Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

The deformation characteristics of idealized granular materials have been studied from the micro-mechanical viewpoint, using Bagi’s three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165–177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles. Bagi’s formulation expresses the continuum, macro-scale strain as an average over all edges, of their relative displacements (between two successive states) and the complementary-area vectors. This latter vector is a geometrical quantity determined from the set of edges, i.e. from the structure of the particle packing.\ud \ud Results from Discrete Element Method simulations of isotropic and triaxial loading of a three-dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary-area vectors of edges (subdivided into physical and virtual contacts) and of the relative displacements of edges. The investigated statistics are probability density functions and averages over groups of edges with the same orientation. It is shown that these averages can be represented by second-order Fourier series in edge orientation.\ud \ud Edge orientations are distributed isotropically, contrary to contact orientations. The average lengths of the branch vectors and the normal component of the complementary-area vectors are distributed isotropically (with respect to the edge orientation) and their average values are related to each other and to the volume fraction of the assembly. The other two components of the complementary-area vector are zero on average.\ud \ud The total deformation of the assembly, as given by the average of the relative displacements of the edges of the Delaunay tessellation follows the uniform-strain prediction. However, neither the deformation of the physical contact network nor of the virtual contact network has this property. The average relative displacement of physical edges in the normal direction (determined by the branch vector) is smaller than that according to the uniform-strain assumption, while that of virtual contacts is larger. This is caused by the high interparticle stiffness that hinders compression. The reverse observation holds for the tangential component of the relative displacement vector. The contribution of the deformation of the empty space between physical contacts to the continuum, macro-scale strain tensor is therefore very important for the understanding and the prediction of the macro-scale deformation of granular materials

Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile

Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition.Comment: 13 pages, 15 figures, soumis \`{a} Phys. Rev.

Frictionless bead packs have macroscopic friction, but no dilatancy

The statement of the title is shown by numerical simulation of homogeneously sheared packings of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate γ in the limit of small γ and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle ϕ, equal to 5.76 $\pm$ 0.22 degrees in simple shear, is independent on the average pressure P in the rigid limit. It is shown to stem from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, like the effective friction of a frictionless slider on a bumpy surface. Solid fraction Φ remains equal to the random close packing value ≃ 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit, and we conclude that the same friction law for simple shear applies in the large psystem limit if normal stress or density is externally controlled. Defining the inertia number as I = γ m/(aP), with m the grain mass and a its diameter, both internal friction coefficient $\mu$∗ = tan ϕ and volume 1/Φ increase as powers of I in the quasistatic limit of vanishing I, in which all mechanical properties are determined by contact network geometry. The microstructure of the sheared material is characterized with a suitable parametrization of the fabric tensor and measurements of connectivity and coordination numbers associated with contacts and near neighbors.Comment: 19 pages. Additional technical details may be found in v

Rheophysics of dense granular materials : Discrete simulation of plane shear flows

We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.Comment: 24 pages, 19 figure

Scaffolds with a standardized macro-architecture fabricated from several calcium phosphate ceramics using an indirect rapid prototyping technique

Calcium phosphate ceramics, commonly applied as bone graft substitutes, are a natural choice of scaffolding material for bone tissue engineering. Evidence shows that the chemical composition, macroporosity and microporosity of these ceramics influences their behavior as bone graft substitutes and bone tissue engineering scaffolds but little has been done to optimize these parameters. One method of optimization is to place focus on a particular parameter by normalizing the influence, as much as possible, of confounding parameters. This is difficult to accomplish with traditional fabrication techniques. In this study we describe a design based rapid prototyping method of manufacturing scaffolds with virtually identical macroporous architectures from different calcium phosphate ceramic compositions. Beta-tricalcium phosphate, hydroxyapatite (at two sintering temperatures) and biphasic calcium phosphate scaffolds were manufactured. The macro- and micro-architectures of the scaffolds were characterized as well as the influence of the manufacturing method on the chemistries of the calcium phosphate compositions. The structural characteristics of the resulting scaffolds were remarkably similar. The manufacturing process had little influence on the composition of the materials except for the consistent but small addition of, or increase in, a beta-tricalcium phosphate phase. Among other applications, scaffolds produced by the method described provide a means of examining the influence of different calcium phosphate compositions while confidently excluding the influence of the macroporous structure of the scaffolds

Identification of Two Protein-Signaling States Delineating Transcriptionally Heterogeneous Human Medulloblastoma

Summary: The brain cancer medulloblastoma consists of different transcriptional subgroups. To characterize medulloblastoma at the phosphoprotein-signaling level, we performed high-throughput peptide phosphorylation profiling on a large cohort of SHH (Sonic Hedgehog), group 3, and group 4 medulloblastomas. We identified two major protein-signaling profiles. One profile was associated with rapid death post-recurrence and resembled MYC-like signaling for which MYC lesions are sufficient but not necessary. The second profile showed enrichment for DNA damage, as well as apoptotic and neuronal signaling. Integrative analysis demonstrated that heterogeneous transcriptional input converges on these protein-signaling profiles: all SHH and a subset of group 3 patients exhibited the MYC-like protein-signaling profile; the majority of the other group 3 subset and group 4 patients displayed the DNA damage/apoptotic/neuronal signaling profile. Functional analysis of enriched pathways highlighted cell-cycle progression and protein synthesis as therapeutic targets for MYC-like medulloblastoma. : Using peptide phosphorylation profiling, Zomerman et al. identify two medulloblastoma phosphoprotein-signaling profiles that have prognostic value and are potentially targetable. They find that these profiles extend across transcriptome-based subgroup borders. This suggests that diverse genetic information converges on common protein-signaling pathways and highlights protein-signaling as a unique information layer. Keywords: medulloblastoma, protein-signaling, protein synthesis, MYC, TP53, proteome, phosphoproteom