Unique Quantum Stress Fields

We have recently developed a geometric formulation of the stress field for an interacting quantum system within the local density approximation (LDA) of density functional theory (DFT). We obtain a stress field which is invariant with respect to choice of energy density. In this paper, we explicitly demonstrate this uniqueness by deriving the stress field for different energy densities. We also explain why particular energy densities give expressions for the stress field that are more tractable than others, thereby lending themselves more easily to first-principles calculations.Comment: To appear in Proceedings for Fundamental Physics of Ferroelectrics (2001

Homogenization in strength and durability analysis of reinforced tooth filling

An asymptotic homogenization procedure is employed to obtain effective elastic properties of the composite tooth filling, a homogenized macro– stress field and a first approximation to the micro-stress field, from properties of the components and applied macro–loads. Using the approximate micro–stress field, a non–local initial strength and fatigue durability macro–conditions for the composite filling material is expressed in terms of the homogenized macro–stresses. An illustrative example with the stress singularity on the tooth–filling interface is presented showing the need in the non-local analysis. Effective elastic properties of the tooth filling is numerically simulated for some size distributions of the reinforcing particles

Residual stress field of HIPed silicon nitride rolling elements

The residual stress field of HIPed Si3N4 rolling elements were studied. Two kinds of HIPed Si3N4 ball blanks self-finished at different nominal lapping loads ranging from 1.3 to 10.87 kgf/ball and four kinds of commercially finished 1/2 in (12.7 mm) HIPed Si3N4 balls before, during and after RCF tests were investigated. The experimental results showed that in the finishing process of HIPed Si3N4 rolling elements. the surface and subsurface compressive residual stress induced is proportional to the lapping load applied. There was initially a high compressive residual stress layer on the HIPed Si3N4 ball blanks and this layer is mostly removed during the finishing process. During the rolling contact fatigue process of HIPed Si3N4 rolling elements, the residual stresses on the rolling track will change dramatically as RCF proceeds

Frictional interface crack-tip singular stress field in anisotropic

This study presents the asymptotic displacement and stress fields at the crack tip of frictional interface where slip can occur along the interface between two anisotropic composite laminates. The results show that real values corresponding to the order of stress singularities may exit at the crack tip of the frictional interface between two anisotropic layers. The order of stress singularity largely depends on the coefficient of friction within the interface and the material properties of anisotropic composite laminates such as fibre orientations

Simulation of subseismic joint and fault networks using a heuristic mechanical model

Flow simulations of fractured and faulted reservoirs require representation of subseismic structures about which subsurface data are limited. We describe a method for simulating fracture growth that is mechanically based but heuristic, allowing for realistic modelling of fracture networks with reasonable run times. The method takes a triangulated meshed surface as input, together with an initial stress field. Fractures initiate and grow based on the stress field, and the growing fractures relieve the stress in the mesh. We show that a wide range of bedding-plane joint networks can be modelled simply by varying the distribution and anisotropy of the initial stress field. The results are in good qualitative agreement with natural joint patterns. We then apply the method to a set of parallel veins and demonstrate how the variations in thickness of the veins can be represented. Lastly, we apply the method to the simulation of normal fault patterns on salt domes. We derive the stress field on the bedding surface using the horizon curvature. The modelled fault network shows both radial and concentric faults. The new method provides an effective means of modelling joint and fault networks that can be imported to the flow simulator

Stress field and spin axis relaxation for inelastic triaxial ellipsoids

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.Comment: 14 pages, 6 figures, published in Monthly Notices RAS (containing misprints

Improved recovery of admissible stress in domain decomposition methods - application to heterogeneous structures and new error bounds for FETI-DP

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization