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About the Tool

The tool SM-08 computes the values of six elasticity constants: Young's modulus (E), Poisson's ratio (ν), shear modulus (G), bulk modulus (K), Lamé's first parameter (λ),and p-wave modulus (M). Given any two of the constants, the tool computes the values of the other four constants.

In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.

Tutorial

Assume the values of bulk modulus (K) and Lamé's first parameter (λ) are 10 and 0.1, respectively.

The input in the tool is

After clicking "Run", the results will be shown as follows in another page.

Bulk Modulus: K = 10

Young's Modulus: E = 29.7993311

Lamé's First Parameter: λ = 0.1

Shear Modulus: G = 14.85

Poisson's Ratio: ν = 0.00334448

P-Wave Modulus: M = 29.8

Subject Review

Conversion of Elasticity Constants

In description of mechanical properties of isotropic linearly elastic materials, the following elasticity constants are often used:

Elasticity Constants

These constants are not independent; any two of them can be used to express the others. For instance, given E and ν, the other elasticity can be written as

Conversion of Elasticity Constants

References

1. Gere, J. M., and Stephen P. Timoshenko, S. P., 1997, Mechanics of Materials, 4th edition, PWS Publishing Co., Boston.

2. Popov, E. P., 1998, Engineering Mechanics of Solids, 2nd ed., Prentice Hall, Upper Saddle River, New Jersey.

3. Yang, B., 2005, Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes, Elsevier Science, Boston.