Idle thoughts on the role of theory in mechanics

As scientists, we like to think our theories are built on a large body of directly observed phenomena, but we can directly observe only a few, primitive things, like the relative position of two objects -- and even that is called into question by modern physics! Instruments that measure abstract quantities like force and temperature depend on the validity of an underlying theory. For example, a scale provides a useful measurement of weight only if we accept a certain definition of weight. Such definitions are objectively arbitrary, because they can only be ranked in terms of usefulness.

Engineers tend to believe force, stress, strain and the like are fundamental quantities beyond the influence of theory. It is often remarked that analyses or simulations are "theoretical", with the implication that test results are "real". But the objective results of tests are not useful. For example, all we can say objectively about a tension test is that specimen 56 broke when the needle on the force gauge was lined up with the 1000 pound mark. We have to accept a whole host of theories to say that specimen 56 had a failure stress of so-and-so.  These may seem like trivial observations, but consider how many times you have seen test results that appeared to give one answer but proved misleading because of incorrect assumptions about how the testing machine worked, or subtler issues like poorly understood or controlled boundary conditions.

The case of strain bears some additional comment. All competent mechanical engineers know there are at least two definitions of strain -- nominal and true. So they are open to the idea that strain is subject to arbitrary definition and not something that can be measured free of underlying assumptions. The situation of course is actually much more complicated - there are many useful definitions of strain, and many useful definitions of the reference configuration.