Ordered rate constitutive theories for non-classical thermoviscoelastic solids with memory incorporating internal and Cosserat rotations

Surana, Karan S.; Joy, A. D.; Reddy, J. N.

doi:10.1007/s00161-018-0697-8

Cited by 5 publications

(4 citation statements)

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“…• ðe : σÞ 0 4.1.9 Constitutive theories Surana et al [68,90,91] have presented ordered rate constitutive theories for nonclassical solid continua incorporating internal and Cosserat rotation: thermoelastic solids, thermoviscoelastic solids without memory and thermoviscoelastic solids with memory. Details of the derivations of these theories are too many to include in this paper due to space consideration.…”

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

“…Details of the derivations of these theories are too many to include in this paper due to space consideration. Instead, we outline a clear procedure in the following based on references [68,90,91] that is rather straight forward to follow to derive the desired constitutive theories.…”

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

“…. ; ðm s σ À 1Þ and noting that ε ½0 is no longer an argument tensor of Φ are given by [91]. Constitutive theories are derived using representation theorem and the material coefficients are established using Taylor series expansion of the coefficients in the constitutive theory used to establish linear combination of the generators.…”

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

“…Constitutive theories are derived using representation theorem and the material coefficients are established using Taylor series expansion of the coefficients in the constitutive theory used to establish linear combination of the generators. See Surana et al [91] for details as well as for the derivation of memory modulus and the specialized form of the general constitutive theory for the constitutive models similar to Maxwell, Oldroyd-B and Giesekus.…”

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

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Non-classical continuum theories for solid and fluent continua and some applications

Surana

Mysore

Reddy

2018

International Journal of Smart and Nano Materials

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This paper presents two specific thermodynamically consistent nonclassical continuum theories for solid and fluent continua. The first non-classical continuum theory for solid continua incorporates Jacobian of deformation in its entirety in the conservation and the balance laws and the derivation of the constitutive theories. The second non-classical continuum theory for solid continua considers Jacobian of deformation in its entirety as well as the Cosserat rotations in the conservation and balance laws as well as the constitutive theories. The first non-classical continuum theory for fluent continua presented here considers velocity gradient tensor in its entirety. The second non-classical continuum theory for fluent continua considers velocity gradient tensor in its entirety as well as Cosserat rotation rates in the derivation of the conservation and balance laws and the constitutive theories. Since the non-classical continuum theories for solid and fluent continua considered here incorporate additional physics of deformation due to rotations and rotation rates compared to classical continuum mechanics, the conservation and balance laws of classical continuum mechanics are shown to require modification as well as a new balance law balance of moment of moments is required to accommodate the new physics due to rotations and rotation rates. Eringen's micropolar, micromorphic and microstretch theories, couple stress theories and nonlocal theories are also discussed within the context of the non-classical theories presented here for solid and fluent continua. Some applications of these theories are also discussed.

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Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

Section: Final Form Of Conservation and Balance Lawsmentioning

confidence: 99%

See 2 more Smart Citations