thermoelastische

Thermoelastische, or thermoelastic, describes the coupling between thermal and mechanical fields in solid bodies. It investigates how temperature changes induce elastic strains and, conversely, how mechanical deformation interacts with heat distribution. This field is a part of continuum mechanics and is used to predict thermal stresses and deformations in engineering components.

In linear thermoelasticity, the stress tensor sigma_ij is related to the elastic strain epsilon_kl by the constitutive equation sigma_ij = C_ijkl (epsilon_kl - alpha_kl Delta T), where C_ijkl is the elastic stiffness tensor, alpha_kl is the thermal expansion tensor, and Delta T is the change in temperature from a reference state. The total strain decomposes into an elastic part and a thermal part, epsilon_ij = epsilon^e_ij + epsilon^th_ij, with epsilon^th_ij = alpha_ij Delta T for many materials, and alpha_ij simplifying to alpha delta_ij in isotropic cases.

The governing equations include mechanical equilibrium div sigma + b = rho a, with appropriate boundary conditions, and a thermal energy equation typically written as rho c dT/dt = k ∇^2 T + Q_mech, where c is specific heat, k is thermal conductivity, and Q_mech represents heat sources from mechanical work or external inputs. In many analyses, coupling terms are neglected or treated as small.

Applications of thermoelastic analysis include predicting thermal stresses in components exposed to temperature gradients (such as turbine blades, bridges, or electronics), guiding design to avoid failure from differential expansion, and supporting non-destructive testing techniques like thermoelastic stress analysis. Numerical methods, especially finite element analysis, are commonly employed for complex, transient, and anisotropic problems.