Pressure deformation

Elastic-Element Methods Elastic-element pressure-measuring devices are those in which the measured pressure deforms some elastic material (usually metallic) within its elastic limit, the magnitude of the deformation being approximately proportional to the applied pressure. These devices may be loosely classified into three types Bourdon tube, bellows, and diaphragm. 

When two elastic and frictionless spheres are brought into contact under compressional forces or pressures, deformation occurs. The maximum displacement and contact area depend not only on the compressional force but also on the elastic material properties and radii of the spheres. The contact between two elastic and frictionless spherical bodies under compression was first investigated by Hertz (1881) and is known as the Hertzian contact. 

Looking closer at the tableting process it becomes clear that the applied forces during tableting are not only the result of machine movement. When punches are moving in a machine without material, no force can be measured. The force only develops when the punches come into contact with the powder bed. The materials resist pressure deformation, and while the punches are moving, a counterforce builds up which is the measured force at the punches. In conclusion punch forces are determined by the material and as a result materials can be characterized by the measured punch forces. 

The Eulerian finite difference scheme aims to replace the wave equations which describe the acoustic response of anechoic structures with a numerical analogue. The response functions are typically approximated by series of parabolas. Material discontinuities are similarly treated unless special boundary conditions are considered. This will introduce some smearing of the solution ( ). Propagation of acoustic excitation across water-air, water-steel and elastomer-air have been computed to accuracies better than two percent error ( ). In two-dimensional calculations, errors below five percent are practicable. The position of the boundaries are in general considered to be fixed. These constraints limit the Eulerian scheme to the calculation of acoustic responses of anechoic structures without, simultaneously, considering non-acoustic pressure deformations. However, Eulerian schemes may lead to relatively simple algorithms, as evident from Equation (20), which enable multi-dimensional computations to be carried out in a reasonable time. 

In composite propellants, the cavitation (or debonding) process, which has been shown to take place near (or at) the particle-matrix interface, is dependent on pressure, deformation, and additional viscoelastic and dissipative considerations (10). 

The characteristic pressure-deformation relationship is shown in Figure 2.6. 

A hard response to the unavoidable gap changes often also results in excessive elastic recovery as a high-pressure deformation in the gap area may occur in the material just before it passes the center line and, therefore, expands immediately afterwards. This causes decrepitation or lamination of the compact or, generally, reduced product quality. 

By definition, miscible polymer blends are singlephase mixtures. Miscibility depends on the molecular weight, concentration, temperature, pressure, deformation rate, etc. Flow of these systems can be compared to that of solutions of low molecular weight, miscible components, or to flow of mixtures of polymeric fractions. Both models are far from perfect, but they serve to illustrate the basic behavior of miscible systems. 

The normal stresses obtained at measurement points El and E2 with displacement boundary conditions are ten times weaker than those obtained with stress boundary conditions. Equivalent results have been obtained for variable ranges of normal and shear fracture stiffnesses. Without on-site stress measurements, choosing between these various boundary conditions is difficult. The simultaneous pressure-deformation measurements at the Coaraze site have however enabled carrying out an analysis on the measurement points as well as determining a threshold for normal stress in the joints (see Table 2). The selected boundary conditions are those that more accurately reproduce the initial stresses at Coaraze (i.e. displacement boundary conditions). 

In the same publications we have reported x-ray diffraction patterns showing a marked increase in crystallinity after high-pressure deformation. 

Show that a sphere cut from an anisotropic crystal subjected to hydrostatic pressure deforms into an ellipsoid and determine the orientation of its principal axes,... 

The relationship between pressure, deformation and geometry plays a critical role in microchip design, as it essentially dictates the actuation pressure of valves and the fluidic capacitance introduced by deformable channels. Table 39.2 summarizes several classical results for simple geometries. 

For obstruction, the shape and especially the deformability of the particles are important. Rigid, long fibres have more difficulty travelling a curvy road than spherical or deformable particles, such as micro-organisms. With increasing load, the filter will eventually clog. If this coincides with an increase in pressure, deformation of the filter material may occur, which can lead to the release of particles that were previously retained. 

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