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Ordered Rate Constitutive Theories for Non-classical Thermoviscoelastic Solids with Dissipation and Memory Incorporating Internal Rotations

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Abstract

This paper presents constitutive theories for non-classical thermoviscoelastic solids with dissipation and memory using thermodynamic framework based on entirety of the displacement gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric parts of the displacement gradient tensor. In this paper, we only consider small deformation small strain; hence, the constitutive theories are basis independent. The constitutive theories are derived in the presence as well as in the absence of balance of moment of moments balance law. It is shown that the energy storage, dissipation mechanism, and the fading memory in the non-classical thermoviscoelastic solids are due to strain rates, rotation rates, stress tensor, moment tensor, and their rates. Constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem. The constitutive theories derived using integrity are followed by simplified constitutive theories. Material coefficients are derived and discussed for both cases. Constitutive models parallel to non-classical Maxwell, Oldroyd-B, and Giesekus models for thermoviscoelastic fluids are derived and shown to be a subset of a more generalized simplified constitutive theory presented in the paper. Retardation moduli are derived for stress tensor as well as moment tensor and are compared with those in classical continuum theories for similar solids.

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Acknowledgments

The first and the third authors are grateful for the support provided by their endowed professorships during the course of this research. Many facilities provided by the Department of mechanical engineering of the University of Kansas are gratefully acknowledged.

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The second author received financial support from the Mechanical Engineering Department of the University of Kansas is also acknowledged.

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Authors and Affiliations

  1. Mechanical Engineering, University of Kansas, Lawrence, KS, USA

    K. S. Surana & D. Mysore

  2. Mechanical Engineering, Texas A&M University, College Station, TX, USA

    J. N. Reddy

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  1. K. S. Surana
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  2. D. Mysore
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  3. J. N. Reddy
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Correspondence to K. S. Surana.

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Surana, K.S., Mysore, D. & Reddy, J.N. Ordered Rate Constitutive Theories for Non-classical Thermoviscoelastic Solids with Dissipation and Memory Incorporating Internal Rotations. Polytechnica 1, 19–35 (2018). https://doi.org/10.1007/s41050-018-0004-2

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