Aspects of Invariance in Solid Mechanics

This chapter is conceived primarily as an account of certain interrelated ideas that have contributed over a long period to the basic mechanics of rate-independent solids and which retrospectively appear to have proved influential. Central to this method is the representation of tensors on trace axes of deformation that sweep through a Lagrangian reference configuration. A Lagrangian viewpoint is also well suited to handling pure mechanics, as it is advocated in relation to incremental boundary-value problems. With “nominal” stress as the primary variable, allied to the notion of convexity with respect to functional, one has an infallible structural guide when investigating uniqueness of solutions and their external characters. The chapter also highlights that the failure of incremental uniqueness, or bifurcation, is arguably the phenomenon that is most typical of continuum response at unrestricted levels of deformation. It is in constitutive analyses of material behaviors that the mathematical apparatus assembled at the outset finds its justification. © 1978, Academic Press Inc.