2.12. For silicates, it is tempting to assume that the 34–36 GPa value, which pertains to melts ranging from pure SiO2 to SiO2-poor melts, results from common structural features. The shear modulus value is always a positive number and is expressed as an amount of force per unit area. It is defined as shear stress/shear strain. It takes the form of stress divided by strain, thus: There are 3 main types of elastic modulus: These are the elastic moduli most frequently used in engineering. The coefficients E, ν, μ, and K are related through the following expression: Detailed interrelations for key elastic constants bulk modulus K, Poisson's ratio ν, Young's modulus E, Lame's coefficient λ, and shear modulus μ with a different sets of elastic properties are summarized in Table 1.1. MC, μC, and νC are compressional modulus, shear modulus, and Poisson's ratio of cement, respectively. Some of the important correlations are presented in Table 4.8. At the standard Tg, the relaxation times for these processes differ by seven orders of magnitude. where p is the mass density of the soil. The glass transition itself has little effect on the calcium-hopping frequency, for Fig. To carry out fluid substitution modeling using Gassmann's equation (4.1), we must first determine: (1) the porosity of the rock, (2) the properties of the fluids that occupy the pore space, and (3) and the bulk modulus of the mineral matrix (Km). A large shear modulus value indicates a solid is highly rigid. It can be described in simple terms as a measure of rigidity. Shear stress is different from tension or compres- sion stress in that it tends to make one side of a member slip past the other side of a member adjacent to it. Similarly, working through the inverse Hooke's law, Poisson's ratio ν and Young's modulus E are the only two requirements. These cookies do not store any personal information. This category only includes cookies that ensures basic functionalities and security features of the website. The bulk modulus (K) is like Young's modulus, except in three dimensions. This does not mean, however, that atomic mobility completely vanishes below the glass transition. It is used when a force parallel to a given axis is met by an opposing force, such as friction. Before diving in to take a deeper look at the different types and units of modulus of elasticity (Young’s Modulus), let’s first take a look at a broad definition of this highly important mechanical property. Decoupling of calcium mobility from network relaxation (Gruener et al., 2001). The shear modulus of a material is a measure of its stiffness. Shear stress is caused by forces acting along the object’s two parallel surfaces. The value of the shear modulus for aluminum is about 3.5 × 10 6 psi, or 2.4 × 10 10 N/m 2. The Gassmann's equation fails to yield reliable results when basic assumptions regarding frequency or pore connectivity are violated, as in the case of shaley sands or carbonate rocks. (2001) determined the rate of exchange of AlO bonds from 27Al spin-lattice NMR experiments, the characteristic time for calcium hopping from electrical conductivity measurements, and structural relaxation times from viscosity and Maxwell model (Fig. The International Standard unit of Flexural Modulus is the pascal (Pa or N/m 2 or m-1.kg.s-2). The main application of Young’s modulus is to predict the extension that may occur under tension or the shortening that may occur under compression. The Lame's constant and shear moduli are the only two elastic constants to define the linear elasticity in an isotropic system through Hooke's law. This can be expressed in terms of shear wave velocity and density as: This is also known as the modulus of rigidity. It can be simplified as the tendency of a substance to change from a rectangular shape to a parallelogram. When the material is subject to hydrostatic pressure, the relationship between the pressure p and the volumetric strain e (= ϵ11 + ϵ22 + ϵ33) is linear through relation: K defines the bulk modulus.