## General Mechanical

#### How to calculate stress tensor in static structural of a body?

• nishantsinghbme
Subscriber

How can we calculate the stress tensor of a body after analysis in ansys workbench.

Formula is attached.

Thanks

• peteroznewman
Subscriber

The Stress Tensor is a 3×3 matrix with six independent components.

Several scalar values called Invariants can be extracted from the Stress Tensor. One example is VonMises equivalent stress.  Another one is called Stress Intensity, which when divided by 3 is called Hydrostatic Stress.

The formula you show has tr( ) indicating a trace matrix operator, but the stuff in the brackets is not a matrix.

Pressure is generally defined as negative one-third the trace of the stress tensor.

If the P in the formula is intended to represent pressure, then the equation is missing the divide by 3 factor.

• nishantsinghbme
Subscriber

Yes factor 3 is missing from the formula.

So you mean P can be calculated by evaluating the principle stresses in x,y and z direction and divided by three?

• peteroznewman
Subscriber

Pressure, also called Hydrostatic Stress, can be calculated by summing the Normal Stress in X, Y and Z and dividing by 3, which gives the same answer as summming the Maximum, Middle and Minimum Principal Stresses and dividing by 3. The Principal Stresses are generally in a different coordinate system than the Normal Stresses.