|
|
| Line 1: |
Line 1: |
| In [[linear elasticity]], the '''Lamé parameters''' are the two parameters
| | The author's title is Christy. It's not a typical factor but what I like doing is to climb but I don't have the time recently. Her family life in Alaska but her husband desires them to move. I am currently a journey agent.<br><br>Feel free to surf to my blog ... [http://www.publicpledge.com/blogs/post/7034 certified psychics] |
| | |
| * λ, also called ''Lamé's first parameter''
| |
| * μ, the [[shear modulus]] or ''Lamé's second parameter'' (also referred to as '''G''')
| |
| | |
| In homogenous and [[isotropic]] materials, these satisfy [[Hooke's law]] in 3D,
| |
| | |
| :<math>\sigma=2\mu \varepsilon +\lambda \; \mathrm{tr}(\varepsilon)I</math>
| |
| | |
| where σ is the [[Stress (physics)|stress]], ε the [[strain tensor]], <math>\scriptstyle I</math> the [[identity matrix]] and <math>\scriptstyle\mathrm{tr}(\cdot)</math> the [[Trace (linear algebra)|trace]] function.
| |
| | |
| The first parameter λ is related to the bulk modulus and the shear modulus via <math>K = \lambda + (2/3) \mu</math> in three-dimensions and <math>K = \lambda + \mu</math> for two-dimensional solids, and serves to simplify the stiffness matrix in Hooke's law.
| |
| Although the shear modulus, μ, must be positive, the Lamé's first parameter, λ, can be negative, in principle; however, for most materials it is also positive. The two parameters together constitute a parameterization of the elastic moduli for homogeneous isotropic media, popular in mathematical literature, and are thus related to the other elastic moduli.
| |
| | |
| The parameters are named after [[Gabriel Lamé]].
| |
| | |
| == References ==
| |
| * K. Feng, Z.-C. Shi, ''Mathematical Theory of Elastic Structures'', Springer New York, ISBN 0-387-51326-4, (1981)
| |
| * G. Mavko, T. Mukerji, J. Dvorkin, ''The Rock Physics Handbook'', Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)
| |
| | |
| | |
| {{Elastic moduli}}
| |
| | |
| {{DEFAULTSORT:Lame parameters}}
| |
| {{physics-stub}}
| |
| | |
| [[Category:Elasticity (physics)]]
| |
The author's title is Christy. It's not a typical factor but what I like doing is to climb but I don't have the time recently. Her family life in Alaska but her husband desires them to move. I am currently a journey agent.
Feel free to surf to my blog ... certified psychics