Existence of rotational waves in non-classical thermoelastic solid continua incorporating internal rotations

Surana, Karan S.; Kendall, J. K.

doi:10.1007/s00161-020-00872-6

Cited by 3 publications

(8 citation statements)

References 86 publications

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“…For small strain, small deformation physics the CBL and the constitutive theories presented in reference [3] modified for dissipation due to rate of strain (CCM) and rate of symmetric part of rotation gradient tensor (micropolar NCCT) are given by…”

Section: Micropolar Thermoviscous Elastic Solid (Without Memory)mentioning

confidence: 99%

“…κ = − q g (8) In the mathematical model we have a total of 25 equations BLM(3), BAM(3), BMM (3), FLT (1), constitutive theories for ( )…”

Section: Micropolar Thermoviscous Elastic Solid (Without Memory)mentioning

confidence: 99%

“…We can nondimensionalize (53) using ( 52) and if we choose 0 ρ ρ = , 0 η η = , then the dimensionless form of (53) can be written as i ω i.e., rotation rate about z . We can write the following (with their usual dimensions) using the CBL and the constitutive theories given for 3  by Equations ( 11)-( 22), in the absence of body forces and body moments.…”

Section: Developing Pressure Driven Flow Between Parallelmentioning

confidence: 99%

“…All other micropolar non-classical continuum theories based on Cosserat rotations and Cosserat rotation rates, those considering internal and Cosserat rotations and rotation rates, couple stress NCCT utilizing polynomial or potential functions approach for deriving constitutive theories are either in violation of thermodynamic consistency and/ or mathematical consistency. In reference [3] Surana et al extended the micropolar NCCT of reference [1] based on internal rotations for solid medium to account for rotational inertial physics. This leads to modification of balance of angular momenta (BAM) and balance of moment of moments (BMM) balance laws of reference [1].…”

Section: Introduction Literature Review and Scope Of Current Workmentioning

confidence: 99%

“…Authors in references [3] [4] showed that the requirement of satisfying entropy inequality necessitated that a constraint equation be considered as part of the mathematical model based on CBL and the constitutive theories. Authors discussed (without model problem studies) similarity of BAM in rotation rates in the case of micropolar fluids [4] with the BAM for micropolar solids in rotations in reference [3], but lack of rotational waves in micropolar fluids due to absence of stiffness (due to lack of strain physics). Influence of rotational inertial physics on the evolution of the IVPs in general resulting due to micropolar NCCT was not discussed.…”

Section: Introduction Literature Review and Scope Of Current Workmentioning

confidence: 99%

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NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

Surana,

Kendall

2023

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This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

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Section: Micropolar Thermoviscous Elastic Solid (Without Memory)mentioning

confidence: 99%

“…κ = − q g (8) In the mathematical model we have a total of 25 equations BLM(3), BAM(3), BMM (3), FLT (1), constitutive theories for ( )…”

Section: Micropolar Thermoviscous Elastic Solid (Without Memory)mentioning

confidence: 99%

Section: Developing Pressure Driven Flow Between Parallelmentioning

confidence: 99%