physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
Continuum mechanics refers to the physics/mechanics of continuous bodies such as notably fluids?. As opposed to the mechanics of point particles (to which it is of course related by various limiting processes).
For standard references see
The axiomatization of continuum mechanics internal to toposes has led William Lawvere to the introduction of synthetic differential geometry
and to the notion of cohesion
William Lawvere, Some Thoughts on the Future of Category Theory in A. Carboni, M. Pedicchio, G. Rosolini, Category Theory , Proceedings of the International Conference held in Como, Lecture Notes in Mathematics 1488, Springer (1991)
William Lawvere, Axiomatic cohesion Theory and Applications of Categories, Vol. 19, No. 3, 2007, pp. 41–49. (pdf)
For more on this see also the collecgtion