Modulus of compression

The reciprocal of the elasticity of volume of a fluid is called its modulus of compressibility (p) ... 

By analogy we can define a uniaxial modulus of compression K(q>) and given that the volume fraction is inversely related to the total volume we get... 

In addition to the tensile and shear moduli, a compressive modulus, or modulus of compressibility, K, exists to describe the elastic response to compressive stresses (see Fignre 5.7). The compressive modulus is also sometimes called the bulk modulus. It is the proportionality constant between the compressive stress, CTc, and the bulk strain, represented by the relative change in bulk volume, AV/Vo-... 

Like any disperse system, foams produce non-Newtonian systems, and to characterize their rheological properties information must be obtained on the elasticity modulus (the modulus of compressibility and expansion), the shear modulus, yield stress and effective viscosity, and elastic recovery. 

Figure 3 Typical example of the stress-strain behaviour (E-modulus) of compression moulded glassy pea starch-based TPS materials (HAP10G50W)...

The propagation of acoustic phonons in amorphous media depends on the mechanical and thermal moduli. We will denote the modulus of compression by K, the shear modulus by G, the longitudinal modulus by M = K + 4/3G, the thermal conductivity by c, the thermal expansion coefficient by a, and the ratio of specific heats by y = Cp/Cy. 

The modulus of elasticity, E, and the modulus of rigidity, G, as defined above, apply under longitudinal and shear forces, respectively. When a hydrostatic force is applied, a third elastic modulus, the modulus of compressibility or bulk modulus, K, is used. It is the reciprocal of compressibility, /J, and is defined as the ratio of the hydrostatic pressure, cri,> to the volumetric strain, AV/Vo ... 

Unit weight/ Modulus of Compression Poisson s Cohesion/ Dilatancy Internal friction... 

Compressive stress Compressive strain Modulus of elasticity (if pressure on all sides, modulus of compression)... 

Modulus of Elasticity, Modulus of Rigidity, and Bulk Modulus of Compressibility... 

Most of you have pumped air into a bicycle tire at one time or another. From this and other experiences you know that gases are more easily compressed than liquids. In et jineering, to see how compressible a fluid is, we look up the value of a bulk modulus of compressibility of the fluid. The value of fluid bulk modulus shows how easily the volume of the fluid can be reduced when the pressure acting on it is increased. 

You should undersmnd what is meant by pressure. For stadc fluids, you diould understand Pascal s law, which states that fluid pressure at a point is the same in all direcdons. You should also remember the reladonship between the fluid pressure and the dq>th of the fluicL You should undemand what the fluid properdes such as viscosity and bulk modulus of compressibility mean. You should also have a good idea of how hydraulic systems work. 

Viscosity, vapor pressure, and bulk modulus of compressibility are adffitional fluid properties that engineers consider in design. 

Bulk Modulus of Compressibility A fluid bulk modulus represents how compressible the fluid is. How easily can one reduce the volume of the fluid when the fluid pressure is increased For example, as we discussed in Chapter 10, it would take a pressure of 2.24 X 10 N/m to reduce 1 m volume of vrater by 1% or, said another w, to a final volume of 0.99 m ... 

Serial number Soil type Unit weight Cohesive strength Friction angle Modulus of compression Poisson s ratio Layer thickness... 

Here, G is the shear modulus. If a compression occurs on all sides, then the proportionality constant between the pressure p and the compression — AF/% is the modulus of compression K ... 

Figure 21.30. Scheme fm the calculation of the modulus of compression from the deformed plateau regime of an isotherm. The calculation can be performed at each point of the plateau down to a relative pressure of plpo, thus yielding the modulus at different stages of compression Kq can be calculated from values near relative pressures of 1. 3> is the porosity of the sample in the respective stale (e.g., partially compressed) and Vo the total specific volume... 

Depending on the average pore size, the modulus of compression, and the type of aerogel under investigation, the compression of the sample can be in part or totally irreversible. In particular, sUica-based aerogels without organic surface modification are irreversibly deformed. 

Figure 6.31. Poly(methyl methacrylate)/poly(butylacrylate) latex semi-IPN. Dependence of tensile modulus of compression-molded specimens on latex particle composition and type Fg is Young s modulus open squares, physical blends open circles, HLPl, open hexagons, HLP2 with BDMA in first stage filled hexagons, HLP2 with BDMA in second stage curve 1, based on BA homopolymer data curve 2, based on BA/BDMA copolymer data broken curves, calculated wilh as noted. ...

The development of the physical chemistry of rubber was greatly aided by the clear definition of an "ideal" state for this material. An ideal rubber is an amorphous, isotropic solid. The liquidlike structure of rubber was discovered very soon after the technique of X-ray scattering was developed. An isotropic material is characterized by physical properties that do not depend on the orientation of the sample. The deformation of an isotropic solid can be characterized by only two unique moduli the modulus of compression, K, and the shear modulus, G. A solid is characterized by equilibrium dimensions that are functions of temperature, pressure, and the externally imposed constraints. It is convenient to define a shape vector, L, whose components are the length, width, and height of a rectangular parallelepiped. For a system with no external constraints, the shape vector can be expressed as ... 

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