A rod fixed between two rigid walls is heated so that it would expand by ΔL if free, but the walls prevent any expansion. If Youngs modulus is Y, area A, and coefficient of linear expansion is α, the thermal stress (compressive force per area) developed is:

A typical stress-strain curve: the initial straight line (Hooke's Law region, slope = Young's modulus) ends at the elastic limit; beyond the yield point, deformation becomes permanent, peaking at the ultimate tensile strength before the wire finally fractures.