The solution of plastic-elastic problems. I

Abstract The complete solution of a general problem in plasticity involves a calculation of the stress and the deformation in both the elastic and plastic regions. In the former the stress is directly connected with the total strain by means of the elastic equations. In the latter there is, as we have seen, no such unique correspondence, and the stress-strain differential relations have to be integrated by following the history of the deformation from the initiation of plasticity at some point of the body. A process of plastic deformation has to be considered mathematically as a succession of small. increments of strain, even where the overall distortion is so small that the change in external surfaces can be neglected. When the strains are large the determination of the changing shape of free plastic surfaces necessitates, in itself, the following of the deformation from moment to moment.