Bore Expansion In A Circular Sheet Of Elastoplastic Material Using Slow Elastoviscoplasticity Through The Differential Equations On A Manifold Method.

Abstract

In this work the differential equations on a manifold method (DEM) was used to
determine different mechanical responses of elastic-viscoplastic materials for the particular
case of a bore expansion in a circular plane sheet subjected to radial tensile uniform
displacements at the outer edge. In particular, the large deformation in-plane strain and
stresses were determined for a bore expansion ratio of 1.6, consideration is given to
anisotropic effects, and hardening. The DEM strategy consists in giving approximate finite
element representation to deformations, effective plastic deformation and to the displacement
functions, at the same time the constitutive equations of large deformation hyper-elastoviscoplasticity
are approximated by collocation at the centroids of the triangular finite
elements used. The result of these approximations is the generation of a system of algebraicdifferential
equations. In addition, since the formulation is based on the principle of virtual
work, the fundamental requirement of equilibrium is guaranteed at all computational steps
using the described procedure. The method, initially devised for viscoplastic materials, is
extended herein for elastoplastic situations, where deformation rates are negligible. To this
end very slow deformation rates were used, thus simulating the elastoplastic response, as a
limiting case, using very slow elastoviscoplasticity. The results using the proposed strategy
exhibit excellent agreement when compared with existing accepted results using different
methods.