Solid-solid phase-transition as a strain transformation.
Carmine Trimarco (1996)
Extracta Mathematicae
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Displaying similar documents to “Unique global solvability of 1D Fried-Gurtin model”
Solid-solid phase-transition as a strain transformation.
Non-local continuum thermodynamic extensions of crystal plasticity to include the effects of geometrically-necessary dislocations on the material behaviour.
Svendsen, B. (2000)
Rendiconti del Seminario Matematico
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Generalized Cahn-Hilliard equations based on a microforce balance.
Miranville, Alain (2003)
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Models for phase separation and their mathematics.
Fife, Paul C. (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Development of three dimensional constitutive theories based on lower dimensional experimental data
Satish Karra, Kumbakonam R. Rajagopal (2009)
Applications of Mathematics
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Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored...
Hysteresis operators in phase-field models of Penrose-fife type
Pavel Krejčí, Jürgen Sprekels (1998)
Applications of Mathematics
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Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical...
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
Pierluigi Colli (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time
Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)
Banach Center Publications
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A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase. ...
Measure-valued solutions of a heterogeneous Cahn-Hilliard system in elastic solids
Irena Pawłow, Wojciech M. Zajączkowski (2008)
Colloquium Mathematicae
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The paper is concerned with the existence of measure-valued solutions to the Cahn-Hilliard system coupled with elasticity. The system under consideration is anisotropic and heterogeneous in the sense of admitting the elasticity and gradient energy tensors dependent on the order parameter. Such dependences introduce additional nonlinearities to the model for which the existence of weak solutions is not known so far.