Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach, to derive the three-dimensional (3D) magnetic field for a neodymium magnet, assuming an idealized block geometry and uniform magnetization. For each field or observation point, the 3D solution involves 24 nondimensional quantities, arising from the eight vertex positions of the magnet and the three components of the magnetic field. The only unknown in the model is the value of magnetization, with all other model quantities defined in terms of field position and magnet location. The longitudinal magnetic field component in the direction of magnetization is bounded everywhere, but discontinuous across the magnet faces parallel to the magnetization direction. The transverse magnetic fields are logarithmically unbounded on approaching a vertex of the magnet.

In this paper, a method is proposed for extracting fracture parameters in anisotropic thermoelasticity cracking via interaction integral method within the framework of extended finite element method (XFEM). The proposed method is applied to linear thermoelastic crack problems. The numerical results of the stress intensity factors (SIFs) are presented and compared with those reported in related references. The good agreement of the results obtained by the developed method with those obtained by other numerical solutions proves the applicability of the proposed approach and confirms its capability of efficiently extracting thermoelasticity fracture parameters in anisotropic materials.

We would like to present a method to compute the incompatibility operator in any system of curvilinear coordinates (components). The procedure is independent of the metric in the sense that the expression can be obtained by means of the basis vectors only, which are first defined as normal or tangential to the domain boundary, and then extended to the whole domain. It is an intrinsic method, to some extent, since the chosen curvilinear system depends solely on the geometry of the domain boundary. As an application, the in-extenso expression of incompatibility in a spherical system is given.

Common silicate glasses are among the most brittle of the materials. However, on warming beyond the glass transition temperature Tg glass transforms into one of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology, indicating that it rests on the disordered structure instead on the nature of the chemical bonds. The micromechanics of a solid with bulk amorphous structure is examined in order to determine the most basic conditions the system must satisfy to be able of plastic flow. The equations for the macroscopic flow, consistent with the constrictions imposed at the atomic scale, prove that a randomly structured bulk material must be either a brittle solid or a liquid, but not a ductile solid. The theory permits to identify a single parameter determining the difference between the brittle solid and the liquid. However, the system is able of perfect ductility if the plastic flow proceeds in two dimensional plane layers that concentrate the strain. Insight is gained on the nature of the glass transition, and the phase occurring between glass transition and melting.

In this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is present. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.

The current geothermal and volcanic activity in the North Island of New Zealand is explained as a consequence of Pacific and Australian plate interactions over the last 20 million years. The primary hypothesis is that the Kermadec subduction zone has for the last 20 million years or more been retreating in a south-easterly direction at about five centimetres per year. It is surmised that this motion and interaction with another subduction zone almost at right angles to it under the North Island resulted in plate tearing due to the incompatibility of the plate geometry where these subduction zones interacted. The nature and consequences of this plate tearing are partially revealed in published maps of the plate currently under the North Island. If the subducted parts of this plate, as shown in Eiby’s maps, [G. A. Eiby, “The New Zealand sub-crustal rift”, New Zeal. J. Geol. Geophy.7 (1964) 109–133] are straightened, then the plate edge lies on a curve giving a rough picture of their position before being torn and subducted by the Kermadec trench motion. This map of the tear suggests the shape of the edge of a missing plate segment torn from the plate, and implies a rotation of the upper North Island, clockwise approximately 20 degrees, about a point just south of the Thames estuary. A consequence of this plate tearing is that the solid retreating crustal wave generating magma pressure beneath the crest of the solid wave has the potential to inject significant basaltic magma into the crust through the tears. These intrusive magma fluxes have the ability to generate geothermal fields and rhyolitic lavas from crustal melts. This could explain the geothermal activity along the Coromandel peninsula five to seven million years ago, the ignimbrite outcrops about Lake Taupo and the current geothermal and volcanic activity stretching from Taupo to Rotorua.

A three-layer compartmental model of the geological structure in the Taupo Volcanic Zone of New Zealand is developed, based on the assumptions of isostasy (constant geostatic pressure at 25 km depth) and a constant rate of volcanism. The upper layer consists of volcanic infill to a depth of about 2500 m, then a middle layer of greywacke-like material to a depth of about 15 km, and a lower layer of andesitic-like material to a depth of 25 km. Our model assumptions predict that the area of each layer increases at a constant rate; that there is a constant ratio between the rate of energy production from volcanic activity and geothermal convection; and that there is the possibility of an abrupt change from rhyolitic to basaltic volcanism, if the middle layer becomes sufficiently thin. Two models are considered: a rifting and a spreading model. Both models predict the lower layer has an andesitic-like density. The spreading model has difficulty matching heat output with observed extension rates. The rifting model predicts the observed extension rates, but requires very deep circulation of groundwater to be consistent with observed chemical and isotopic properties of geothermal fluids.