Finite elastic deformation of incompressible isotropic bodies

Abstract

Abstract The theory of finite elastic deformation of incompressible isotropic bodies is expressed in a simple form in tensor notation, using a general system of co-ordinates which move with the body as it is deformed. In order to illustrate the advantages of the present methods one problem, previously solved by Rivlin, is re-examined. Two new problems are then solved using a completely general form for the strain energy function, the first problem being that of a rotating cylinder, and the second a uniform spherical shell under symmetrical internal and external pressures.