LaméKonstanten

Lamé-Konstanten, also known as Lamé parameters, are fundamental material constants used in the theory of linear elasticity to describe the elastic behavior of isotropic materials. Named after the French mathematician Gabriel Lamé, these parameters characteristically define how a material responds to stress and strain within the elastic regime.

There are two primary Lamé constants: lambda (λ) and mu (μ). The parameter λ, called the first Lamé constant, is associated with volumetric elasticity and contributes to a material’s ability to resist changes in volume. The shear modulus μ, also known as the second Lamé constant, measures the material's resistance to shear deformation. Both constants are intrinsic properties of a material and are typically expressed in units of force per area (e.g., Pascals).

The Lamé constants are directly related to other elastic moduli, such as Young’s modulus (E) and Poisson’s ratio (ν). For isotropic materials, these relationships are expressed as:

E = μ(3λ + 2μ) / (λ + μ)

and

ν = λ / [2(λ + μ)]

Lamé constants are essential in many engineering applications, including structural analysis, seismic wave modeling, and materials science, as they allow the calculation of stress-strain relationships within elastic limits. They are especially useful because they simplify the representation of isotropic elastic behavior, enabling the derivation of fundamental equations governing elastic deformation.

Since they are material constants, Lamé parameters are determined experimentally through mechanical testing or inferred from other elastic moduli. Understanding these constants is crucial for predicting how materials will respond under various loading conditions.