hi.. when is the nine component stress matrix not SYMETRIC ? In what type of situatiosn does such a situation arises ? and how to deal with such situations?

Regards

ram

Hi,

The symmetry of the stress tensor is due to moment equilibrium on an infinitesimal element after neglecting higher order effects such as inertial effects, spatially varying body forces etc. I am not aware of any situation where these higher order terms are significant.

Best wishes.

Madhu

If there is any moment inequilibrium, then how does one handle this?

Typically the effect is 2nd order or higher and can be safely ignored. I have not seen any continuum mechanics book treat consider these higher order terms (not even for Reynolds averaged or Favre averaged equations of turbulent flow). One would have to solve for the moment equilibrium or angular velocity and also change the constitutive equations to account for the non-symmetric tensor. I have never seen a formulation for this.

most continuum mechanics considered only infinitesimal deformation and ignored the higher term in strain/stress tensors. However, under large (finite) deformation theory, the stress matrix is in general not symmetric. Please refer to:

Introduction to Continuum Mechanics, 3rd Ed. by WM Lai, D Rubin, and E Krempl.

Hi,

Only when the force couple is neglected, the stress tensor is symmetric.

In fluid mechanics, in most cases the stress tensor is symmetric except for electric or magnetic field there.

Even in inertia cases, the stress tensor is still symmetric, like in ploymer fluid.

I remember Batchelor ever stated these problem in his classic book "An Introduction to Fluid Dynamics".

Best, Xiaoming