The ProblemTake the process of free metal forming: you need to understand the framework of the elastoplasticity theory and the complexity and limits of its mathematics derived from the mathematics of continuum mechanics. Deformation is decomposed (replicated?) into elastic and plastic parts and for simplicity decompositions shall determine stress and kinematical quantities. However, resulting PDEs can be solved by finite element schemes. They "only" need to be calibrated related to the physical properties of the material that is dependent on recipes, and properties that are result of the process - like rolling and thermal treatment? And work as predictive models for shapes? If you buy a metal sheet you order it by standardized "names". And this is where the headache begins.
The SolutionStandardized mass-steel allows ranges of physical properties of up to 15%. But each single sheet has its own metallurgical fingerprints. It is impossible, to measure the properties before bending, because you needed to destroy part of the sheet. So, you need to recalibrate your models during the forming process ("continuously"), say, by observing the force-at-angle trajectory over thprocess (transformed from a value that itself is not only a geometrical calculation, but dependent on material). For explanation of the quantified elastoplastic behavior in this step. The closer you come to the final shape the more your system knows about the concrete material and the better it can explain ....
You could make continuous measurements of the shape? First, this has cost. Second, the material does not stay in the form you brought it by the machine, it uses its elasticity memory and reshapes.
As coal-faced mathematicians, we know, how to model, solve and recalibrate such processes - fast and accurate. With this respect metal forming dynamics is not so different from financial market dynamics. A concrete angle has been materialized from the many possible .... Sounds familiar?