The fact that matter is made of atoms and that it commonly has some sort of heterogeneous microstructure is ignored in the simplifying approximation that physical quantities, such as energy and momentum, can be handled in the infinitesimallimit. Differential equations can thus be employed in solving problems in continuum mechanics. Some of these differential equations are specific to the materials being investigated and are called constitutive equations, while others capture fundamental physical laws, such as conservation of mass or conservation of momentum. In fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.
The physical laws of solids and fluids do not depend on the coordinate system in which they are observed. Continuum mechanics thus uses tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems, for computational convenience.
Elasticity, which describes materials that return to their rest shape after an applied stress.
Plasticity, which described materials that permanently deform (change their rest shape) after a large enough applied stress.
Rheology Given that some materials are viscoelastic (a combination of elastic and viscous), the boundary between solid mechanics and fluid mechanics is blurry.
Fluid mechanics (including Fluid statics and Fluid dynamics), which deals with the physics of fluids. An important property of fluids is its viscosity, which is the force generated by a fluid in response to a velocity field.
