A unified model for adhesive interfaces with damage, viscosity and friction (original) (raw)

A unified model for adhesive interfaces with damage, viscosity and friction [conference 2009]

HAL (Le Centre pour la Communication Scientifique Directe), 2009

A general framework for models describing adhesive contact between rigid bodies is proposed. The intensity of adhesion is supposed to decrease under the action of prescribed tangential and normal relative displacements. The reduction is attributed to progressive damage, and comes with energy dissipation. Additional dissipation due to viscosity and friction is also taken into account. The response of the interface is described by a single state variable. It is determined by general laws expressing a mechanical version of the first two laws of thermodynamics, combined with a set of phenomenological assumptions.

Analysis of a temperature-dependent model for adhesive contact with friction

Physica D: Nonlinear Phenomena, 2014

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 momentum balance for the vector of small 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.

Multiphysics modeling of adhesive interface with damage

HAL (Le Centre pour la Communication Scientifique Directe), 2022

In the context of fuel-cladding interaction modelling in fast nuclear reactors, a multiphysics cohesive zone model of an adhesive interface with damage is proposed in this work. For the moment, only traction/compression behaviour can be described with this model. The effects of temperature, mechanical state, damage and chemical reactions are incorporated in adhesive links modelling. Thermal conductivity is affected by damage. In traction, we model elastic-brittle behaviour which depends on temperature and adhesive links. In compression, we model solid-solid contact.

Friction and adhesion

2006

The studies carried out on adhesion by the group "Modeling in Contact Mechanics" at the LMA are reviewed in this paper and recent applications are presented. Based on the introduction of the adhesion intensity variable developed by M. Frémond, different forms of a model coupling adhesion to unilateral contact and friction have been developed. The formulations are given either under the form of implicit variational inequalities or the one of complementarity problems. Both quasi-static and dynamic formulations are considered. The model is non smooth because we do not use any regularization for the unilateral conditions and for the friction, i.e. Signorini conditions and strict Coulomb law are written. In the thermodynamics analysis, the state and the complementarity laws are then written using subdifferentials and differential inclusions because of the non convexity and non differentiability of the potentials. For the dynamics, the formulation is given in term of differential measures in order to deal with the non continuity of the velocities that may occur in the solutions. This work therefore owes much to the theories and the numerical scheme developed by J.-J. Moreau and M. Jean.

Adhesive Contact of Visco-elastic Bodies and Defect Measures Arising by Vanishing Viscosity

SIAM Journal on Mathematical Analysis, 2013

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow rule for debonding the adhesive is considered rate-independent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when delamination is in Mode II (pure shear). The solutions thus obtained involve certain defect-like measures recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity. Reflecting also the conventional engineering concept, the delamination is thus driven by stress rather than energy. An explicit example leading to a nontrivial defect measure is given. Summary of the basic notation used throughout the paper.

Theory of viscoelastic adhesion and friction

Extreme Mechanics Letters

We present a novel theory of the adhesive contact of linear viscoelastic materials against rigid substrates moving at constant velocity. Despite the non-conservative behavior of the system, the closure equation of the contact problem can be rigorously formulated in the form of a local energy balance. In the case of adhesiveless contacts, this is equivalent to enforce the stationarity of the total energy stored into the viscoelastic material. However, in the presence of interfacial adhesion, the appearance of non-conservative terms leads to different values of the energy release rates G1 and G2 at the contact trailing and leading edges, respectively. Specifically, the present theory predicts a non-monotonic trend of G1 and G2 as function of the indenter velocity, as well as a very significant enhancement of hysteretic friction due to the coupling between adhesion and viscoelasticity, compared to the adhesiveless case. Both predictions are in very good agreement with existing experimental data.

Interface models coupling adhesion and friction

Comptes Rendus Mecanique, 2011

Interface models coupling friction and adhesion, where adhesion is regarded as interface damage, are briefly reviewed. The most widely used cohesive zone models are presented and discussed. A general framework for these laws, recently developed by Del Piero and Raous in the form of a unified model, is outlined. As an example, it is here established that the RCCM (Raous-Cangémi-Cocou-Monerie) model is a specific case in this general framework. The variational formulation and some associated solvers are briefly recalled in the context of non smooth mechanics in the cases of both quasi-static and dynamic problems. A few examples in various fields of application are given. Lastly, some open problems and ongoing researches in this field are presented and discussed.

Long-time behaviour of a thermomechanical model for adhesive contact

Discrete and Continuous Dynamical Systems - Series S, 2010

This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a surface damage model proposed by M. Frémond. Thermal effects are governed by entropy balance laws. The resulting system is highly nonlinear, mainly due to the presence of internal constraints on the physical variables and the coupling of equations written in a domain and on a contact surface. We prove existence of solutions on the whole time interval (0, +∞) by a double approximation procedure. Hence, we are able to show that solution trajectories admit cluster points which fulfil the stationary problem associated with the evolutionary system, and that in the large-time limit dissipation vanishes. AMS (MOS) Subject Classification: 35K55, 74A15, 74M15.

Thermodynamics and analysis of rate-independent adhesive contact at small strains

2011

We address a model for adhesive unilateral frictionless Signorini-type contact between bodies of heatconductive viscoelastic material, in the linear Kelvin-Voigt rheology, undergoing thermal expansion. The flow-rule for debonding the adhesion is considered rate-independent and unidirectional, and a thermodynamically consistent model is derived and analysed as far as the existence of a weak solution is concerned.

Existence and Regularity for Dynamic Viscoelastic Adhesive Contact with Damage

Applied Mathematics and Optimization, 2006

A model for the dynamic process of frictionless adhesive contact between a viscoelastic body and a reactive foundation, which takes into account the damage of the material resulting from tension or compression, is presented. Contact is described by the normal compliance condition. Material damage is modelled by the damage field, which measures the pointwise fractional decrease in the loadcarrying capacity of the material, and its evolution is described by a differential inclusion. The model allows for different damage rates caused by tension or compression. The adhesion is modelled by the bonding field, which measures the fraction of active bonds on the contact surface. The existence of the unique weak solution is established using the theory of set-valued pseudomonotone operators introduced by Kuttler and Shillor (1999). Additional regularity of the solution is obtained when the problem data is more regular and satisfies appropriate compatibility conditions.