State Of Homogeneous Deformation Research Articles

A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

Aspects of cauchy elastic materials

The Darboux theorem on the classification and canonical forms of first degree exterior differential forms is used to obtain a canonical representation of Cauehy elastic materials. It is shown that the balance of moment of momentum and the principle of material indifference are independent for materials whose Darboux class is greater than 1. By means of the Caratheodory's theorem on inaccessibility it is shown that any homogeneous deformation state can be reached from any other homogeneous deformation state by a path of zero work whenever the Darboux class of the material is 3 or greater.

The growth of plane discontinuities propagating into a homogeneously deformed elastic material

It is shown that, in general, plane acceleration discontinuities propagating into an isotropic elastic material in a state of homogeneous deformation either become infinite in a finite time or decay to zero in an infinite time. Exceptions to this result are transverse discontinuities which propagate along a principal axis of strain without change in strength. Conditions governing the growth of acceleration discontinuities travelling into undeformed material are found to be identical with the thermodynamic conditions derived by Bland [2] for shock propagation. Plane discontinuities of order higher than the second are shown to propagate with constant strength.