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Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the pressure varies during compression: constant- temperature (isothermal ), constant- entropy (isentropic ), and other variations are possible. Such distinctions are especially relevant for gases.
The third-order Birch–Murnaghan isothermal equation of state is given by = [() / /] {+ (′) [() /]}. where P is the pressure, V 0 is the reference volume, V is the deformed volume, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from ...
In materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain.
The bulk modulus is an extension of Young's modulus to three dimensions. Flexural modulus ( E flex ) describes the object's tendency to flex when acted upon by a moment . Two other elastic moduli are Lamé's first parameter , λ, and P-wave modulus , M , as used in table of modulus comparisons given below references.
In fluid mechanics, the Tait equation is an equation of state, used to relate liquid density to hydrostatic pressure. The equation was originally published by Peter Guthrie Tait in 1888 in the form [1] A Π {\displaystyle {\frac {V_ {0}-V} {PV_ {0}}}= {\frac {A} {\Pi +P}}} where is the hydrostatic pressure in addition to the atmospheric one, is ...
Stress-strain relation in a linear elastic material. The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [1][2] Other names are elastic modulus tensor and stiffness tensor. Common symbols include and . The defining equation can be written as.
In practice, the Murnaghan equation is used to perform a regression on a data set, where one gets the values of the coefficients K 0 and K′ 0. These coefficients obtained, and knowing the value of the volume to ambient conditions, then we are in principle able to calculate the volume, density and bulk modulus for any pressure.
In mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (compression). It is opposed to tensile strength which withstands loads tending to elongate, resisting tension (being pulled apart). In the study of strength of materials, compressive strength ...