1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The elasticity/stiffness tensor for an isotropic materials

  1. Feb 23, 2016 #1
    Hi PF,

    As you may know, is the the elasticity/stiffness tensor for isotropic and homogeneous materials characterized by two independant material parameters (λ and μ) and is given by the bellow representation.
    [tex]C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu(\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk})[/tex]
    Do any of you know a sound argument, mostly relaying on physical intuition, for why this is the most general form of the elasticity tensor for isotropic and homogeneous materials?

    Of course one could always impose all the symmetries (for an isotropic material) upon the elasticity tensor and go through all the necessary and tedious computations to derive this result... But this is unfortunately not what I'm looking for.

    And furthermore, what are/is the difference between isotropic materials and materials possessing cubic symmetry, where the most general elasticity tensor instead is written
    [tex]C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu\delta_{ik}\delta_{jl} + \nu\delta_{il}\delta_{jk}[/tex]
    and is characterized by three (instead of two) independant material parameters.
    That is, why is μ = ν for isotopic materials ?

    Thanks in advance :-))
     
  2. jcsd
  3. Feb 23, 2016 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The most general isotropic rank four tensor is of the form with three independent parameters. However, this does not satisfy the symmetries expected from the stiffness tensor. It only does so when ##\mu = \nu##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The elasticity/stiffness tensor for an isotropic materials
Loading...