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A Dynamic Frictionless Contact Problem with Adhesion and Damage

Mohamed Selmani, Lynda Selmani (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with...

A frictional contact problem with adhesion for viscoelastic materials with long memory

Abderrezak Kasri (2021)

Applications of Mathematics

We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Emilio Silva, Clemens Först, Ju Li, Xi Lin, Ting Zhu, Sidney Yip (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials and the...

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