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Effective thermal properties of viscoelastic composites having field-dependent constituent properties

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Abstract

This study introduces a micromechanical model for predicting effective thermal properties (linear coefficient of thermal expansion and thermal conductivity) of viscoelastic composites having solid spherical particle reinforcements. A representative volume element (RVE) of the composites is modeled by a single particle embedded in the cubic matrix. Periodic boundary conditions are imposed to the RVE. The micromechanical model consists of four particle and matrix subcells. Micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the subcells. Perfect bonds are assumed along the subcell’s interfaces. Stress and temperature-dependent viscoelastic constitutive models are used for the isotropic constituents in the micromechanical model. Thermal properties of the particle and matrix constituents are temperature dependent. The effective coefficient of thermal expansion is derived by satisfying displacement and traction continuity at the interfaces during thermo-viscoelastic deformations. This formulation leads to an effective time–temperature–stress-dependent coefficient of thermal expansion. The effective thermal conductivity is formulated by imposing heat flux and temperature continuity at the subcells’ interfaces. The effective thermal properties obtained from the micromechanical model are compared with analytical solutions and experimental data available in the literature. Finally, parametric studies are also performed to investigate the effects of nonlinear thermal and mechanical properties of each constituent on the overall thermal properties of the composite.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843-3123, USA

    Kamran A. Khan & Anastasia H. Muliana

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  1. Kamran A. Khan
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  2. Anastasia H. Muliana
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Correspondence to Anastasia H. Muliana.

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Khan, K.A., Muliana, A.H. Effective thermal properties of viscoelastic composites having field-dependent constituent properties. Acta Mech 209, 153–178 (2010). https://doi.org/10.1007/s00707-009-0171-6

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  • DOI: https://doi.org/10.1007/s00707-009-0171-6

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