Micro mechanics of the critical state line at high stresses

A critical state line is presented for a crushable numerical soil, which is parallel to the isotropic normal compression line. A previous theory for the normal compression line, which correctly predicts the slope as a function of the size-effect on particle strength is extended to justify the slope of the critical state line. The micro mechanics behind critical states are examined, leading to a theory for a relationship between the volume of smallest particles and mean effective stress. A unique relationship exists for crushed states, leading to a two-dimensional interpretation of the state boundary surface for soils looser than critical

The fractal micro mechanics of normal compression

The fundamental fractal micro mechanics of normal compression of granular materials is studied using DEM. This paper examines the emergence of a finite fractal bounded by two particle sizes as stress increases, and the evolution of various definitions of the ‘smallest particles’. It is revealed that if particles are categorised according to their coordination number, then the volume of all particles with 4 contacts or fewer is directly proportional to the void space. These particles are called ‘critical particles’ and are shown, for the first time, to explain quantitatively the voids reduction with increasing vertical stress

Micro mechanics of drained and undrained shearing of compacted and overconsolidated crushable sand

A numerical crushable soil sample has been created using the previously published McDowell and de Bono (2013) model and subjected to a range of stress paths. Compacted sand simulations are performed using conventional triaxial stress paths, constant mean stress and constant volume conditions and a critical state line established. Overconsolidated samples have been created by crushing the soil down the isotropic normal compression line, unloading, and shearing at constant radial stress, constant mean stress or constant volume and a critical state line is again established. The critical state line is unique at high stresses for the simulated compacted and overconsolidated sands and is parallel to the isotropic normal compression line, in agreement with available data and a previously published theory. The critical state line at low stress levels is non-unique and a function of the particle size distribution, in agreement with available data. Constant volume tests exhibit the well-known phenomena of phase transformation points and peak strengths are observed for ‘drained’ soils on the dense side of critical. The numerical soil produces a state boundary surface that compares well to available data

On the packing and crushing of granular materials

This paper is a study of the dependence of the volume of voids in a granular material on the particle size distribution. It has previously been proposed that the volume of voids is proportional to the volume of the smallest particles. In a particle size distribution which is progressively becoming wider (e.g. as occurs due to crushing during the compression of sand), the smallest size of particle decreases, yet there are only ever a few of these particles out of many thousands or millions. This paper attempts to identify which particles govern the overall density of a granular material, and a new definition of the ‘smallest particles’ is proposed. These particles are shown to govern the void space in a range of simulations of spherical and non-spherical crushable particles. The theory also applies to idealised Apollonian sphere packings

Cepheid Mass-loss and the Pulsation -- Evolutionary Mass Discrepancy

I investigate the discrepancy between the evolution and pulsation masses for Cepheid variables. A number of recent works have proposed that non-canonical mass-loss can account for the mass discrepancy. This mass-loss would be such that a 5Mo star loses approximately 20% of its mass by arriving at the Cepheid instability strip; a 14Mo star, none. Such findings would pose a serious challenge to our understanding of mass-loss. I revisit these results in light of the Padova stellar evolutionary models and find evolutionary masses are ($17\pm5$)% greater than pulsation masses for Cepheids between 5<M/Mo<14. I find that mild internal mixing in the main-sequence progenitor of the Cepheid are able to account for this mass discrepancy.Comment: 15 pages, 3 figures, ApJ accepte

Discrete element modelling of a flexible membrane for triaxial testing of granular material at high pressures

The discrete element method (DEM) has been used to simulate triaxial tests on a bonded material at high pressures. A key feature of the model is the use of a flexible membrane that allows the correct volumetric deformation and the true failure mode to develop while applying constant confining pressure to the triaxial sample. The correct pattern of behaviour has been observed across a wide range of confining pressures, with both shear planes and barrelling failure being observed. The radial pressure applied by the membrane remains constant after large strains and deformation

Galactic Cepheids with Spitzer: I. Leavitt Law and Colors

Classical Cepheid variable stars have been important indicators of extragalactic distance and Galactic evolution for over a century. The Spitzer Space Telescope has opened the possibility of extending the study of Cepheids into the mid- and far-infrared, where interstellar extinction is reduced. We have obtained photometry from images of a sample of Galactic Cepheids with the IRAC and MIPS instruments on Spitzer. Here we present the first mid-infrared period-luminosity relations for Classical Cepheids in the Galaxy, and the first ever Cepheid period-luminosity relations at 24 and 70 um. We compare these relations with theoretical predictions, and with period-luminosity relations obtained in recent studies of the Large Magellanic Cloud. We find a significant period-color relation for the [3.6]-[8.0] IRAC color. Other mid-infrared colors for both Cepheids and non-variable supergiants are strongly affected by variable molecular spectral features, in particular deep CO absorption bands. We do not find strong evidence for mid-infrared excess caused by warm (~500 K) circumstellar dust. We discuss the possibility that recent detections with near-infrared interferometers of circumstellar shells around delta Cep, l Car, Polaris, Y Oph and RS Pup may be a signature of shocked gas emission in a dust-poor wind associated to pulsation-driven mass loss.Comment: Accepted by The Astrophysical Journal on Nov 11, 200

Micro mechanics of critical states for isotropically overconsolidated sand

The discrete element method has been used to investigate the micro mechanics of shearing to a critical state on the loose and dense sides of critical. Isotropic compression has previously been modelled in 3D using a large number of particles and without the use of agglomerates. The same procedure is used here. Particle fracture is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Isotropic compression of a silica sand has been simulated to 20 MPa and followed by unloading to a range of stresses before shearing to a critical state, using micro parameters which relate to the silica sand particle strengths. The samples at the lowest stress levels exhibit peak strength and dilation. The sample at the highest stress exhibits contraction and ductile yielding to a critical state. A critical state line is established, which appears to become parallel to the isotropic line in log e-log p space at high stress levels. This paper shows that it is the evolving fractal particle size distribution during isotropic normal compression which governs the behaviour on unloading to different overconsolidation ratios. The micro mechanics of the critical state line are shown to be in the evolving particle size distribution during normal compression, and how such an aggregate behaves when it is unloaded

Micro mechanics of isotropic normal compression

Discrete element modelling has been used to investigate the micro mechanics of isotropic normal compression. One-dimensional (1D) normal compression has previously been modelled in three dimensions using an oedometer and a large number of particles and without the use of agglomerates, and it was shown that the compression index was solely related to the strengths of the particles as a function of size. The same procedure is used here to model isotropic normal compression. The fracture of a particle is governed by the octahedral shear stress within the particle (due to the multiple contacts) and a Weibull distribution of strengths. The octahedral shear stresses, due to local anisotropic stresses within a sample with isotropic boundary stresses, are shown to give rise to a normal compression line (NCL) and the evolution of a distribution of particle sizes. The compression line is parallel to the 1D NCL in log e–log p space, in agreement with traditional critical state soil mechanics and confirming that the compression index is solely a function of the size effect on average particle strength, which determines the hardening law for the material. The paper shows, for the first time, how local octahedral shear stresses induced in the particles within the sample generate an isotropic normal (clastic) compression line