Quasi-linear versus potential-based formulations of force–flux relations and the GENERIC for irreversible processes: comparisons and examples

Hütter, Markus; Svendsen, Bob

doi:10.1007/s00161-012-0289-y

Cited by 31 publications

(23 citation statements)

References 37 publications

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“…When the mean free path is negligible, Equation (24) reduces to Cattaneo's equation [80,83] τ∂ t q + q = −λ∇T (27) Equation (26) yields the classical entropy flux, while Equation (25) remains unaltered. Finally, when the relaxation time and the mean free path are both negligible, Equation (24) reduces to Fourier's law…”

Section: The Entropy Principle In Extended Irreversible Thermodynamicsmentioning

confidence: 99%

“…Nowadays, this approach has ramifications into the general equation for non-equilibrium reversible-irreversible coupling (GENERIC) [26,27]. Mainly two major directions have been followed in the literature for the specification of force-flux relations.…”

Section: Introductionmentioning

confidence: 99%

“…The second law of thermodynamics is respected by requiring certain properties of the potential, primarily its convexity. It can be proved that every potential-based force-flux relation can be cast into quasi-linear form, while the reverse statement does not hold true [27]. It is worth noting that GENERIC can be formulated either in a quasi-linear form [26] or in a dissipation-potential based form [28].…”

Section: Introductionmentioning

confidence: 99%

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Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

Entropy

102

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We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

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Section: The Entropy Principle In Extended Irreversible Thermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

Entropy

102

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“…Requiring these to satisfy Onsager-Casimir conditions (e.g., [35,36]) ensures (sufficient) satisfaction of the dissipation principle δ 0. Assuming the kinetic coefficients satisfy additional constraints (e.g., integrability: [37]), (31) reduce to potential form, i.e.,…”

Section: Basic Constitutive Relations and Dissipation Principlementioning

confidence: 99%

“…Consider next the model for the free energy density. For purposes of comparison with the phenomenological approach of [1], this model is formulated in a form comparable to (37). To this end, the dependence of ψ in (37) on p is replaced by one on p R (λ(μ)) from (48) via (51).…”

Section: Model Based On Sequential Laminatesmentioning

confidence: 99%

Comparison of phenomenological and laminate‐based models for rate‐dependent switching in ferroelectric continua

2015

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MSC (2000) 74A20, 74A60, 74F15, 74N15The purpose of the current work is the comparison of a phenomenological and a laminatebased model for rate-dependent switching in ferroelectric single crystals. To this end, the phenomenological model formulation of [1] is considered. In this model, the polarization vector is treated as an internal variable. The evolution of the polarization determines the remanent strain; dependence of energy storage on its direction results in generally transverse isotropic material behavior. This is compared here with a laminate-based model in which the volume fractions of ferroelectric variants are treated as internal variables. The evolution of these volume fractions determines in turn the remanent strain and polarization as volume averages of corresponding ferroelectric variant quantities. Besides a comparison of the respective model formulations, the phenomenological and laminate models are compared in the context of numerical simulation examples. It turns out that both modeling frameworks nicely recapture the underlying dissipative and rate-dependent effects, which is represented by means of simulated butterfly curves and hysteresis loops under homogeneous loading conditions as well as by finite element simulations.

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Examples

Saramito

2023

Surveys and Tutorials in the Applied Mathematical Sciences

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Quasi-linear versus potential-based formulations of force–flux relations and the GENERIC for irreversible processes: comparisons and examples

Cited by 31 publications

References 37 publications

Entropy Principle and Recent Results in Non-Equilibrium Theories

Entropy Principle and Recent Results in Non-Equilibrium Theories

Comparison of phenomenological and laminate‐based models for rate‐dependent switching in ferroelectric continua

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