From classical to Voigt’s molecular models in elasticity

Abstract

In the first decades of the nineteenth century the French mechanicians—Cauchy and Poisson amongst them—developed a theory of linear elasticity according to which matter is composed of material points. They believed that these points interact by means of opposite central forces, whose magnitude depends on the length of the segment joining the particles. This theory suggested that homogeneous isotropic materials were characterized by a unique elastic constant. Later experiments, however, showed that two elastic constants were necessary. These results undermined the corpuscular model of matter as well as the interpretation of elasticity in terms of central intermolecular actions. The continuous theory of Green, based on the postulate that a potential function exists, gained fresh consensus in light of these experiments. These opposite views continued throughout the nineteenth century until Woldemar Voigt proposed a molecular model confirmed by experiments. This article presents the theories of each of these scientists and describes the contrasting views of nineteenth-century mechanicians.