thermoviscoelasticity

Thermoviscoelasticity is the study of materials whose mechanical response exhibits both viscous (time-dependent) behavior and sensitivity to temperature, with mechanical and thermal fields being mutually coupled. In such materials, stress depends on strain, strain rate, temperature, and sometimes the history of these quantities. The theory combines viscoelastic constitutive models with thermoelastic coupling to describe how temperature changes affect deformation and how mechanical work influences heat flow.

Governing equations in thermoviscoelasticity include the balance of linear momentum and the balance of energy, supplemented by constitutive relations that link stress to strain and temperature, and heat flux to temperature and deformation history. In small-strain form, stress can be represented by a viscoelastic model (such as Maxwell, Kelvin-Voigt, or a generalized standard linear solid) with moduli that may vary with temperature. The temperature field is governed by an energy equation that includes heat conduction and possible coupling terms due to thermoelasticity. Common constitutive forms use relaxation (or creep) functions, often represented by Prony series, and may assume Fourier heat conduction with temperature-dependent properties; some generalized theories allow non-Fourier heat laws and thermal inertia.

The field employs several theoretical frameworks, including generalized thermoelasticity (e.g., Lord–Shulman, Green–Lindsay theories) extended to viscoelastic materials. Time-temperature superposition, material anisotropy, and nonlinear effects at large strains or high temperatures are important considerations. Experimental characterization determines relaxation spectra, thermal expansion, specific heat, and thermal conductivity.

Applications span polymers, coatings, adhesives, biological tissues, and geological materials, with numerical modeling typically based on finite element methods to predict coupled thermo-mechanical responses under transient or periodic loading.