In most mathematical problems considering voids, why does the equation of balance of Equilibrated force not include any thermal relaxation parameter considering Green-Lindsay theory or any higher order of thermoelasticity?
If we consider piezoelectricity, the extra equation arising due to the presence of an electric field (gauss law) has a thermal relaxation parameter. By the same logic, shouldn't the equation of balance of Equilibrated force also involve a thermal relaxation parameter?
A literature survey reveals that most papers haven't considered any. Can someone please provide some justification?
Dear Sayantan Guha,
generally speaking the GL- or TRD- model is the basic model for its advanced modifications (mainly) in the area of the Extended Thermodynamics.
Maybe the modification is the key-element for your notable question.
The Reason of the Potential Modifications
Besides the mathematical/theoretical interest for extension & generalization, there is also an engineering/numerical interest/reason, which is the Field-Discontinuity Problem (jump/discontinuity of the kinematic field distributions) especially for the security of any fast multi-field process.
Various Potential Modifications
A recent "Elastic"-modification of GL-model [1₁,₂] introduces the strain rate in order to face the above "Elastic"-Discontinuity Problem (jump/discontinuity of the displacement distribution).
Potentially-similar modifications:
1. "(Multi-)Void"-modification [2₁,₂,₃,₄,₅,₆,₇,₈,₉,₁₀,₁₁] ...
... of the GL-model introducing the (multi-)void-gradient rate about the "(Multi-)Void"-Discontinuity.
2. "MicroPolar"-modification [3₁,₂] ...
... of the GL-model introducing the 1st & 2nd micropolar/Cosserat strain rates about the "MicroPolar"-discontinuity.
3. "MicroStretch"-, "Incompressibly-Microstrain"-, "MicroStrain"-, "Incompressibly-Micromorphic", "MicroMorphic"-, "MultiPolar"- modifications [4₁,₂,₃,₄,₅] ...
... of the GL-model are potentially-possible modifications in order to face any microstructural-discontinuity due to the coupling with non mechanical (thermal, diffusive/chemical, hydraulic, EM, ...) fields.
* Relative 20-Bibliography *
- [1₁] Yu, Y.-J., Zhang, N.-X. & Tian, X.-G.: A Modified Green–Lindsay Thermoelasticity with Strain Rate to Eliminate the Discontinuity (2018).
- [1₂] Sarkar, S., De, S. & Sarkar, N.: Modified Green–Lindsay Model on the Reflection and Propagation of Thermoelastic Plane Waves at an Isothermal Stress-Free Surface (2019).
- [2₁] Cowin, S.C. & Nunziato, J.W.: Linear Elastic Materials with Voids (1983).
- [2₂] Cowin, S.C. & Puri, P.: The Classical Pressure Vessel Problems for Linear Elastic Materials with Voids (1983).
- [2₃] Wilson, R.K. & Aifantis, E.C.: On the Theory of Consolidation with Double Porosity — I (1982).
- [2₄] Beskos, D.E. & Aifantis, E.C.: On the Theory of Consolidation with Double Porosity — II (1986).
- [2₅] Khaled, M.Y., Beskos, D.E. & Aifantis, E.C.: On the Theory of Consolidation with Double Porosity — III (1984).
- [2₆] Straughan, B.: Modelling Questions in Multi-Porosity Elasticity (2016).
- [2₇] Straughan, B.: Uniqueness and Stability in Triple Porosity Thermoelasticity (2017).
- [2₈] Svanadze, M: Potential Method in the Linear Theory of Triple Porosity Thermoelasticity (2018).
- [2₉] Svanadze, M: Potential Method in Mathematical Theories of Multi-Porosity Media (2019).
- [2₁₀] Svanadze, M: Fundamental Solutions in the Linear Theory of Thermoelasticity for Solids with Triple Porosity (2019).
- [2₁₁] Svanadze, M: Potential Method in the Theory of Thermoelasticity for Materials with Triple Voids (2019).
- [3₁] Cosserat, E. & Cosserat, F.: Théorie des Corps Déformables (1909).
- [3₂] Kafadar, C.B. & Eringen, A.C.: Micropolar Media — (I) the Classical Theory | — (II) the Relativistic Theory (1971).
- [4₁] Green, A.E. & Rivlin, R.S.: Multipolar Continuum Mechanics (1964).
- [4₂] Green, A.E.: Micro-Materials and Multipolar Continuum Mechanics (1965).
- [4₃] Atkin, R.J. & Fox, N.: A Multipolar Approach to Liquid Helium II (1975).
- [4₄] Eringen, A.C.: Theory of Thermo-Microstretch Elastic Solids (1990).
- [4₅] Eringen, A.C.: Theory of Thermo-Microstretch Fluids and Bubbly Liquids (1990).
Dear Dr. Νικόλαος Κωνσταντής,
Thank you for your answer. It's very informative.
You can see how to obtain the equations of the GL thermoelasticity with voids in the book of Iesan https://www.springer.com/gp/book/9781402023095
If you read how to obtain the equations you will understand
Dear Sayantan,
See the attached paper. Though it is with LS model, but I think you must find some clues of your answer.
With regards
Dr. Nantu Sarkar
Dear Dr. Nantu Sarkar ,
I have gone through some of your remarkable works which include voids and I have some idea on how to proceed.
Grateful for your response.
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