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Ordered rate constitutive theories for thermoviscoelastic solids without memory incorporating internal and Cosserat rotations

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Abstract

The work in this paper is based on a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory in which the conservation and balance laws are derived by incorporating internal rotations (\({}_i \pmb {\varvec{{\varTheta } }}\)) arising from the Jacobian of deformation (\( \pmb {\varvec{J }}\)), as well as Cosserat rotations (\({}_e \pmb {\varvec{{\varTheta } }}\)) at a material point. Such non-classical solids have additional energy storage due to rotations and additional dissipation due to rotation rates compared to classical continuum theories. Rotations \({}_i \pmb {\varvec{{\varTheta } }}\) are completely defined by \( \pmb {\varvec{J }}\), whereas displacements \( \pmb {\varvec{u }}\) and Cosserat rotations \({}_e \pmb {\varvec{{\varTheta } }}\) are degrees of freedom at each material point. When \({}_i \pmb {\varvec{{\varTheta } }}\) and \({}_e \pmb {\varvec{{\varTheta } }}\) are resisted by the deforming matter, conjugate moments arise, which together with (\({}_i \pmb {\varvec{{\varTheta } }},{}_e \pmb {\varvec{{\varTheta } }}\)) and (\({}_i\overset{\,\text{. }}{ \pmb {\varvec{{\varTheta } }}},{}_e\overset{\,\text{. }}{ \pmb {\varvec{{\varTheta } }}}\)) result in additional work and rate of work. This paper utilizes thermodynamic framework for non-classical solids derived based on internal as well as Cosserat rotations and presents a thermodynamically consistent derivation of the constitutive theories that incorporate the aforementioned deformation physics. The constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem.

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

    K. S. Surana & A. D. Joy

  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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Surana, K.S., Joy, A.D. & Reddy, J.N. Ordered rate constitutive theories for thermoviscoelastic solids without memory incorporating internal and Cosserat rotations. Acta Mech 229, 3189–3213 (2018). https://doi.org/10.1007/s00707-018-2163-x

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