Stress field

About: Stress field is a research topic. Over the lifetime, 11926 publications have been published within this topic receiving 226417 citations.

Stress propagation through frictionless granular material.

Abstract: We examine the network of forces to be expected in a static assembly of hard, frictionless spherical beads of random sizes, such as a colloidal glass. Such an assembly is minimally connected: the ratio of constraint equations to contact forces approaches unity for a large assembly. However, the bead positions in a finite subregion of the assembly are underdetermined. Thus to maintain equilibrium, half of the exterior contact forces are determined by the other half. We argue that the transmission of force may be regarded as unidirectional, in contrast to the transmission of force in an elastic material. Specializing to sequentially deposited beads, we show that forces on a given buried bead can be uniquely specified in terms of forces involving more recently added beads. We derive equations for the transmission of stress averaged over scales much larger than a single bead. This derivation requires the ansatz that statistical fluctuations of the forces are independent of fluctuations of the contact geometry. Under this ansatz, the d(d+1)/2-component stress field can be expressed in terms of a d-component vector field. The procedure may be generalized to nonsequential packings. In two dimensions, the stress propagates according to a wave equation, as postulated in recent work elsewhere. We demonstrate similar wave-like propagation in higher dimensions, assuming that the packing geometry has uniaxial symmetry. In macroscopic granular materials we argue that our approach may be useful even though grains have friction and are not packed sequentially.

The Hertzian fracture test

Abstract: The crack growth in the non-uniform stress field due to the contact loading of a spherical ball on an elastic half-space is described quantitatively for the case of an isotropic brittle solid. This theoretical understanding provides a basis for the Hertzian test which may be used to measure three important surface properties of strong solids and consequently their strength. These are fracture toughness, surface crack size densities and residual stress. All examples of applications of the test are described in detail for glass but the application to a wider variety of strong materials is implied and gives the test a wider significance.

Stress buildup in the Himalaya

Abstract: The seismic cycle on a major fault involves long periods of elastic strain and stress accumulation, driven by aseismic ductile deformation at depth, ultimately released by sudden fault slip events. Coseismic slip distributions are generally heterogeneous with most of the energy being released in the rupture of asperities. Since, on the long term, the fault's walls generally do not accumulate any significant permanent deformation, interseismic deformation might be heterogeneous, revealing zones of focused stress buildup. The pattern of current deformation along the Himalayan arc, which is known to produce recurring devastating earthquakes, and where several seismic gaps have long been recognized, might accordingly show significant lateral variations, providing a possible explanation for the uneven microseismic activity along the Himalayan arc. By contrast, the geodetic measurements show a rather uniform pattern of interseismic strain, oriented consistently with long-term geological deformation, as indicated from stretching lineation. We show that the geodetic data and seismicity distribution are reconciled from a model in which microseismicity is interpreted as driven by stress buildup increase in the interseismic period. The uneven seismicity pattern is shown to reflect the impact of the topography on the stress field, indicating low deviatoric stresses (<35 MPa) and a low friction (<0.3) on the Main Himalayan Thrust. Arc-normal thrusting along the Himalayan front and east-west extension in southern Tibet are quantitatively reconciled by the model.

Regional stress field of the Indian plate

Abstract: We have calculated the regional stress field in the Indian plate, implementing dependence of slab pull and ridge push on the age of the oceanic lithosphere in the finite element procedure. The high level of the calculated stress field (order of a few kbar) and the dominance of compression in the plate are consequences of the unique dynamic situation of the present-day Indian plate. The calculated stress field explains the concentration of intraplate deformation in the region of the Ninetyeast Ridge and yields insight into the variations in stress directions in the Australian continent.