Module 4 : Nonlinear elasticity
  Lecture 28 : Boundary Conditions
 

 

Equation 28.15 and 28.16 are the incremental stress-strain relations. They can be written in more symmetric form by using the incompressibility relation,

(28.17)

which can be used in 28.15 to yield,

(28.18)

We then write,

(28.19)

The stress-strain relations then have the form,

(28.20)

Which contain three incremental elastic coefficients,  and . We can write also the expressions for incremental shear stresses,

(28.21)

The six equations 28.19 and 28.20 are the complete set of incomplete stress relations for the orthotropic incompressible medium when the principal directions of the initial stress are located in the planes of the elastic symmetry.

(28.22)

                    

(28.23)

Shear components can be written as                                                           

(28.24)

In which the elastic constants are obtained as (the derivation of these equations are not being presented here)                                                

(28.25)

In the above set of equations, in case, , the elastic constant  can be obtained as

(28.26)