We address the analysis of a model for brittle delamination of two visco-elastic bodies, bonded along a prescribed surface. The model also encompasses thermal effects in the bulk. The related PDE system for the displacements, the absolute temperature, and the delamination variable has a highly nonlinear character. On the contact surface, it features frictionless Signorini conditions and a nonconvex, brittle constraint acting as a transmission condition for the displacements. We prove the existence of (weak/energetic) solutions to the associated Cauchy problem, by approximating it in two steps with suitably regularized problems. We perform the two consecutive passages to the limit via refined variational convergence techniques.
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    From damage to delamination in nonlinearly elastic materials at small strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander; Roubíček, Thomáš; Thomas, Marita
    Brittle Griffith-type delamination of compounds is deduced by means of Gamma-convergence from partial, isotropic damage of three-specimen-sandwich-structures by flattening the middle component to the thickness 0. The models used here allow for nonlinearly elastic materials at small strains and consider the processes to be unidirectional and rate-independent. The limit passage is performed via a double limit: first, we gain a delamination model involving the gradient of the delamination variable, which is essential to overcome the lack of a uniform coercivity arising from the passage from partial damage to delamination. Second, the delamination-gradient is supressed. Noninterpenetration- and transmission-conditions along the interface are obtained
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    Towards doping optimization of semiconductor lasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Peschka, Dirk; Rotundo, Nella; Thomas, Marita
    We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantum-well lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights.
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    Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica
    This note deals with the analysis of a model for partial damage, where the rate-independent, unidirectional ow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubí£ek [Rou09, Rou10] with the methods from Lazzaroni/Rossi/Thomas/Toader [LRTT14]. The present analysis encompasses, dierently from [Rou10], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [LRTT14], a nonconstant heat capacity and a time-dependent Dirichlet loading.
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    A rate-independent gradient system in damage coupled with plasticity via structured strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Bonetti, Elena; Rocca, Elisabetta; Rossi, Riccarda; Thomas, Marita
    This contribution deals with a class of models combining isotropic damage with plasticity. It has been inspired by a work by Freddi and Royer-Carfagni [FRC10], including the case where the inelastic part of the strain only evolves in regions where the material is damaged. The evolution both of the damage and of the plastic variable is assumed to be rate-independent. Existence of solutions is established in the abstract energetic framework elaborated by Mielke and coworkers (cf., e.g., [Mie05, Mie11b]).
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    Rate-independent damage in thermo-viscoelastic materials with inertia
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica
    We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.
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    Coupling rate-independent and rate-dependent processes: Existence results
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Rossi, Riccarda; Thomas, Marita
    We address the analysis of an abstract system coupling a rate-independent process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.
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    Gradient structure for optoelectronic models of semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Mielke, Alexander; Peschka, Dirk; Rotundo, Nella; Thomas, Marita
    We derive an optoelectronic model based on a gradient formulation for the relaxation of electron-, hole- and photon- densities to their equilibrium state. This leads to a coupled system of partial and ordinary differential equations, for which we discuss the isothermal and the non-isothermal scenario separately.
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    From adhesive to brittle delamination in visco-elastodynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Rossi, Riccarda; Thomas, Marita
    In this paper we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvability concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit.