113 research outputs found
Global existence for a nonlocal model for adhesive contact
In this paper we address the analytical investigation of a model for adhesive
contact, 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 integral 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
Analysis of a unilateral contact problem taking into account adhesion and friction
AbstractIn 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
A coupled rate-dependent/rate-independent system for adhesive contact in Kirchhoff-Love plates
We perform a dimension reduction analysis for a coupled
rate-dependent/rate-independent adhesive-contact model in the setting of
visco-elastodynamic plates. We work with a weak solvability notion inspired by
the theory of (purely) rate-independent processes, and accordingly term the
related solutions `Semistable Energetic'. For Semistable Energetic solutions,
the momentum balance holds in a variational sense, whereas the flow rule for
the adhesion parameter is replaced by a semi-stability condition coupled with
an energy-dissipation inequality. Prior to addressing the dimension reduction
analysis, we show that Semistable Energetic solutions to the three-dimensional
damped adhesive contact model converge, as the viscosity term tends to zero, to
three-dimensional Semistable Energetic solutions for the undamped corresponding
system. We then perform a dimension reduction analysis, both in the case of a
vanishing viscosity tensor (leading, in the limit, to an undamped model), and
in the complementary setting in which the damping is assumed to go to infinity
as the thickness of the plate tends to zero. In both regimes, the presence of
adhesive contact yields a nontrivial coupling of the in-plane and out-of-plane
contributions. In the undamped scenario we obtain in the limit an
energy-dissipation inequality and a semistability condition. In the damped
case, instead, we achieve convergence to an enhanced notion of solution,
fulfilling an energy-dissipation balance
The Alestle - Vol. 61 No. 43 - 02/17/2009
Vol. 61 No. 4
Thermal effects in adhesive contact: modelling and analysis
In this paper, we consider a contact problem with adhesion between a
viscoelastic body and a rigid support, taking thermal effects into account. The
PDE system we deal with is derived within the modelling approach proposed by M.
Fremond and, in particular, includes the entropy balance equations, describing
the evolution of the temperatures of the body and of the adhesive material. Our
main result consists in showing the existence of global in time solutions (to a
suitable variational formulation) of the related initial and boundary value
problem
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