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In this paper we introduce a model describing a layered structure composed by two thermoelastic adherents and a thin adhesive subject to a degradation process. By an asymptotic expansion method, we derive a model of imperfect interface coupling damage and temperature evolution. Moreover, assuming that the behaviour of the adhesive is ruled by two different regimes, one in traction and one in compression, we derive a second limit model where unilateral contact conditions on the interface are also included. [ABSTRACT FROM AUTHOR]

In this paper, we address the analytical investigation into a model for adhesive contact introduced in a paper by Freddi and Fremond, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities rendering the unilateral contact conditions, the physical constraints on the internal variables, as well as the contributions related to the nonlocal forces. For the associated initial-boundary value problem, we obtain a global-in-time existence result by proving the existence of a local solution via a suitable approximation procedure and then by extending the local solution to a global one by a nonstandard prolongation argument. [ABSTRACT FROM AUTHOR]

In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system combines heat equations, in the bulk domain and on the contact surface, with mechanical force balances, including micro-forces, that result in the equation for the displacements and in the flow rule for the damage-type internal variable describing the state of the adhesive bonds. Nonlocal effects are accounted for by terms featuring integral operators on the contact surface. The analysis of this system poses several difficulties due to its overall highly nonlinear character, and in particular to the presence of quadratic terms, in the rates of the strain tensor and of the internal variable, that appear in the bulk and surface heat equations. Another major challenge is related to proving strict positivity for the bulk and surface temperatures. We tackle these issues by very careful estimates that enable us to prove the existence of global-in-time solutions and could be useful in other contexts. All calculations are rigorously rendered on an accurately devised time discretization scheme in which the limit passage is carried out via variational techniques. [ABSTRACT FROM AUTHOR]

We propose a model for (unilateral) contact with adhesion between a viscoelastic body and a rigid support, encompassing thermal and frictional effects. Following Frémond ’s approach, adhesion is described in terms of a surface damage parameter χ . The related equations are the (quasistatic) momentum balance for the vector of displacements, and parabolic-type evolution equations for χ , and for the absolute temperatures of the body and of the adhesive substance on the contact surface. All of the constraints on the internal variables, as well as the contact and the friction conditions, are rendered by means of subdifferential operators. Furthermore, the temperature equations, derived from an entropy balance law, feature singular functions. Therefore, the resulting PDE system has a highly nonlinear character. After introducing a suitable regularization of the Coulomb law for dry friction, we address the analysis of the resulting PDE system. The main result of the paper states the existence of global-in-time solutions to the associated Cauchy problem. It is proved by passing to the limit in a carefully tailored approximate problem, via variational techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate a contact problem between a viscoelastic body and a rigid foundation, when both the effects of the (irreversible) adhesion and of the friction are taken into account. We describe the adhesion phenomenon in terms of a damage surface parameter according to Frémondʼs theory, and we model unilateral contact by Signorini conditions, and friction by a nonlocal Coulomb law. All the constraints on the internal variables as well as the contact and the friction conditions are rendered by means of subdifferential operators, whence the highly nonlinear character of the resulting PDE system. Our main result states the existence of a global-in-time solution (to a suitable variational formulation) of the related Cauchy problem. It is proved by an approximation procedure combined with time discretization. [Copyright &y& Elsevier]

A dynamic unilateral contact problem between two thermoelastic beams is considered. Under thermal boundary conditions involving heat transfer, the evolution problem is shown to possess an energy decaying exponentially to zero, as time goes to infinity. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a phase transitions model describing the evolution of damage in thermoviscoelastic materials. The resulting system is highly non-linear, mainly due to the presence of quadratic dissipative terms and non-smooth constraints on the variables. Existence and uniqueness of a solution are proved, as well as regularity results, on a suitable finite time interval. [Copyright &y& Elsevier]

Abstract: In this paper we analyze a dynamic unilateral contact problem between two thermoelastic beams. We establish the existence of a weak global-in-time solution, by a penalization method. Moreover, we study the asymptotic behavior of such a solution proving that the energy associated to the system decays exponentially to zero, as time goes to infinity. [Copyright &y& Elsevier]

Abstract: We obtain an existence and uniqueness result to Frémond''s phase transition model which take into account microscopic movements and accelerations. Moreover, the irreversible evolution of the phase variable is considered. Next, we perform an asymptotic analysis on the solution to the above problem, as the power of the microscopic acceleration forces goes to zero. [Copyright &y& Elsevier]

A recent phase transition model, proposed by Frémond, is based on the consideration that the microscopic movements are responsible for the phase transition at the macroscopic level. A last version of the model, accounting also for the microscopic accelerations has been investigated in Ref. 4, where well-posedness results are established for related Cauchy–Neumann problems. The aim of this paper is the study of the asymptotic behavior of the solution to one of the above problems, as the power of the microscopic acceleration forces goes to zero. [ABSTRACT FROM AUTHOR]

Microscopic movements are responsible for the phase transition at the macroscopic level. The power of the microscopic accelerations of these motions is not neglected, as opposed to some previous works, in the derivation of phase transition models accounting for strong dissipation or irreversible phenomena. Such models lead to nonlinear parabolic–hyperbolic systems. Some existence and uniqueness results are established, through fixed point and regularization arguments, for related Cauchy–Neumann problems. [Copyright &y& Elsevier]

This paper presents results on existence and uniqueness of solutions to a three-dimensional thermoviscoelastic system. The constitutive relations of the model are recovered by a free energy functional and a pseudo-potential of dissipation. Using a fixed point argument, combined with an a priori estimates-passage to the limit technique, we prove a local existence result for a related initial and boundary values problem. Hence, uniqueness of the solution is proved on the whole time interval, as well as positivity of the absolute temperature. [ABSTRACT FROM AUTHOR]