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Lame's First Parameter (K,ν)

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Last modified by
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Feb 20, 2024, 8:08:59 PM
Created by
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Dec 27, 2013, 6:43:29 AM
λ=3Kν1+ν
(K)Bulk Modulus
(ν)Poisson's Ratio
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The Lame's First Parameter (K,ν) calculator computes Lame's First Parameter based on the bulk modulus and Poisson's ratio.

INSTRUCTIONS: Choose units and enter the following:

  • ) Poisson's Ratio
  • (K) Bulk Modulus

Lame's First Parameter (K,ν) (λ): The parameter is returned 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 (K,ν) equation computes Lame's First Parameter, λ, computing the stress in 3D satisfying Hooke's Law.  This equation defines Lame's First Parameter in terms of the Bulk Modulus (K) and Poisson's Ratio (ν).

λ= 3Kν1+ν

where:

  • λ = Lame's First Parameter
  • K = Bulk Modulus
  • ν = Poisson's Ratio


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:

σij​=λϵkk​δij​ + 2μϵij​

Where:

  • σij is the stress tensor,
  • ϵij is the strain tensor,
  • δij​ 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=Eν(1+ν)(12ν)

μ=E2(1+ν)

Lame's Parameter Calculators


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