Plastic work and strain paths: the common geometric basis with phase stability

The paper shows by a graphical method that the path, between two states of homogenous deformation that minimises plastic work, is a straight line in the principal strain space between the two states. The method is valid for the condition that the same triad of material fibres remains mutually orthogonal throughout the deformation. The material deformed is considered to be rigid/hardening with a convex yield surface. Using a procedure very similar to that used to show the stability of a solution, it is shown that a straight line path results in less plastic work than two non collinear straight lines paths between the same points. By considering any path to be made up of infinitesimally small linear paths, this result is extended for any arbitrary path.