Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling

Roubíček, Tomáš; Stefanelli, Ulisse

doi:10.1137/17m1137656

Cited by 13 publications

(10 citation statements)

References 56 publications

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“…(F, c, θ), and ξ from (2.10). In (6.12b), the variable μ is called the chemical potential that is thermodynamically conjugate to c. One can also augment the model by some inelastic (plastic or creep-type) strain like in [45], where also the inertial forces are included, whereas viscosity is ignored and the restriction to small elastic strains is imposed.…”

Section: M(∇ Yc)mentioning

confidence: 99%

Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains

Mielke

Roubíček

2020

Arch Rational Mech Anal

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The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization.

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Section: M(∇ Yc)mentioning

confidence: 99%

Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains

Mielke

Roubíček

2020

Arch Rational Mech Anal

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“…9.4.2]. A combination of the Cahn-Hilliard models with plasticity can also be considered, like [3,31].…”

Section: Remark 3 (Allen-cahn Modification: Damage or Phase-transformmentioning

confidence: 99%

“…Nevertheless, when the transport by Fick/Darcy law is considered in actual space deforming configuration as e.g. in [3,20,31,32], it rather mis-conceptual to involve gradient of concentration in the material configuration. And indeed, sometimes the Cahn-Hilliard with the concentration gradient in the actual configuration can be found in engineering literature [9,18,23] but, of course, without any analysis.…”

Section: Introductionmentioning

confidence: 99%

Cahn-Hilliard equation with capillarity in actual deforming configurations

Roubíček¹

2021

Discrete &Amp; Continuous Dynamical Systems - S

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Dedicated to Alexander Mielke on the occasion of his sixtieth birthday.Abstract. The diffusion driven by the gradient of the chemical potential (by the Fick/Darcy law) in deforming continua at large strains is formulated in the reference configuration with both the Fick/Darcy law and the capillarity gradient term considered at the actual configurations deforming in time. Static situations are analysed by the direct method. Evolution (dynamical) problems are treated by the Galerkin method, the actual capillarity giving rise to various new terms as e.g. the Korteweg-like stress and analytical difficulties related to them. Some other models (namely plasticity at small elastic strains or damage) with gradients at actual configuration allow for similar models and analysis. AMS Subj. Classification: 35Q74, 37N15, 65M60, 74A30, 74G25, 74H20, 76S05.

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“…Still, it allows for some simplification, for it avoids the need for implementing pullback/pushforward of fileds from the reference to the actual configuration, ultimately simplifying transport coefficients. Let us note however, that alternative Lagrangian formulations have been considered in [27][28][29] or [16,Sect.9.6]. In spite of the above mentioned specific analytic intricacies, in contrast with our current Eulerian one, these Lagrangian models allow for a possible treatment of nonhomogeneous Dirichlet conditions on the solid.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastodynamics of swelling porous solids at large strains by an Eulerian approach

Roubíček¹,

Stefanelli²

2022

Preprint

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A model of saturated hyperelastic porous solids at large strains is formulated and analysed. The material response is assumed to be of a viscoelastic Kelvin-Voigt type and inertial effects are considered, too. The flow of the diffusant is driven by the gradient of the chemical potential and is coupled to the mechanics via the occurrence of swelling and squeezing. Buoyancy effects due to the evolving mass density in a gravity field are covered. Higher-order viscosity is also included, allowing for physically relevant stored energies and local invertibility of the deformation. The whole system is formulated in a fully Eulerian form in terms of rates. The energetics of the model is discussed and the existence and regularity of weak solutions is proved by a combined regularization-Galerkin approximation argument.

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Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling

Cited by 13 publications

References 56 publications

Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains

Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains

Cahn-Hilliard equation with capillarity in actual deforming configurations

Viscoelastodynamics of swelling porous solids at large strains by an Eulerian approach

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