# Mechanics- stress tensor

1. Apr 2, 2009

### gsh84

The following information is given:

The Cartesian components of stress tensor are: $$\sigma_{ij}=m(\hat \lambda _{i}\hat \mu _{j}+\hat \lambda _{j}\hat \mu _{i}) , (i=1,2,3; \ j=1,2,3)$$.

$$\hat \lambda _{i}$$ and $$\hat \mu_{j}$$ are the Cartesian components of the unit vectors $$\hat \lambda$$ and $$\hat \mu$$ , who enclose an angle of $$2 \alpha$$.

m is a scalar with a stress dimension.

Now my question. What are the components($$\sigma_{11}, \sigma_{12}.. \sigma_{33}$$) of the the stress tensor based based on this formulation?

According to the information you can say: $$\hat \lambda \cdot \hat \mu = \cos 2\alpha$$

Is for $$\sigma_{11}$$ example: $$(\cos 2\alpha+\cos 2\alpha)p$$?
And what would $$\sigma_{12}$$ be? 0?

Last edited: Apr 2, 2009