Elasticity/Principal stresses

(Redirected from Principal stresses)

Principal Stresses in Two and Three Dimensions

edit

The principal stresses are the components of the stress tensor when the basis is changed in such a way that the shear stress components become zero. To find the principal stresses in two dimensions, we have to find the angle   at which  . This angle is given by

 

Plugging   into the transformation equations for stress we get,

 

Where are the shear tractions usually zero in a body?

The principal stresses in three dimensions are a bit more tedious to calculate. They are given by,

 

where,

 

The quantities   are the stress invariants.

Note: Be careful while implementing above relations in a solver, as the value of:

 

can be out of range of  , which is (-1, 1).

edit

Introduction to Elasticity

edit