Let's take a step back and look at the more general case, as follows.
We model an elastic solid as if it were a coil spring. Pull on its ends, and it stretches while generating an opposing force to your hands, in proportion to the amount of displacement.
In system dynamics we learn that it is impossible to instantaneously assign a displacement to a spring, a current flow through an inductor, a voltage across a capacitor, or a velocity to a mass. For example, in the case of a mass, it responds to a force by integrating it over time to yield a velocity- and we say that masses possess integral causality when forces are applied: you apply a force as an input, and obtain an output- velocity- as a causal consequence.
In the case of a spring, you apply a velocity difference across the ends and the spring integrates this to yield an opposing force: the reverse of the situation with a mass. Springs have integral causality to velocity differences whereas masses have integral causality to forces.
An elastic solid is a spring, which means that the velocity difference imposed across its ends produces a force. This means that the velocity difference comes first and the stress (caused by deflection of the spring) is the causal result.
If our dynamical system contains for example a voltage source driving a capacitor, the system is unphysical as the current would go to infinity. It exhibits what is called differential causality and when excited, the system "looks for" any stray series inductance (however tiny) it can find which would permit an integral-causality solution.
A similar situation exists for an inductor driven by a current source.