A viscoelastic contact problem with adhesion and surface memory effects

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The material’s behavior is modelled with a constitutive law with long memory. The contact is with normal compliance, unilateral constraint, memory effects and adhesion. We present the classical formulation of the problem, then we derive its variational formulation and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities and fixed point.

Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

existence, fixed point, mathematical model

M. Sofonea, F. Pătrulescu, A viscoelastic contact problem with adhesion and surface memory effects, Math. Model. Anal., vol. 19, no. 5 (2014), pp. 607-626

https://ictp.acad.ro/patrulescu/papers/2014_Patrulescu_MMA_Viscoelastic_contact_pb_adhesion.pdf

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https://scholar.google.ro/scholar?oi=bibs&hl=ro&cites=10295188013742281490