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On a contact problem for a viscoelastic von Kármán plate and its semidiscretization

Igor Bock, Ján Lovíšek (2005)

Applications of Mathematics

We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of...

On implicit constitutive theories

Kumbakonam R. Rajagopal (2003)

Applications of Mathematics

In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....

On one mathematical model of creep in superalloys

Jiří Vala (1998)

Applications of Mathematics

In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the...

On some viscoelastic models

Pasquale Renno (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Sia ℬ n un sistema linearmente viscoelastico, omogeneo ed isotropo, caratterizzato dalla funzione di memoria g n ⁢ ( t ) = ∑ k = 1 n B k ⁢ exp ⁡ ( - β k ⁢ t ) , tipica di numerosi polimeri solidi. Si dimostra che la soluzione fondamentale E n dell’operatore integrodifferenziale che descrive i moti di ℬ n è, in ogni punto del suo supporto, maggiorata da quella relativa ad un opportuno solido standard ℬ 1 Di conseguenza, è possibile applicare all’analisi qualitativa dei moti di ℬ n alcuni risultati stabiliti in [10], quali proprietà asintotiche, principi...

On the Cauchy problem in linear viscoelasticity

Pasquale Renno (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Con riferimento all’operatore integrodifferenziale della viscoelasticità lineare nella formulazione creep, si determina la soluzione fondamentale E in corrispondenza di un’arbitraria funzione di memoria. Di conseguenza viene risolto esplicitamente il problema di Cauchy relativo al moto unidimensionale di un sistema viscoelastico ℬ , omogeneo ed isotropo, determinato da dati iniziali e storia di stress comunque prefissati. Successivamente, nell’ambito di opportune ipotesi di memoria labile, si dimostrano...

One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.

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