From classical to Voigt's molecular models in elasticity
In the first decades of the 19th century Cauchy, Poisson and others developed a corpuscular theory of elasticity based on the assumption that matter consists of material points that interact by means of opposite central forces. Their theory suggested that homogeneous isotropic materials were characterized by means of one unique constant of elasticity. However, experiments showed that two constants were necessary instead of only one and in 1839 searching for a model of the aether, George Green came up with another approach based on the assumption that matter can be considered as continuous. By postulating the existence of a potential function Green succeeded in explaining the existence of the two constants and his theory meant serious competition for the corpuscular theory. However, in the 1880s, basing himself on Bravais' crystallographic work, Woldemar Voigt developed a corpuscular theory that was confirmed by experiments. In this paper this development is discussed, although the emphasis is on Voigt's work. The authors argue that although Voigt's model of an elastic material is forgotten now, it is still important and it deserves to be studied by those who are today studying complex or new materials.
scientific article; zbMATH DE number 5805945