Multiphysics computation of thermal tissue damage as a consequence of electric power absorption

Abali, Bilen Emek; Zohdi, Tarek I.

doi:10.1007/s00466-019-01757-5

Cited by 7 publications

(2 citation statements)

References 36 publications

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“…The use of a variational principle is a highly effective and safe conceptual tool for developing complex theories regarding generalized continua [21][22][23][24][25][26][27][28], or approximate theories of structural components, alongside natural boundary conditions [29]. Additionally, it may serve as a preparatory step towards the establishment of a comprehensive thermo-mechanical formulation, a synthetic viewpoint to facilitate the proof of many mathematical theorems, and the theoretical basis for the application of modern numerical techniques like, for instance, the finite element method [30][31][32][33][34][35][36][37][38]. Variational principles are a widely accepted method of organizing information about dynamic systems and developing their evolution equations [7,[39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

Giorgio,

Placidi

2024

Meccanica

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A variational model has been developed to investigate the coupled thermo-mechanical response of a three-dimensional continuum. The linear Partial Differential Equations (PDEs) of this problem are already well-known in the literature. However, in this paper, we avoid the use of the second principle of thermodynamics, basing the formulation only on a proper definition (i) of kinematic descriptors (the displacement and the entropic displacement), (ii) of the action functional (with kinetic, internal and external energy functions) and (iii) of the Rayleigh dissipation function. Thus, a Hamilton–Rayleigh variational principle is formulated, and the cited PDEs have been derived with a set of proper Boundary Conditions (BCs). Besides, the Lagrangian variational perspective has been expanded to analyze linear irreversible processes by generalizing Biot’s formulation, namely, including thermal inertia in the kinetic energy definition. Specifically, this implies Cattaneo’s law for heat conduction, and the well-known Lord–Shulman model for thermo-elastic anisotropic bodies is then deduced. The developed variational framework is ideal for the perspective of analyzing the thermo-mechanical problems with micromorphic and/or higher-order gradient continuum models, where the deduction of a coherent system of PDEs and BCs is, on the one hand, not straightforward and, on the other hand, natural within the presented variational deduction.

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Section: Introductionmentioning

confidence: 99%

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

Giorgio,

Placidi

2024

Meccanica

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“…Adding higher gradients to the formulation [33,34] is powerful for computational reasons; not only in ductile materials [35], but also in general [36][37][38]. Variational formulation for generalized mechanics [39,40] is challenging and including damage is yet unresolved, among others, we refer to [41] for parameter sensitivity in brittle materials, to [42,43] for elastoplasticity, to [44,45] for involving anisotropy, to [46] for viscoelastoplasticity, to [47] for crack branching, to [48] for thermal damage, and to [49] for multiphysics applications.…”

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confidence: 99%

A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

et al. 2021

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Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher-order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open-source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.

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Plane Waves Transmission and Reflection at the Interface Between Thermoelastic Continua in Absence of Dissipation: The Influence of Magnetic Field and Rotation

Abo‐Dahab

Abd-Alla

Elsagheer

2020

Advanced Structured Materials

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Multiphysics computation of thermal tissue damage as a consequence of electric power absorption

Cited by 7 publications

References 36 publications

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

Plane Waves Transmission and Reflection at the Interface Between Thermoelastic Continua in Absence of Dissipation: The Influence of Magnetic Field and Rotation

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