Before entering into some details of the integration of the previous equations, it is interesting to consider a few comments on the physics that produces residual stresses and deformations. Imagine an initially stress-free glass sample at a high and uniform temperature. The sample is cooled via a heat exchange with the outside world (for example, convection). The actual temperature decreases nonuniformly at a rate that depends on the cooling conditions. We already understand that the thermal history of individual glass particles will differ. From Equation 26–8, we see that a nonuniform fictive temperature field develops, at the same time as a nonuniform thermal strain field . Simultaneously, with the decay of both actual and fictive temperatures, the reduced time scale is modified and slows down. Stresses develop in accordance with the constitutive Equation 26–2; they relax at a decreasing speed, since the reduced time slows down.

It is important to note that the nonuniform thermal history of the individual glass particles creates a nonuniform field of thermal strain. Thus, even though elastic boundary conditions may be selected in such a way that no mechanical stress is generated, internal stresses will be created because of the thermal history. From Equation 26–8, we also understand that residual stresses and deformations will be reduced when the cooling rate is low. Indeed, under such conditions, the fictive temperature will remain close to the actual one. When the cooling rate is fast, the fictive temperature can be frozen at a high value, and this will then be accompanied by an extremely long relaxation mechanism due to the sharp decrease of the reduced time.