Volume 20, Issue 4-6

The purpose of this paper was to study the propagation of longitudinal waves in non-homogeneous four-parameter viscoelastic rods of arbitrary thickness. The rods were initially supposed to be unstressed and at rest. Apart from a sudden rising traction uniformly applied over the boundary of the opening and parallel to the faces of the plates, which is steadily maintained thereafter, the rods are otherwise free from loading. Methods for treating reflection at the free end of the finite rod and reflection and transmission at an interface between two media in the semi-infinite bi-viscoelastic rod are also presented. Asymptotic techniques are used throughout, and formal asymptotic wave-front expansions of the solution functions are obtained.

Up to now, models for single crystal plasticity predict unbounded lattice rotations under simple shear. Asaro et al. proposed a model that predicts bounded rotations as long as the viscosity parameters are appropriately chosen. In every case, ideal plasticity models imply unbounded lattice rotations. Hence, it leads to the question whether one can develop a single crystal plasticity theory exhibiting hardening effects, which can predict bounded lattice rotations dependent on the choice of the hardening parameters. It is shown that this is possible by assuming latent hardening to apply.

The effect of wave propagation in nonhomogeneous elastic solid whose elastic parameters depend on one space coordinate only is considered. The stress and displacement components are assumed to depend on this same space coordinate and time alone. Taking Young’s modulus E = E 0 cos αx and density ρ = ρ 0 cos αx , we obtain the general solution for the problem of wave propagation in nonhomogeneous elastic rod. Particular cases in which a modified sawtooth, square, and half sine wave rectifier output as input wave, fed through one end of the rod, are studied, and the displacement u ( x , t ) is obtained. Graphs are drawn to study the behaviour of the input waves at time t =2 s, α =0.01, and =3.5.

The aim of the present article is to investigate the surface waves in anisotropic, elastic solid medium under the influence of gravity. The theory of generalised surface waves has first been developed and then used to investigate particular cases of waves, viz., Stoneley, Rayleigh, and Love. The wave velocity equations have been obtained for different cases and are in well agreement with the corresponding classical result, when the effect of gravity, viscosity, and fibre-reinforced parameters of the material medium are ignored.

A theoretical analysis on three different geometrical limits during axial compression of a cylindrical workpiece under monotonically increasing external load is presented. Barreling is the main factor in metalworking industries, and it depends highly on several dimensional ratios such as initial aspect ratio (height/diameter), work/platen contact diameter ratios, etc. For a known material, barreling can be predicted from the mathematical formulations on the geometrical limits presented herein.

Cold-rolled 1018 (CR-1018) carbon steel has been well known for its susceptibility to adiabatic shear banding under dynamic loadings. Analysis of these localizations highly depends on the selection of the constitutive model. To deal with this issue, a constitutive model that takes temperature and strain rate effect into account is proposed. The model is motivated by two physical-based models: the Zerilli and Armstrong and the Voyiadjis and Abed models. This material model, however, incorporates a simple softening term that is capable of simulating the softening behavior of CR-1018 steel. Instability, localization, and evolution of adiabatic shear bands are discussed and presented graphically. In addition, the effect of hydrostatic pressure is illustrated.

No abstract available.

No abstract available.