Deformations of an elastic, internally constrained material. I: Homogeneous deformations
Subject of this extensive research are the finite homogeneous deformations and the stresses accompanying them of an isotropic elastic material subject to Bell's constraint, i.e., the sum of the principal stretches equals three. Firstly, the authors study the kinematics of deformation. Though any small strain deformation is isochoric, large volume preserving deformations as pure shear or simple shear cannot occur. Another consequence of Bell's constraint is that pure dilatation does not exist, i.e., a cube cannot be transformed into a cube of different size. Secondly, based on ordered forces inequalities and ad hoc inequalities, the authors determine the response functions of isotropic elastic materials. Finally, they consider hyperelastic behavior, i.e., they postulate the existence of a strain energy function. It is interesting to note that James F. Bell found the above mentioned constraint experimentally by deforming samples of different annealed metals plastically. He also studied their behavior theoretically within the frame of incremental plasticity. Besides a few exceptions, the results of the present paper are in excellent agreement with Bell's. This is possible since an elastic body and an elastic-plastic body may exhibit the same material response as long as unloading does not occur. This clearly written paper contains an abundancy of results interesting to researchers in elasticity and continuum mechanics. Two additional papers on this topic are announced.
scientific article; zbMATH DE number 147030