Elastic and isotropic constitutive relationship

[ftarak]

Hi everybody,
I have just a question about elastic and isotropic constitutive relationship

Why does the stress tensor need an indeterminate hydrostatic term for an incompressible material? for both solids and fluids.

 

[AlephZero]

"Incompressible" means that if you have a hydrostatic stress (or a constant pressure, which is the same thing), the strain is zero.

So you can't get the hydrostatic stress by multiplying the strain tensor by something.

But it is a phsyically real stress, that transmits loads through the solid or fluid, so you have to include it in the model some other way.

 

[ftarak]

"Incompressible" means that if you have a hydrostatic stress (or a constant pressure, which is the same thing), the strain is zero.

So you can't get the hydrostatic stress by multiplying the strain tensor by something.

But it is a phsyically real stress, that transmits loads through the solid or fluid, so you have to include it in the model some other way.

thank you for your answer. that was helpful. I got the point, the point is that the hydrostatic pressure is mean normal stress. and we cannot cancel out the hydrostatic term in the Hooke's law in the situation, which is indeterminate.