0.0.1 Thermal strains We are going to consider the strains produced by changes of temperature (e). These strains have inherently a dilatational nature(thermal expansion or contraction) and do not cause any shear. Thermal strains are proportional to temperature changes. For isotropic materials △66 The total strains (Eii) are then due to the(additive) contribution of the mechanical strains(EM), i.e., those produced by the stresses and the thermal strains. ki(Ek- Ekl Practice problem: Write the relationship between stresses and strains for an isotropic elastic material whose Lame constants are A and u and whose coefficient of thermal expansion is a. constants and0.0.1 Thermal strains We are going to consider the strains produced by changes of temperature (�θ). These strains have inherently a dilatational nature (thermal expansion or contraction) and do not cause any shear. Thermal strains are proportional to temperature changes. For isotropic materials: � θ = αΔθδij (40) ij The total strains (�ij ) are then due to the (additive) contribution of the mechanical strains (�M ij ), i.e., those produced by the stresses and the thermal strains: �ij = � M + � θ (41) ij ij σij = Cijkl� M = Cijkl(�kl − � θ kl kl), or (42) σij = Cijkl(�kl − αΔθδkl) (43) Practice problem: Write the relationship between stresses and strains for an isotropic elastic material whose Lam´e constants are λ and µ and whose coefficient of thermal expansion is α. constants and 7