# Continuum mechanical analogous of Maxwell stress tensor

• I
Maxwell stress tensor ##\bar{\bar{\mathbf{T}}}## in the static case can be used to determine the total force ##\mathbf{f}## acting on a system of charges contanined in the volume bounded by ##S##

$$\int_{S} \bar{\bar{\mathbf{T}}} \cdot \mathbf n \,\,d S=\mathbf{f}= \frac{d}{dt} \mathbf {{Q_{mech}}}\tag{1}$$

Where ## \mathbf {{Q_{mech}}}## is the (mechanical) momentum of the system of charges.

What theorem/relation is formally analogous to ##(1)## in continuum mechanics? I've read that also in continuum mechanic one can introduce a tensor such that the value of its components on a surface ##S## enclosing a system of masses determines the forces acting on the masses completely.

I could not find this analogy on Jackson or Griffiths, so what is the tensor that is similar to Maxwell stress tensor in mechanics? Is it the stress tensor? By which theorem does it determine the forces on a system of masses?

Related Other Physics Topics News on Phys.org
Orodruin
Staff Emeritus