Timeline for Why do we include both local and temporal acceleration in fluid mechanics but only consider temporal acceleration in solid-body mechanics?

5 events

when toggle format	what		by	license	comment
2 days ago	comment	added	J. Murray		@BezinaTaki Can you point me toward a resource which treats solid mechanics and doesn't utilize the spatial coordinates? If the body is assumed to be rigid, than the "velocity field" (by which I mean, rate of change of local displacements) is spatially uniform. But in general (e.g. elastodynamics) this isn't true, and you need the spatial term also.
2 days ago	comment	added	mindfulamatter		In solid-mechanics we normally consider rigid bodies, in which every particle has zero relative velocity to all other particles in the solid (which is how solids maintain shape), so you don't normally have spatially varying velocities.
2 days ago	comment	added	Bezina Taki		@J.Murray Thank you, sir, for the detailed and beautiful answer, which I think provides half of the answer to my question. The other half, as Mr. Kyle mentioned in the comment, can be phrased differently: Why is velocity in solid body mechanics related only to time and not to spatial coordinates, whereas in fluid mechanics, it is related to both time and spatial coordinates
2 days ago	comment	added	Kyle Kanos		While accurate, OP seems to be more interested in the lack of the $\mathbf{u}\cdot\nabla$ term in solid body dynamics than the definition/use of the material derivative in fluids.
2 days ago	history	answered	J. Murray	CC BY-SA 4.0