Analysis of a unilateral contact problem taking into account adhesion and friction

Bonetti, Elena; Bonfanti, Giovanna; Rossi, Riccarda

doi:10.1016/j.jde.2012.03.017

Cited by 22 publications

(33 citation statements)

References 17 publications

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“…Then, existence of at least one solution can be proved by adapting the procedure given, e.g., in [7]. Here we just reproduce the corresponding regularity estimate, which is needed in order to get (3.14).…”

Section: Proofmentioning

confidence: 99%

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints

Scala

Schimperna²

2016

Eur. J. Appl. Math

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We consider a viscoelastic body occupying a smooth bounded domain Ω ⊂ R 3 under the effect of a volumic traction force g. The macroscopic displacement vector from the equilibrium configuration is denoted by u. Inertial effects are considered; hence the equation for u contains the second order term utt. On a part ΓD of the boundary of Ω, the body is anchored to a support and no displacement may occur; on a second part ΓN ⊂ ∂Ω, the body can move freely; on a third portion ΓC ⊂ ∂Ω, the body is in adhesive contact with a solid support. The boundary forces acting on ΓC due to the action of elastic stresses are responsible for delamination, i.e., progressive failure of adhesive bonds. This phenomenon is mathematically represented by a nonlinear ODE settled on ΓC and describing the evolution of the delamination order parameter z. Following the lines of a new approach outlined in [8] and based on duality methods in Sobolev-Bochner spaces, we define a suitable concept of weak solution to the resulting PDE system. Correspondingly, we prove an existence result on finite time intervals of arbitrary length.

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Section: Proofmentioning

confidence: 99%

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints

Scala

Schimperna²

2016

Eur. J. Appl. Math

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“…The mathematical aspects of the adhesion formulation of [153] have been pursued further in the works of [207,208,209,210] and [211,212,213]. The distance at which the traction according to laws like (37), (38), or (39) decays to zero may be very small, so that in this case, separation is often modeled by disregarding the actual traction-separation law but accounting instead only for the (total bonding) energy change (i.e., release or storage) due to debonding and bonding, which is given by w adh .…”

Section: Survey Of Computational Adhesion 99mentioning

confidence: 99%

A Survey of Computational Models for Adhesion

Sauer

2015

The Journal of Adhesion

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This work presents a survey of computational methods for adhesive contact focusing on general continuum mechanical models for attractive interactions between solids that are suitable for describing bonding and debonding of arbitrary bodies. The most general approaches are local models that can be applied irrespective of the geometry of the bodies. Two cases can be distinguished: local material models governing the constitutive behavior of adhesives, and local interface models governing adhesion and cohesion at interfaces in the form of traction-separation laws. For both models various subcategories are identified and described, and used to organize the available literature that has contributed to their advancement. Due to their popularity and importance, this survey also gives an overview of effective adhesion models that have been formulated to characterize the global behavior of specific adhesion problems.

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“…Their mathematical analysis was developed in a large number of works. Thus, various existence and uniqueness results, examples, numerical analysis and mechanical interpretation in the study of contact problems can be found in [1][2][3][4][5][6][7][8][9][10]. To be accurate mathematical models need to take into consideration the additional phenomena as friction, heat generation, wear or adhesion.…”

Section: Introductionmentioning

confidence: 99%

A mixed variational formulation of a contact problem with adhesion

Pătrulescu

2016

Applicable Analysis

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A mathematical model describing the contact between a viscoplastic body and a deformable foundation is analyzed under small deformation hypotheses. The process is quasistatic and in normal direction the contact is with adhesion, normal compliance, memory effects and unilateral constraint. We derive a mixed-variational formulation of the problem using Lagrange multipliers. Finally, we prove the unique weak solvability of the contact problem. ARTICLE HISTORY

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Analysis of a unilateral contact problem taking into account adhesion and friction

Cited by 22 publications

References 17 publications

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints

A Survey of Computational Models for Adhesion

A mixed variational formulation of a contact problem with adhesion

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