Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.

Fundamental Problems in Viscoplasticity

Static and dynamic axial crushing of foam-filled sheet metal tubes

Publisher Summary This chapter examines the derivation of constitutive relations from the free energy and the dissipation function. Continuum mechanics allows one to establish constitutive relations, deducing them from a single pair of scalar functions characterizing the material. The simplest materials dealt with in continuum mechanics are elastic. More general processes and those taking place in more general materials are irreversible and require more constitutive relations, connecting the dissipative forces with the velocities. The orthogonality condition and the equivalent extremum principles have been established for velocities in the form of vectors or symmetric tensors. It is found that if the deformation of an elastic body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable. The connection between stress and elastic strain is given by the generalized Hooke's law and connects the stress with the plastic strain and its time rate. It is found that orthogonality in velocity space, which is essentially responsible for the results, does not necessarily imply orthogonality in force space.

G R Cowper

Papers

Strain-hardening and strain-rate effects in the impact loading of cantilever beams