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search.filters.applied.f.access: openAccess × Author: Roubíček, Tomáš × End date: 2020 × Start date: 2010 ×

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    Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains
    (Berlin ; Heidelberg : Springer, 2020) Mielke, Alexander; Roubíček, Tomáš
    The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization. © 2020, The Author(s).
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    Thermoviscoelasticity in Kelvin--Voigt rheology at large strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Mielke, Alexander; Roubíček, Tomáš
    The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e. inertial forces are ignored, is shown by time discretization.
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    Stress-driven local-solution approach to quasistatic brittle delamination
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Roubíček, Tomáš; Thomas, Marita; Panagiotopoulos, Christos
    A unilateral contact problem between elastic bodies at small strains glued by a brittle adhesive is addressed in the quasistatic rate-independent setting. The delamination process is modelled as governed by stresses rather than by energies. This results in a specific scaling of an approximating elastic adhesive contact problem, discretised by a semi-implicit scheme and regularized by a BV-type gradient term. An analytical zero-dimensional example motivates the model and a specific local-solution concept. Two-dimensional numerical simulations performed on an engineering benchmark problem of debonding a fiber in an elastic matrix further illustrate the validity of the model, convergence, and algorithmical efficiency even for very rigid adhesives with high elastic moduli.