thermomechanics

Thermomechanics is an interdisciplinary field that studies the interaction between thermal and mechanical processes in materials and structures. It addresses how temperature fields influence stresses, strains, and deformation, and how mechanical states affect heat generation and temperature distribution. The subject combines principles from thermodynamics, heat transfer, and continuum mechanics to predict the coupled behavior of systems undergoing thermal and mechanical loading.

At the core are balance laws for momentum and energy, coupled through constitutive relations that depend on temperature. The mechanical response is described by the Navier-Cauchy equations or their variants, while heat transfer is described by the heat equation, which may include conduction, convection, radiation, and internal heat sources. Temperature-dependent material properties, such as density, thermal conductivity, specific heat, and elastic moduli, are essential in modeling. Thermomechanics often requires considering nonlinear or rate-dependent effects and may involve phase changes, damage, or plastic deformation.

Thermoelasticity deals with small deformations and linear coupling between temperature and strain. More general models cover thermoelastic-plasticity and thermo-viscoelasticity to account for large deformations, rate effects, and irreversible processes, including phase changes and creep.

Key phenomena include thermal expansion, temperature-dependent stiffness, thermal stresses due to gradients, creep and fatigue at high temperature, phase transformations with latent heat, and thermally induced vibrations or instabilities. Boundary conditions for thermomechanics often involve prescribed temperatures or heat fluxes on surfaces, along with mechanical loads.

Common methods include analytical solutions for simple geometries, and numerical approaches such as finite element analysis to solve coupled field equations. Experimental techniques combine thermography, digital image correlation, and strain/stress measurements to validate models.

Applications span electronics cooling and thermal management, aerospace and automotive components subject to thermal cycling, energy systems, and additive manufacturing, where temperature histories influence microstructure and mechanical properties.