Thermo-Elastic Similarity Laws
In a book edited by Hetenyi [1], Mindlin and Salvadori have discussed certain similarity laws for thermo-elastic problems. They were, however, primarily concerned with the replacement of thermo-elastic problems by purely elastic problems involving dislocations. In the present paper we are concerned with the conditions which must be satisfied by the physical parameters describing the properties of a body and a scale model (scaled both in linear dimensions and time) in order that the stress in the original body may be determined from that at the corresponding position and time in the scale model by means of the multiplier M (= rigidity modulus of body/ rigidity modulus of model). It will be seen that the conditions for the stresses in the body to be an arbitrary constant C times those in the model are then easily obtained. In deriving these conditions much of the mathematical analysis of Mindlin and Salvadori could have been used. However, we have preferred to obtain them by somewhat different methods.