I have a couple of questions about the stress tensor. I am not an engineering student, so this is the first time I have dealt with internal forces, stress, shears, and such. It is my understanding that the entries in the stress tensor are forces per unit area. I assume this means the total force per unit area. Considering the case of a cylinder with axis along the x axis... Say you press the two flat ends towards each other, i.e, exert a force F on the left surface and -F on the right, such that the cylinder does not move. Is the T_xx entry in the stress tensor then zero for any point inside the cylinder, since the surface forces should cancel so that the point remains stationary? In other words, if I have an object that experiences only surface forces, no body forces, should the stress tensor have all zeros along the diagonal?