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Global existence for a nuclear fluid in one dimension: the T > 0 case

Bernard Ducomet (2002)

Applications of Mathematics

We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure P which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system,...

Implicit constitutive solution scheme for Mohr-Coulomb plasticity

Sysala, Stanislav, Čermák, Martin (2017)

Programs and Algorithms of Numerical Mathematics

This contribution summarizes an implicit constitutive solution scheme of the elastoplastic problem containing the Mohr-Coulomb yield criterion, a nonassociative flow rule, and a nonlinear isotropic hardening. The presented scheme builds upon the subdifferential formulation of the flow rule leading to several improvements. Mainly, it is possible to detect a position of the unknown stress tensor on the Mohr-Coulomb pyramid without blind guesswork. Further, a simplified construction of the consistent...

Non unicità dell'energia libera per materiali viscoelastici

Dario Graffi, Mauro Fabrizio (1989)

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

La non unicità dell'energia libera per un materiale viscoelastico di tipo «rate» viene provata mediante la determinazione di un controesempio.

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme...

Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics

Kamran Kazmi, Mikael Barboteu, Weimin Han, Mircea Sofonea (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities...

Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

José R. Fernández (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, the quasistatic thermoviscoelastic thermistor problem is considered. The thermistor model describes the combination of the effects due to the heat, electrical current conduction and Joule's heat generation. The variational formulation leads to a coupled system of nonlinear variational equations for which the existence of a weak solution is recalled. Then, a fully discrete algorithm is introduced based on the finite element method to approximate the spatial variable and an Euler scheme...

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...

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