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The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume .
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 ...
Generally, at constant temperature, the bulk modulus is defined by: = (). The easiest way to get an equation of state linking P and V is to assume that K is constant, that is to say, independent of pressure and deformation of the solid, then we simply find Hooke's law. In this case, the volume decreases exponentially with pressure.
A pressure gauge's bulk modulus is known, and its thermal equation of state is well known. To study a solid with unknown bulk modulus, it has to be loaded with a pressure gauge, and its pressure will be determined from its pressure gauge. The most common pressure gauges are Au, Pt, Cu, and MgO, etc.
The Poisson's ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. [3] Most materials have Poisson's ratio values ranging between 0.0 and 0.5.
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.
where () and () are the rock bulk moduli saturated with fluid 1 and fluid 2, () and () are the bulk moduli of the fluids themselves, and is the rock's porosity. Step 3: Leave the shear modulus unchanged (rigidity is independent of fluid type):
The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters. Young's modulus [ edit ]