Elastic Moduli Converter E G K
Our geology & geophysics calculator computes elastic moduli e, g, k, accurately. Enter measurements for results with formulas and error analysis.
Formula
E = 2G(1+v) = 3K(1-2v) = 9KG/(3K+G)
For isotropic linear elastic materials, only two independent elastic constants are needed. All others can be derived. E = Young's Modulus, G = Shear Modulus, K = Bulk Modulus, v = Poisson's Ratio. Lambda (first Lame parameter) = K - 2G/3.
Worked Examples
Example 1: Steel Properties Conversion
Problem: Steel has Young's Modulus E = 200 GPa and Poisson's Ratio v = 0.30. Calculate all other elastic moduli.
Solution: G = E / (2(1 + v)) = 200 / (2 x 1.30) = 76.92 GPa\nK = E / (3(1 - 2v)) = 200 / (3 x 0.40) = 166.67 GPa\nLambda = K - 2G/3 = 166.67 - 51.28 = 115.38 GPa\nM = K + 4G/3 = 166.67 + 102.56 = 269.23 GPa\nVp/Vs = sqrt(M/G) = sqrt(3.50) = 1.871
Result: G = 76.92 GPa | K = 166.67 GPa | Lambda = 115.38 GPa
Example 2: Sandstone from Seismic Data
Problem: A sandstone sample has Shear Modulus G = 12 GPa and Bulk Modulus K = 20 GPa. Determine E and Poisson's Ratio.
Solution: E = 9KG / (3K + G) = 9 x 20 x 12 / (60 + 12) = 2160 / 72 = 30 GPa\nv = (3K - 2G) / (2(3K + G)) = (60 - 24) / (2 x 72) = 36 / 144 = 0.25\nLambda = K - 2G/3 = 20 - 8 = 12 GPa\nVp/Vs = sqrt((K + 4G/3) / G) = sqrt(36/12) = 1.732
Result: E = 30 GPa | v = 0.25 | Vp/Vs = 1.732
Frequently Asked Questions
What are elastic moduli and why are they important in geology and engineering?
Elastic moduli are fundamental material properties that describe how a material deforms under stress and returns to its original shape when the stress is removed. The four primary elastic moduli are Young's Modulus (E), which measures resistance to axial stretching or compression; Shear Modulus (G), which measures resistance to shape change; Bulk Modulus (K), which measures resistance to uniform compression; and Poisson's Ratio, which describes how a material contracts laterally when stretched. In geology and geophysics, these parameters are essential for understanding seismic wave propagation, rock mechanics, reservoir characterization, and earthquake analysis. In engineering, they determine structural behavior under load and are critical for design calculations.
How are the different elastic moduli related to each other mathematically?
For isotropic, linearly elastic materials, only two independent elastic constants are needed to fully describe the material's elastic behavior. All other moduli can be derived from any known pair. The key relationships include: E = 2G(1 + v), which connects Young's Modulus to Shear Modulus and Poisson's Ratio; E = 3K(1 - 2v), which links Young's Modulus to Bulk Modulus and Poisson's Ratio; and G = E / (2(1 + v)), which derives Shear Modulus from Young's Modulus and Poisson's Ratio. The Lame parameters (lambda and mu, where mu equals G) provide an alternative description commonly used in seismology. These relationships assume the material is homogeneous and isotropic, meaning its properties are the same in all directions.
What are typical elastic moduli values for common rocks and minerals?
Rock elastic properties vary widely depending on composition, porosity, saturation, and confining pressure. Granite typically has a Young's Modulus of 40 to 70 GPa, Shear Modulus of 20 to 30 GPa, Bulk Modulus of 25 to 55 GPa, and Poisson's Ratio of 0.20 to 0.30. Sandstone ranges from 10 to 40 GPa for Young's Modulus depending on porosity and cementation. Limestone has Young's Modulus of 20 to 70 GPa. Shale is highly anisotropic but typically shows 5 to 30 GPa. Basalt has values of 50 to 100 GPa for Young's Modulus. These values increase with confining pressure and decrease with increasing porosity, temperature, and fluid saturation. In geophysics, dynamic moduli measured from seismic waves are typically higher than static moduli measured in laboratory tests.
How are elastic moduli used in seismic wave velocity calculations?
Elastic moduli directly control the velocities of seismic waves through Earth materials. The P-wave (compressional wave) velocity is calculated as Vp = sqrt((K + 4G/3) / rho), where rho is density. The S-wave (shear wave) velocity is Vs = sqrt(G / rho). The ratio Vp/Vs is related to Poisson's Ratio by the equation v = (Vp/Vs)^2 - 2) / (2((Vp/Vs)^2 - 1)). These relationships are fundamental in seismology for determining rock properties from seismic surveys, earthquake analysis, and reservoir characterization. AVO (Amplitude Versus Offset) analysis in petroleum exploration uses changes in elastic moduli at geological boundaries to predict fluid content and lithology from surface seismic data.
What formula does Elastic Moduli Converter E G K use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.