Lame's First Parameter (G,`nu`)

The Lame's First Parameter (G,`nu`) calculator computes Lame's first parameter based on the Shear Modulus and Poisson's Ratio.

INSTRUCTIONS: Choose units and enter the following:

• (G) Shear Modulus
• (ν) Poisson's Ratio

Lame's First Parameter (G,`nu`) (λ): The results are return in Newtons per square meter (N/m²).  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Lame's First Parameter, `lambda`, is used in the equation computing the stress in 3D satisfying Hooke's Law.  This equation defines Lame's First Parameter in terms of the Shear Modulus (G) and the Poisson's Ratio (`nu`).

`lambda = (2 G nu)/(1-2nu)`

where:

• λ = Lame's First Parameter
• ν = Poisson's Ratio
• G = Shear Modulus

Lame` Parameters

In the context of solid mechanics and material science, Lame's parameters, also known as Lame constants or elastic constants, are two parameters used to describe the elastic properties of an isotropic (uniform in all directions) linear elastic material. These parameters are denoted by λ (lambda) and μ (mu).

The Lame constants are used in the linear elasticity theory to relate stress and strain in a material. The relationship between stress (σ) and strain (ε) in a three-dimensional isotropic linear elastic material is given by:

σ_ij​=λϵ_kk​δ_ij​ + 2μϵ_ij​

Where:

• σ_ij is the stress tensor,
• ϵ_ij is the strain tensor,
• δ_ij​ is the Kronecker delta (equal to 1 for i=j and 0 for i≠j),
• λ is Lame's first parameter,
• μ is Lame's second parameter.

The Lame parameters are related to other elastic constants, such as Young's modulus (E) and Poisson's ratio (ν), through the following relationships:

`λ=(E⋅ν)/((1+ν)(1−2ν))`

`μ=E/(2(1+ν))`​

Lame's Parameter Calculators

• Lame's First Parameter (G,M): Lame's first parameter (λ) based on the shear modulus and p-wave modulus.
• Lame's First Parameter (K,E):Lame's First Parameter (λ) based on the Bulk Modulus and Young's Modulus.
• Lame's First Parameter (K,ν):  Lame's First Parameter based on the bulk modulus and Poisson's ratio.
• Lame's First Parameter (E,G): Lame's First Parameter in terms of the Young's Modulus and the Shear Modulus.
• Lame's First Parameter (K,G): Lame's First Parameter in terms of the Bulk Modulus and the Shear Modulus.
• Lame's First Parameter (E,ν):  Lame's First Parameter based on the Young's modulus and Poisson's ratio.
• Lame's First Parameter (G,ν):  Lame's First Parameter based on the Shear modulus and Poisson's ratio.