Viscoplastic similarities
13-04-2023 | Posted by Joaquín Martí
What do they have in common: glacier ice, rock salt, and metals near the melting point? Well, they behave similarly: apart from the numerical value of the parameters, all those materials essentially share the same constitutive law, loosely speaking their rate of deformation is proportional to a power of the stress. And they are not the only ones, many polymers or the Earth’s upper mantle also behave that way.
Viscoplastic laws, because of the pervasiveness of the materials that display them, are among the more frequently used constitutive models, apart of course from linear elasticity. And, therefore, all consultants in applied mechanics have probably been compelled to use them often. This certainly includes Principia.
The mechanisms that give rise to viscoplastic behaviour in solids are typically the migration of dislocations, vacancies or defects, mechanisms that are strongly affected by temperature. As a consequence, the mechanical problems originated tend to be non-linear, time-dependent and, at least, weakly coupled to an associated thermal problem. Such characteristics make them interesting from a numerical standpoint.
We have been involved in may exercises of this type, starting with modelling the extrusion of aluminium alloys many years ago; at that time, we also had to develop the software to carry out the analyses, which for that task had to include full thermal coupling. Fortunately, Abaqus came soon afterwards and allowed us to concentrate on the engineering aspects of the projects, without having to mind the software development. On that same line, but far more recently, we have conducted several investigations dealing with the extrusion of optical fibre for various applications.
Materials like salt and potash also display viscoplastic behaviour. They have been the motivation for many of our projects, dealing with different aspects. For example, we carried out exhaustive studies as the expert witness for an accident in a potash mine in Canada. Or studied the suitability of salt formations for housing an underground repository for high-level nuclear waste. Or investigated the feasibility of solution mining of salt. And, of course, have supported the exploitation of several salt mines. We have even studied the behaviour of molten salts for energy storage in solar plants.
And viscoplastic models are not restricted to solid-looking materials. For example, we applied them in the analysis of the mixing element for the various flows involved in the manufacture of plastic bottles. We also used them extensively for simulating the oil behaviour in the ill-fated Prestige tanker: extraction through orifices in the deck, effectiveness of flexible and rigid containers for transferring the oil, possible operation of a canopy and of pipelines to the surface, etc.
In summary, viscoplastic descriptions are inevitable for representing the mechanical behaviour of many materials and, if they didn’t exist, we would have to invent them.
