Module 1 : Introduction : Review of Basic Concepts in Mechanics
Lecture
3 : Constitutive Relations and Compatibility Conditions
1.3.6
Generalized Hooke's Law
This is an extension of the Hooke's Law to three dimensions considering both linear and shears deformations. It is based on the generalized definitions of strain. As for the Hooke's Law for linear strain/deformation, the equations for Generalized Hooke's Law are applicable for linear elastic isotropic homogeneous materials only. The 6 equations for linear and shear strains are:
(1.12a)
(1.12b)
(1.12c)
(1.12d)
(1.12e)
(1.12f)
which can also be expressed alternatively as expressions for stress:
(1.13a)
(1.13b)
(1.13c)
(1.13d)
(1.13e)
(1.13f)
where and are the Lame parameters which are related to the Young's modulus E and Poisson's ratio :
and 
are the Lame parameters which are related to the Young's modulus E and Poisson's ratio 
: 
