I think everyone would agree that when a potential difference delta-V is
applied across virtually anything, some current I will flow through
it, and there will be a functional relation between the two.
Likewise, if a mechanical force F (either tension or compression) is
applied to virtually anything, a deformation delta-x will result (let's
not get sidetracked into the cause-and/or-effect discussion here), and
there will be a functional relation between the two.
[SIMPLE PREMISE:] IF the functional relations mentioned above are
CONTINUOUS functions,
[SIMPLE CONSEQUENCE:] THEN, over SOME finite range of values, EITHER
relationship is very nearly LINEAR. (In calculus terms, every
continuous function, over some finite domain, may be described
arbitrarily accurately in terms of its value and its first derivative at
a point inside that finite domain.)
In the second case, we describe materials as obeying Hooke's Law F =
(+/-) k times (delta-x) AS LONG AS THE ELASTIC LIMIT IS NOT EXCEEDED.
(The plus/minus depends on whether we are talking about the force
exerted BY the spring or ON the spring.)
In the first case, virtually everything obey's Ohm's Law AS LONG AS THE
"OHMIC" LIMIT IS NOT EXCEEDED.
BTW, writing Newton's Second Law in the form a = F/m suggests that we
interpret the mass m as the "resistance" of the object to being
accelerated, in other words, its tendency to stay in the same state of
motion in which it had been prior to the application of the force.