Elastic-viscoplastic Medium Research Articles

Progressive failure in elastic–viscoplastic media: from theory to practice

In the risk assessment of soil movement, the comprehension of unexpected collapses involving creeping landslides is crucial. The transition from creeping to fast landslides is very hard to justify theoretically and simulate numerically. In this paper, the authors intend to demonstrate that even the integration of a basic elastic strain softening constitutive relationship under simple shear conditions is sufficient to capture such a transition. With this aim, an infinite slope, a homogeneous cemented/bonded soil and an oscillating water table level are considered. The onset of instability is shown to be anticipated by a local increase in strain rate within the shear band, behaving like a precursory signal. The size of the shear band, evolving with time and not depending only on the material grain size distribution, is governed by both the amplitude of the imposed perturbation and the material constitutive parameters.

Quasi-static analysis of microvoid growth in elastic-viscoplastic materials under thermal shock

The dynamic growth of void in an infinite elastic-viscoplastic medium under thermal shock is analyzed theoretically. The technique of direct integration is presented to obtain the analytic solutions of stress and displacement. The initial purely elastic deformation before the viscoplastic deformation is considered. Especially, the nonlinear ODE for moving interface of the elastic and viscoplastic zone is derived from the interface conditions. The dynamic evolution of void growth is different from the static case, since the moving interface leads to the intrinsic nonlinearity. The numerical results indicate that the effect of viscosity has significant influence on void growth.

Plane wave propagation through a layer of dislocation-containing inelastic media

The mechanisms of plane harmonic wave propagation through a layer of viscoelastic and elastic-viscoplastic media with dislocations were investigated using equations of the field theory of defects descriptive of dynamics of dislocation continua. The reflection and refraction coefficients of the layer for displacement waves and defect field waves propagating in the media were determined. The reflection and refraction coefficients of the layer were analyzed depending on parameters of the contact media and thickness of the layer. Relations between extreme reflectivity and layer thickness were found.

Wave processes in elastic-viscoplastic media with dislocations

The mechanisms of plane harmonic wave propagation in homogeneous and interfaced elastic-viscoplastic media are considered using the field theory of defects with kinematic identities of a dislocation-containing elastic continuum and dynamic equations of the gauge theory of dislocations. The reflection and refraction coefficients were determined for displacement waves and defect field waves with the defect field characterized by the dislocation density tensor and flux density tensor. The dependence of the coefficients on the parameters of the interfaced media is analyzed.

The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading

We have examined the problem of the dynamic growth of a single spherical void in an elastic-viscoplastic medium, with a view towards addressing a number of problems that arise during the dynamic failure of metals. Particular attention is paid to inertial, thermal and rate-dependent effects, which have not previously been thoroughly studied in a combined setting. It is shown that the critical stress for unstable growth of the void in the quasistatic case is strongly affected by the thermal softening of the material (in adiabatic calculations). Thermal softening has the effect of lowering the critical stress, and has a stronger influence at high strain hardening exponents. It is shown that the thermally diffusive case for quasistatic void growth in rate-dependent materials is strongly affected by the initial void size, because of the length scale introduced by the thermal diffusion. The effects of inertia are quantified, and it is demonstrated that inertial effects are small in the early stages of void growth and are strongly dependent on the initial size of the void and the rate of loading. Under supercritical loading for the inertial problem, voids of all sizes achieve a constant absolute void growth rate in the long term. Inertia first impedes, but finally promotes dynamic void growth under a subcritical loading. For dynamic void growth, the effect of rate-hardening is to reduce the rate of void growth in comparison to the rate-independent case, and to reduce the final relative void growth achieved.

Dynamic transient mode of shear strain of an elastic viscoplastic medium in a long channel

A transient regime with insignificant travel of a nondestructed structure along the channel is possible due to the excess of dynamic loads over static ones in elastoviscoplastic medium. A short-time slip of the elastic frame relative to the channel walls is bound up with propagation of loading and unloading waves in a nondestructed structure.

Response of a spherical cavity in an elastic viscoplastic medium under a variable internal pressure

A closed-form solution is given for the problem of a spherical cavity in an infinite elastoviscoplastic medium with kinematic hardening, when the cavity is subjected to an internal pressure that varies in any prescribed way.Under certain assumptions this problem takes account of the unit weight of the medium, and is particularly applicable to the deep underground storage of natural gas in rock salt.Some typical loading cases are shown.

An average theory for the dynamic behaviour of a laminated elastic-viscoplastic medium under general loading

An average theory which models the dynamic behaviour of a bi-laminated composite medium made of elastic-viscoplastic work hardening constituents is presented. The resulting effective theory is represented by a system of nonlinear differential equations for the average stresses, displacements and the plastic work. The theory can be applied to three-dimensional problems under general types of loading.The theory is applied for the special cases of waves propagating normal to the layering and for waves propagating in a thin composite rod.

Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques

The paper is concerned with the structure of the constitutive equations of either an elastic-plastic or an elastic-viscoplastic medium in a finite transformation. As the plastic deformation results from discontinuities of either displacements or rotations between the oriented microelements, some hidden director vectors must be introduced, or equivalently internal hidden variables and a hidden orthonormal triad, the director frame.In order to decompose the thermoelastic-viscoplastic transformation, a relaxed (or intermediate) configuration is used. An important feature of the theory is that, except in the case ofisotropy in the relaxed configurations, the constitutive equations contain not only the stretching tensor, but also the spin relative to the director frame.

Ray method of solving dynamic problems in elastic-viscoplastic media: PMM Vol. 37, N°1, 1973, pp. 145–155

The velocity and stress fields behind the shock wave front are investigated by a ray method in a three-dimensional elastic viscoplastic medium with hardening. Recursion equations are obtained to determine the terms of the ray series. In the case of load propagation by a spherical shock wave an analytical solution is obtained for the velocity to second order accuracy in the distance along the normal from the wave front. The solution of wave problems in elasticity theory by a wave method has been elucidated in [1], and in a one-dimensional viscoelastic medium in [2].

On equilibrium stability of an elastic-viscoplastic medium

We consider the stability of an elastic-plastic medium when one part of the body is in an elastic state and the other part in a plastic state.