The Theory of Elasticity in the 19th Century

Abstract

Until 1820 there was a limited knowledge about the elastic behavior 1of materials: one had an inadequate theory of bending, a wrong theory of torsion, the definition of Young’s modulus. Studies were made on one-dimensional elements such as beams and bars, and two-dimensional, such as thin plates (see for instance the work of Marie Sophie Germain). These activities started the studies on three dimensional elastic solids that led to the theory of elasticity of three-dimensional continua becoming one of the most studied theories of mathematical physics in the 19th century. In a few years most of the unresolved problems on beams and plates were placed in the archives. In this chapter we report briefly a summary on three dimensional solids, focusing on the theory of constitutive relationships, which is the part of the theory of elasticity of greatest physical content and which has been the object of major debate. A comparison of studies in Italy and those in the rest of Europe is referenced