Fluid boundary of a viscoplastic Bingham flow for finite solid deformations

The modelling of viscoplastic Bingham fluids often relies on a rheological constitutive law based on a "plastic rule function" often identical to the yield criterion of the solid state. It is also often assumed that this plastic rule function vanishes at the boundary between the solid and fluid states, based on the fact that it is true in the limit of small deformations of the solid state or for simple yield criteria. We show that this is not the case for finite deformations by considering the example of a two state flow on a tilted plane where the solid state is described by a Neo-Hookean model with a Von Mises yield criterion. This opens new approaches for the modelling and the computation of the fluid state boundaries

Some features of anisothermal solid-state transformations in alloy 718

This paper presents an attempt to use differential thermal analysis to study anisothermal precipitation of both the stable delta and the metastable gamma-second phases during cooling of alloy Inconel 718. Observation of the samples by scanning and transmission electron microscopy was carried out to identify the thermal arrests observed upon cooling. When the upper temperature of the cycle is above the solvus of the delta phase, a clear peak is observed that could be related to precipitation of gamma-second for all the cooling rates used in the present work. When this temperature is below the delta solvus, no thermal arrest can be observed, while when it is close to it two faint peaks were noted and associated with stable and metastable precipitation. The most striking result was that dissolution of the metastable gamma-second phase during the heating stage was found to proceed heterogeneously in the material, and this affected reprecipitation of the phases upon subsequent cooling

Resolved simulations of submarine avalanches with a simple soft-sphere / immersed boundary method

Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing