experimentally, stresses cannot be measured directly

photoelasticity gives you maximum shear stress contours

No, not quite. One can take photoelasticity to measure *strains*. In fact the argument that it is strains that photoelasticity measures, would be more sound.

So, essentially, Henry Tan's beginning position is correct. Stress can never be measured directly in any experiment. It's always an inferred (i.e. indirectly defined) quantity.

I have posted a separate entry in my blog on this issue. Please check it there. If necessary, I will move that entry to the main forum as well.

Dr. Adams in Bristol uses probe to measure fluid pressure in intervertebral disc and treats it as the stress component in the soft tissue. Maybe this is not considered as a direct measurement.

Since hydrated soft tissues are poroelastic, this could be only a direct measure of the pore pressure in the fluid, which is only one component of the total Terzaghi effective stress. The stress in the solid phase (in disc, a collagen-proteoglycan composite) is also potentially important in this tissue.

In some simple cases, such as in the uniaxial tension test, the stresses can be measured directly. Then with these incomplete experimental results, the relation between stresses and strains is established to predict more complex stresses when the strains are known. I think this is a typical strategy people use.  

Dear Bin Liu, even in a uniaxial tension test, is it not the force that is measured and then divided by the crossectional area to find the stress? Whether the area is the original area or the current area can result in different names for the measured stress.

I agree with Dr Tan's statement that stresses cannot be measures directly. Forces and displacements are the quantities one usually measures.

On a related note, if one defines the spatially varying microscopic stress density to be a tensor field whose divergence is the vectorial force density then this stress field density is rendered ambiguos because then one can add a divergence free quantity  e.g. the curl of an arbitrary tensor field to the stress density without affecting the "physical" force. This issue of uniqueness of stress has been discussed at length in the literature on the subject of defining stress in a quantum-mechanical framework and a common consesus does not exist.