Definition and properties of ideal amorphous solids

It is proposed that two ideal amorphous structures, type I and type II, based on maximally random jammed packing of spheres of equal size, form a distinct class of ideal amorphous solids. The ideal amorphous structures contain wide variations in local density, limited by the condition of solidity. Four distinct characteristics, based on statistical geometry and topology, are shown to define this class. Voronoi tessellations carried out on simulated cells of random packed spheres and amorphous polymers give a broad distribution of individual volumes, skewed, with a tail at the high volume end

Microstructure of horseshoe nails using neutron diffraction

Neutron diffraction allows non-destructive testing of the bulk microstructure of mechanical components. The microstructures of horseshoe nails made through three different processes have been explored as a function of position along the nail. Despite all nails being made of similar plain low carbon steel and being process annealed after manufacture, the microstructures are far from the same. Nails made from strip, using a cold forging stamping process, show narrower diffraction peaks indicating a narrower distribution of lattice parameters and also show diffraction peak intensity ratios closer to those expected for unstrained steel. Thus the distribution of the orientation of grains in these nails is closer to that of undistorted steel compared to nails made through the other two processes considered – one a drawing from wire, the other a combination of rolling and cold forging. The blades of the drawn nails showed little preferred orientation but the converse was true in the heads. Differing patterns of preferred orientation suggest that the various manufacturing approaches result in substantially different mechanical advantages for the three types of nails, a result in accord with mechanical testing

The geometry, topology and structure of amorphous solids

Clusters of atoms can be divided into three categories depending on their topology. One of the categories provides the basis for development of a model of a perfectly random structure (ideal amorphous solid) using the non-equilateral triangle topology i

Micromechanics of sea urchin spines

The endoskeletal structure of the Sea Urchin, Centrostephanus rodgersii, has numerous long spines whose known functions include locomotion, sensing, and protection against predators. These spines have a remarkable internal microstructure and are made of single-crystal calcite. A finite-element model of the spine's unique porous structure, based on micro-computed tomography (microCT) and incorporating anisotropic material properties, was developed to study its response to mechanical loading. Simulations show that high stress concentrations occur at certain points in the spine's architecture; brittle cracking would likely initiate in these regions. These analyses demonstrate that the organization of single-crystal calcite in the unique, intricate morphology of the sea urchin spine results in a strong, stiff and lightweight structure that enhances its strength despite the brittleness of its constituent material

Computing expected moments of the R\'enyi parking problem on the circle

A highly accurate and efficient method to compute the expected values of the count, sum, and squared norm of the sum of the centre vectors of a random maximal sized collection of non-overlapping unit diameter disks touching a fixed unit-diameter disk is presented. This extends earlier work on R\'enyi's parking problem [Magyar Tud. Akad. Mat. Kutat\'{o} Int. K\"{o}zl. 3 (1-2), 1958, pp. 109-127]. Underlying the method is a splitting of the the problem conditional on the value of the first disk. This splitting is proven and then used to derive integral equations for the expectations. These equations take a lower block triangular form. They are solved using substitution and approximation of the integrals to very high accuracy using a polynomial approximation within the blocks

Lateral drill holes decrease strength of the femur: An observational study using finite element and experimental analyses

Background: Internal fixation of femoral fractures requires drilling holes through the cortical bone of the shaft of the femur. Intramedullary suction reduces the fat emboli produced by reaming and nailing femoral fractures but requires four suction port

Lateral drill holes decrease strength of the femur: An observational study using finite element and experimental analyses

BACKGROUND: Internal fixation of femoral fractures requires drilling holes through the cortical bone of the shaft of the femur. Intramedullary suction reduces the fat emboli produced by reaming and nailing femoral fractures but requires four suction portals to be drilled into the femoral shaft. This work investigated the effect of these additional holes on the strength of the femur. METHODS: Finite element analysis (FEA) was used to calculate compression, tension and load limits which were then compared to the results from mechanical testing. Models of intact femora and fractured femora internally fixed with intramedullary nailing were generated. In addition, four suction portals, lateral, anterior and posterior, were modelled. Stresses were used to calculate safety factors and predict fatigue. Physical testing on synthetic femora was carried out on a universal mechanical testing machine. RESULTS: The FEA model for stresses generated during walking showed tensile stresses in the lateral femur and compression stresses in the medial femur with a maximum sheer stress through the neck of the femur. The lateral suction portals produced tensile stresses up to over 300% greater than in the femur without suction portals. The anterior and posterior portals did not significantly increase stresses. The lateral suction portals had a safety factor of 0.7, while the anterior and posterior posts had safety factors of 2.4 times walking loads. Synthetic bone subjected to cyclical loading and load to failure showed similar results. On mechanical testing, all constructs failed at the neck of the femur. CONCLUSIONS: The anterior suction portals produced minimal increases in stress to loading so are the preferred site should a femur require such drill holes for suction or internal fixation

On Structure and Properties of Amorphous Materials

Mechanical, optical, magnetic and electronic properties of amorphous materials hold great promise towards current and emergent technologies. We distinguish at least four categories of amorphous (glassy) materials: (i) metallic; (ii) thin films; (iii) org