I've recently been reading through introductory texts on the mechanical properties of materials such as this. Most start with a description of various material constants such as Young's modulus, Poisson's ratio and a zoo of other properties, and try to determine these properties through a study of dislocations and interatomic interactions.
However, when I read about the very specific test conditions for these kinds of properties, it's not immediately obvious how well these kinds of coefficients and measurements translate to the real world.
For example, I can find coefficients describing hardness, toughness, etc. from laboratory experiments under specific experimental conditions, but it's not obvious that these coefficients can give a more than qualitative description description of how well my nail can hold together a desk, how well my steel truss can hold up a roof, etc., which are ultimately the questions I might be interested in. These coefficients seem to describe very specific geometries, and it seems that I can only get answers about more general geometries using FEA, leaving these kinds of measurements as useful for 1) qualitative descriptions and 2) feeding parameters into FEA.
I think some of the confusion stems from the seemingly arbitrary nature of all these parameters. It appears that someone designed a test and came up with a new parameter every time they were interested in a behavior under different conditions, and there's no minimal degrees-of-freedom type argument that prevents me from coming up with my own test and modulus.
Put another way, what is the argument that the mechanical properties covered by the usual texts (Young's, Poisson's, hardness, toughness, etc.) can give me a complete mechanical description of a system under arbitrary geometries and loads?
Thinking about the parameter space more abstractly, each test can be represented as a material-dependent function that accepts a given material geometry and load geometry and maps it onto strain (throwing out hysteresis and time dependent phenomena for simplification). If we represent our inputs in R^n and our outputs in, say, R^m, what is the minimum number of moduli and constants needed to define this function? What's the argument I won't open up a textbook and find that it defines a new and non-redundant mechanical parameter.
And, if such a well defined relationship exists, where might I find out more about how to go from the parameters derived from well defined experiments (stretching a cylinder, squeezing a flat plate, etc.) and more general material and stress geometries?