Tomáš Roubíček | Charles University, Prague (original) (raw)

Papers by Tomáš Roubíček

Research paper thumbnail of Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Applications of Mathematics

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Research paper thumbnail of Rate-Independent Damage Processes in Nonlinear Elasticity

Mathematical Models and Methods in Applied Sciences, 2006

Damage of an elastic body undergoing large deformations by a "hard-device" loading poss... more Damage of an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process. The damage is assumed to absorb a specific and prescribed amount of energy. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on a part of the boundary. Rigorous analysis by time discretization is performed.

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Research paper thumbnail of Martensitic transformation in NiMnGa single crystals: Numerical simulation and experiments

International Journal of Plasticity, 2006

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Research paper thumbnail of Thermodynamics of shape-memory alloys under electric current

Phase transformation in shape-memory alloys is known to cause electric resistivity variation that... more Phase transformation in shape-memory alloys is known to cause electric resistivity variation that, under electric current, may conversely influence Joule heat production and thus eventually the martensitic transformation itself. A ther-modynamically consistent general continuum-mechanical model at large strains is presented. In special cases, a proof of the existence of a weak solution is outlined, using a semidiscretization in time. Mathematics Subject Classification (2000). 35K55 · 74A15 · 74N10 · 80A17.

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Research paper thumbnail of FERROMAGNETS WITH EDDY CURRENTS AND PINNING EFFECTS: THEIR THERMODYNAMICS AND ANALYSIS

Existence of weak solutions is proved for a system of nonlinear parabolic equations/inequalities ... more Existence of weak solutions is proved for a system of nonlinear parabolic equations/inequalities describing evolution of magnetization, temperature, magnetic ¯eld, and electric ¯eld in electrically-conductive unsaturated ferromagnets. The system is derived from a recently-proposed thermodynamically-consistent continuum theory for the ferro/paramagnetic transition. Besides the standard viscous-like damping, dissipation due to eddy currents and domain-wall pinning is considered.

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Research paper thumbnail of Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis

We derive a thermodynamically consistent general continuum-mechanical model describing mutually c... more We derive a thermodynamically consistent general continuum-mechanical model describing mutually coupled martensitic and ferro/paramagnetic phase transformations in electrically-conductive magnetostrictive materials such as NiMnGa. We use small-strain and eddy-current approximations, yet large velocities and electric current injected through the boundary are allowed. Fully nonlinear coupling of magneto-mechanical and thermal effects is considered. The existence of energy-preserving weak solutions is proved by showing convergence of time-discrete approximations constructed by a carefully designed semi-implicit regular-ized scheme.

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Research paper thumbnail of THERMOMECHANICS OF HYDROGEN STORAGE IN METALLIC HYDRIDES: MODELING AND ANALYSIS

A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is pr... more A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat transfer, strain, and stress. We prove existence of solutions of the ensuing system of partial differential equations by a carefully-designed, semi-implicit approximation scheme. A generalization for a drift-diffusion of multi-component ionized " gas " is outlined, too.

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Research paper thumbnail of Thermomechanics of damageable materials under diffusion: modelling and analysis

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute ... more We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat genera-tion/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation , water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type. Mathematics Subject Classification. 35K55 · 35Q74 · 74A15 · 74R20 · 74N10 · 74F10 · 76S99 · 80A17 · 80A20.

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Research paper thumbnail of A Thermodynamically Consistent Theory of the Ferro/Paramagnetic Transition

We propose a continuum theory describing the evolution of magnetization and temperature in a rigi... more We propose a continuum theory describing the evolution of magnetization and temperature in a rigid magnetic body. The theory is based on a microforce balance, an energy balance, and an entropy imbalance. We advance the choice of a class of constitutive equations, consistent with the entropy imbalance, that appear appropriate to describe the phase transition taking place in a ferromagnet at the Curie point. By combining these constitutive equations with the balance laws, we formulate an initial-boundary value problem for the magnetization and temperature fields, and we prove existence of weak solutions.

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Research paper thumbnail of BEM implementation of energetic solutions for quasistatic delamination problems

The problem of the onset and propagation of an elastic-brittle delamination is considered. We stu... more The problem of the onset and propagation of an elastic-brittle delamination is considered. We study delamination processes for elastic bodies glued by an adhesive to each other or to a rigid outer boundary. The interfacial adhesive is assumed to store and also dissipate a specific amount of energy during the delamination process. Damage along the interfaces is taken into account by introducing an interface damage variable. The present approach is based on the so-called energetic-solution concept. After introducing an implicit time discretization and a spatial discretization along the boundaries, the boundary element method (BEM) is utilized to solve the pertinent recursive boundary-value problems arising at each time step and compute the stored elastic energy. The whole solution process is based on the global minimization of the sum of the elastic potential energy in the solids and adhesive layer, defined in terms of the displacements along boundaries and the damage parameter along th...

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Research paper thumbnail of BEM solution of delamination problems using an interface damage and plasticity model

Computational Mechanics, 2013

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Research paper thumbnail of Quasistatic adhesive contact of visco-elastic bodies and its numerical treatment for very small viscosity

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

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Research paper thumbnail of A quasistatic mixed-mode delamination model

Discrete and Continuous Dynamical Systems - Series S, 2013

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Research paper thumbnail of Optimal control of variational inequalities. Approximation theory and numerical realization

Applied Mathematics & Optimization, 1986

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Research paper thumbnail of Adaptive approximation algorithm for relaxed optimization problems

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Research paper thumbnail of Quasistatic delamination models for Kirchhoff-Love plates

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2011

... Lorenzo Freddi1,∗ , Roberto Paroni2, Tomáš Roubıcek3,4, and Chiara Zanini1 1 Dipartimento di ... more ... Lorenzo Freddi1,∗ , Roberto Paroni2, Tomáš Roubıcek3,4, and Chiara Zanini1 1 Dipartimento di Matematica e Informatica, Universit`a di Udine, Via ... We further confine ourselves to Griffith-type delamination on such a prescribed surface which is positioned in a normal direction ...

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Research paper thumbnail of A visco-elasto-plastic model for phase transformations

Mathematical Methods in the Applied Sciences

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Research paper thumbnail of Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations

Optimization, 1997

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Research paper thumbnail of Visco-elasto-plastic model for martensitic phase transformation in shape-memory alloys

Mathematical Methods in the Applied Sciences, 2002

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Research paper thumbnail of A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys

Multiscale Modeling & Simulation, 2003

We formulate a model describing rate-independent hysteretic re- sponse of shape-memory alloys und... more We formulate a model describing rate-independent hysteretic re- sponse of shape-memory alloys under slow external forcing. Under natural as- sumptions we prove that this model has solution. The microstructure is treated on a \mesoscopic" level, described by volume fractions of particular phases in terms of Young measures. The whole formulation is based on energetic function- als for energy storage and

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Research paper thumbnail of Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Applications of Mathematics

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Research paper thumbnail of Rate-Independent Damage Processes in Nonlinear Elasticity

Mathematical Models and Methods in Applied Sciences, 2006

Damage of an elastic body undergoing large deformations by a "hard-device" loading poss... more Damage of an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process. The damage is assumed to absorb a specific and prescribed amount of energy. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on a part of the boundary. Rigorous analysis by time discretization is performed.

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Research paper thumbnail of Martensitic transformation in NiMnGa single crystals: Numerical simulation and experiments

International Journal of Plasticity, 2006

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Research paper thumbnail of Thermodynamics of shape-memory alloys under electric current

Phase transformation in shape-memory alloys is known to cause electric resistivity variation that... more Phase transformation in shape-memory alloys is known to cause electric resistivity variation that, under electric current, may conversely influence Joule heat production and thus eventually the martensitic transformation itself. A ther-modynamically consistent general continuum-mechanical model at large strains is presented. In special cases, a proof of the existence of a weak solution is outlined, using a semidiscretization in time. Mathematics Subject Classification (2000). 35K55 · 74A15 · 74N10 · 80A17.

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Research paper thumbnail of FERROMAGNETS WITH EDDY CURRENTS AND PINNING EFFECTS: THEIR THERMODYNAMICS AND ANALYSIS

Existence of weak solutions is proved for a system of nonlinear parabolic equations/inequalities ... more Existence of weak solutions is proved for a system of nonlinear parabolic equations/inequalities describing evolution of magnetization, temperature, magnetic ¯eld, and electric ¯eld in electrically-conductive unsaturated ferromagnets. The system is derived from a recently-proposed thermodynamically-consistent continuum theory for the ferro/paramagnetic transition. Besides the standard viscous-like damping, dissipation due to eddy currents and domain-wall pinning is considered.

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Research paper thumbnail of Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis

We derive a thermodynamically consistent general continuum-mechanical model describing mutually c... more We derive a thermodynamically consistent general continuum-mechanical model describing mutually coupled martensitic and ferro/paramagnetic phase transformations in electrically-conductive magnetostrictive materials such as NiMnGa. We use small-strain and eddy-current approximations, yet large velocities and electric current injected through the boundary are allowed. Fully nonlinear coupling of magneto-mechanical and thermal effects is considered. The existence of energy-preserving weak solutions is proved by showing convergence of time-discrete approximations constructed by a carefully designed semi-implicit regular-ized scheme.

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Research paper thumbnail of THERMOMECHANICS OF HYDROGEN STORAGE IN METALLIC HYDRIDES: MODELING AND ANALYSIS

A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is pr... more A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat transfer, strain, and stress. We prove existence of solutions of the ensuing system of partial differential equations by a carefully-designed, semi-implicit approximation scheme. A generalization for a drift-diffusion of multi-component ionized " gas " is outlined, too.

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Research paper thumbnail of Thermomechanics of damageable materials under diffusion: modelling and analysis

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute ... more We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat genera-tion/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation , water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type. Mathematics Subject Classification. 35K55 · 35Q74 · 74A15 · 74R20 · 74N10 · 74F10 · 76S99 · 80A17 · 80A20.

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Research paper thumbnail of A Thermodynamically Consistent Theory of the Ferro/Paramagnetic Transition

We propose a continuum theory describing the evolution of magnetization and temperature in a rigi... more We propose a continuum theory describing the evolution of magnetization and temperature in a rigid magnetic body. The theory is based on a microforce balance, an energy balance, and an entropy imbalance. We advance the choice of a class of constitutive equations, consistent with the entropy imbalance, that appear appropriate to describe the phase transition taking place in a ferromagnet at the Curie point. By combining these constitutive equations with the balance laws, we formulate an initial-boundary value problem for the magnetization and temperature fields, and we prove existence of weak solutions.

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Research paper thumbnail of BEM implementation of energetic solutions for quasistatic delamination problems

The problem of the onset and propagation of an elastic-brittle delamination is considered. We stu... more The problem of the onset and propagation of an elastic-brittle delamination is considered. We study delamination processes for elastic bodies glued by an adhesive to each other or to a rigid outer boundary. The interfacial adhesive is assumed to store and also dissipate a specific amount of energy during the delamination process. Damage along the interfaces is taken into account by introducing an interface damage variable. The present approach is based on the so-called energetic-solution concept. After introducing an implicit time discretization and a spatial discretization along the boundaries, the boundary element method (BEM) is utilized to solve the pertinent recursive boundary-value problems arising at each time step and compute the stored elastic energy. The whole solution process is based on the global minimization of the sum of the elastic potential energy in the solids and adhesive layer, defined in terms of the displacements along boundaries and the damage parameter along th...

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Research paper thumbnail of BEM solution of delamination problems using an interface damage and plasticity model

Computational Mechanics, 2013

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Research paper thumbnail of Quasistatic adhesive contact of visco-elastic bodies and its numerical treatment for very small viscosity

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013

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Research paper thumbnail of A quasistatic mixed-mode delamination model

Discrete and Continuous Dynamical Systems - Series S, 2013

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Research paper thumbnail of Optimal control of variational inequalities. Approximation theory and numerical realization

Applied Mathematics & Optimization, 1986

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Research paper thumbnail of Adaptive approximation algorithm for relaxed optimization problems

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Quasistatic delamination models for Kirchhoff-Love plates

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2011

... Lorenzo Freddi1,∗ , Roberto Paroni2, Tomáš Roubıcek3,4, and Chiara Zanini1 1 Dipartimento di ... more ... Lorenzo Freddi1,∗ , Roberto Paroni2, Tomáš Roubıcek3,4, and Chiara Zanini1 1 Dipartimento di Matematica e Informatica, Universit`a di Udine, Via ... We further confine ourselves to Griffith-type delamination on such a prescribed surface which is positioned in a normal direction ...

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Research paper thumbnail of A visco-elasto-plastic model for phase transformations

Mathematical Methods in the Applied Sciences

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Research paper thumbnail of Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations

Optimization, 1997

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Research paper thumbnail of Visco-elasto-plastic model for martensitic phase transformation in shape-memory alloys

Mathematical Methods in the Applied Sciences, 2002

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Research paper thumbnail of A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys

Multiscale Modeling & Simulation, 2003

We formulate a model describing rate-independent hysteretic re- sponse of shape-memory alloys und... more We formulate a model describing rate-independent hysteretic re- sponse of shape-memory alloys under slow external forcing. Under natural as- sumptions we prove that this model has solution. The microstructure is treated on a \mesoscopic" level, described by volume fractions of particular phases in terms of Young measures. The whole formulation is based on energetic function- als for energy storage and

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