Dynamic solid-solid transitions with phase characterized by an order parameter

Fried, Eliot; Gurtin, Morton E.

doi:10.1016/0167-2789(94)90234-8

Cited by 222 publications

(142 citation statements)

References 28 publications

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“…Prior to presenting such results we first derive an expression for the Eshelby driving force on a domain wall following the procedure of Fried and Gurtin (1994).…”

Section: Planar Domain Wall Solutionsmentioning

confidence: 99%

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Landis

2007

Journal of the Mechanics and Physics of Solids

265

207

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“…Prior to presenting such results we first derive an expression for the Eshelby driving force on a domain wall following the procedure of Fried and Gurtin (1994).…”

Section: Planar Domain Wall Solutionsmentioning

confidence: 99%

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Landis

2007

Journal of the Mechanics and Physics of Solids

265

207

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“…This view may appear reminiscent of those of Fried and Gurtin [2,3] and Frémond et al (see, e.g. [4,5]) in which the phase transition is based on a balance equation of microforces.…”

Section: Fabrizio C Giorgi and A Morromentioning

confidence: 87%

“…The model so established is shown to involve the free energy in the rescaled form (see [7]). In [2,3], the crucial step is the introduction of microforces and the associated power in the balance of energy, whereas the second law is kept in the classical Clauius-Duhem form. In [5], the modelling equations are established through the principle of virtual power involving the microscopic velocities and the virtual power of acceleration.…”

Section: Fabrizio C Giorgi and A Morromentioning

confidence: 99%

A continuum theory for first‐order phase transitions based on the balance of structure order

Fabrizio¹,

Giorgi

Morro

2007

Math Methods in App Sciences

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SUMMARYFirst-order phase transitions are modelled by a non-homogeneous, time-dependent scalar-valued order parameter or phase field. The time dependence of the order parameter is viewed as arising from a balance law of the structure order. The gross motion is disregarded and hence the body is regarded merely as a heat conductor. Compatibility of the constitutive functions with thermodynamics is exploited by expressing the second law through the classical Clausius-Duhem inequality. First, a model for conductors without memory is set up and the order parameter is shown to satisfy a maximum theorem. Next, heat conductors with memory are considered. Different evolution problems are established through a system of differential equations whose form is related to the manner in which the memory property is represented.

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“…where the last equality is obtained by using (7). Within the present purely mechanical context, the Second Law, or Dissipation Inequality, takes the form:…”

Section: Basic Notionsmentioning

confidence: 99%

“…Thus, π is constitutively determined only wheṅ α = 0. Otherwise, it is constitutively indeterminate and defined by (7). By inserting (12) into the dissipation inequality (10) we obtain the functional inequality:…”

Section: Constitutive Theorymentioning

confidence: 99%

On a continuum theory of brittle materials with microstructure

Duda¹,

Souza²

2004

Mat. apl. comput.

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Abstract. This paper deals with a finite strain continuum theory of elastic-brittle solids with microstructure. A single scalar microstructural field is introduced, meant to represent -even if in a summary way -the concentration of microdefects within the material. A system of microforces, dual to the microstructural field, is axiomatically introduced. The corresponding balance, augmented with suitable constitutive information, yields, inter alia, a kinetic equation for the microstructural field, criteria for damage nucleation, growth and healing as well as a failure criterion based on attainment of a critical value of the microstructural field. The theory is applied for the description of the Mullins effect.Mathematical subject classification: 74C15, 74C20.

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Dynamic solid-solid transitions with phase characterized by an order parameter

Cited by 222 publications

References 28 publications

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

A continuum theory for first‐order phase transitions based on the balance of structure order

On a continuum theory of brittle materials with microstructure

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