1.5.1. Thermal strain

It is well known that (most) materials expand or contract under a temperature change. Let us consider an elastic rod, which is free to expand. The initial temperature is T ₀, and the temperature is changed to some other value T. The axial thermal strain resulting from the temperature change is then given by

where ? _T is the coefficient of linear thermal expansion. The minus sign ensures that ? _T is positive (for the normal cases where a temperature increase gives expansion). Some examples of the numerical values for thermal properties of rocks may be found in Appendix A.

When comparing the thermal expansion for rocks with that of fluids, it is important to be aware that for fluids one often specifies the coefficient of volumetric thermal expansion, ? _{T , V} = 3 ? _T.

1.5.2. Thermal stress

If the rod is constrained at the ends, such that it can not change it s length, a thermal stress will build up when the temperature increases. The magnitude of the thermal stress may be inferred by requiring that the thermal stress should give a strain of opposite sign and equal magnitude to the thermal strain computed from Eq. (1.116). FromEq. (1.91) we see that the thermal stress resulting from a temperature change T ? T ₀ for a rod which is fully constrained in one direction is

1.5.3. Stress strain relation for linear thermoelasticity

In order...