#4 - Theoretical Models
I’d like to continue this train of thought on models as ways for engineers to simplify reality. Previously, I talked about empirical models derived from observation and experience. This time, we’ll discuss theoretical or analytical models. This, I think, is what most people imagine as engineering. Some sort of clever mathematical formula is created, usually in a lab, to describe a piece of nature. That formula is then extrapolated and used to describe things not under laboratory conditions.
If the theory is useful in the real world, it gets adopted. If not, it should go by the wayside. It’s no different to kitchen gadgetry. Things you reach for often that are useful to you, like knives and cutting boards, will be close at hand. Things that you maybe try once or twice for the novelty of it, like a lychee peeler, will be relegated to the dusty cupboards above the microwave. But, in the engineering world, I know of at least one major example where that doesn’t seem to be the case: the Tsai-Wu Failure Criteria.
It sounds fancy, but the Tsai-Wu part just refers to the two guys who came up with the thing, Prof. Tsai and Prof. Wu (both career academics). And Failure Criteria is what it sounds like - it should tell you when something will fail - in this case composites like carbon fiber. Carbon fiber is called a composite because it’s a composite of two different materials - a cloth (carbon fiber) and glue (epoxy). It’s no different in principal from paper mâché - strips of paper soaked in glue that get hard when dried. The Tsai-Wu model simplifies reality by treating composites as one homogenous material. In other words, in the paper mâché example, it treats the material as if you blended the paper and the glue together into a paste. It’s not hard to imagine that this paste will behave differently than distinct strips of paper soaked in glue.
This simplification is not inherently a bad thing. But as shown by Dr. LJ Hart-Smith, an engineer of forty years at Boeing, it simply does not represent reality. The Tsai-Wu theory has survived so long because the model itself has adjustments to “calibrate” it to reality. Companies test extensively to calibrate, from small material samples to parts to assemblies. As Dr. Hart-Smith wrote, “The illusion is thereby created that the theory has been validated by this process. In truth, at best, the design has thereby been validated by test because the theories were not sufficiently scientific.”
What I intend is not to discredit the use of theory-based models as a whole, but as a reminder of caution for myself and others to approach models with a healthy skepticism. In my view, it’s much harder to fake empirical models because those are products of painful failures. Theoretical models, on the other hand, can be placed at the same level of importance with much lower levels of practical rigor because of the way engineering education is structured (a topic for later discussion) and because they can be made defaults in widely used computer programs.
Dr. Hart Smith sums it up well:
And to the users of any theories who accept them blindly because other people already have, and they are easily available in computer codes; “Shouldn’t you first have understood what was in the models to know what they could cover and what they couldn’t?” This particular issue has far more widespread implications, particularly in the context of finite element analyses. The computer can, at best, analyse the structural (or whatever) model. It cannot correct for any omissions from the real situation – and it cannot provide any warning if the model was either incomplete or non-representative. Only experience can do that.