The influences of mechanical loads on the form of a growing elastic body.

Abstract In this paper the influences of certain classes of mechanical loads on the configuration of a growing body are studied for a special class of linear material. The specific problem is: If the form to which a body grows under no externally applied loads is known, what will be the form of the body if some mechanical loads are applied to it during growth? Constitutive equations are formulated for the particular class of materials satisfying the following requirements: 1. (a) The material grows isotropically in normal growth. 2. (b) The material is normal. 3. (c) The state of growth of the material is completely determined by the current mechanical conditions. 4. (d) The growth is relatively slow and the stress field is quasi-static. The cases of simple tension and simple shear are analyzed for various boundary conditions and the resulting effects of stress on growth are discussed.