termoviscoelastic

Thermoviscoelastic, or thermo-viscoelastic, describes the time- and temperature-dependent mechanical behavior of materials whose viscoelastic response is strongly influenced by thermal conditions. In these materials, stresses and strains depend not only on deformation history but also on the temperature field, which can vary in space and time and may be coupled to the mechanical state through partial differential equations.

In linear thermo-viscoelastic theory, the stress-strain relation is often expressed as a convolution with a relaxation modulus that depends on temperature, G(t, T). Temperature changes shift and reshape the material’s relaxation spectrum, which is commonly represented by a Prony-series expansion using generalized Maxwell or Kelvin-Voigt models. Time-temperature superposition principles (TTSP) allow properties measured at one temperature to be shifted to another, using shift factors from Arrhenius-type or Williams–Landel–Ferry (WLF) equations. More advanced formulations incorporate nonlinearities, anisotropy, and large deformations.

Governing equations couple mechanics and heat transfer. The momentum balance ∇·σ + b = ρa uses a stress σ that reflects thermo-viscoelastic history. The energy balance, ρc ∂T/∂t = ∇·(k∇T) + r, includes mechanical dissipation Q = σ:ε̇, linking temperature evolution to deformation. Constitutive models may be implemented in finite-element analyses to predict behavior under complex loading and thermal histories.

Key materials include polymers, elastomers, bituminous mixtures, coatings, and some biological tissues. Experimental characterization uses dynamic mechanical analysis, creep and stress-relaxation tests at various temperatures, and calibration of Prony-series parameters. Thermoviscoelasticity is essential for design in damping, adhesives, packaging, and thermal-stress analysis where temperature and time effects are intertwined.