Determination of non!contact deformation of a material under the orbital action of an indenter

The influence of kinematic loading schemes on the formation of an elastoplastic wave under the orbital action of an indenter is considered. A mathematical model of hardening is presented, which determines the size and stressstrain state of the wave. The loading parameters influencing the wave size are determined. Keywords: kinematic diagram, orbital loading, deforming element, elastoplastic deformation, non-contact deformation, elastoplastic wave [email protected]

Mathematical modelling of elastoplasticity at high stress

This study describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focused on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave.

Elastoplastic Wave Propagation in a Rate-Sensitive Finite Rod Having a Thermal Gradient

In this paper, the problem of one-dimensional wave propagation in a bar of a thermally sensitive viscoplastic material is considered. A constitutive equation is developed which explicitly accounts for the thermal state in both the elastic and inelastic components of the strain rate. A computational technique is proposed for solving the governing hyperbolic system of equations. This technique is a synthesis of the finite-difference method and the method of characteristics, and utilizes the most attractive features of both for solving nonlinear problems involving the propagation of strong discontinuities. Some results are shown for the propagation of waves through both decreasing and increasing temperature fields.

Effect of Temperature Gradients on the Propagation of Elastoplastic Waves

In this paper, the writers consider the problem of the propagation of an extensional elastoplastic wave through a long thin bar heated at the end to produce a continuously decreasing temperature profile. The temperature distribution is approximated as an exponential function, and the stress-strain curve is considered to be bilinear with temperature-dependent mechanical properties. The problem is formulated and solved numerically by the method of characteristics. Several graphical results are provided, and the effects of the temperature gradient and the mechanical properties are discussed in terms of plastic wave attenuation.