Systems and methods for deriving material coefficient values from physical measurements of physical objects are described. These physical measurements can provide material test data. In one embodiment of a method described herein, the material test data can be used to calculate a first subset of material coefficients for use in one or more material models from material test data; the method can define a set of optimization parameters and define a set of relationships between a second subset of the material coefficients and the set of optimization parameters such that values of the material coefficients in the second subset of material coefficients can be calculated from the set of optimization parameters, wherein the first subset and the second subset include all of the material coefficients in the one or more material models and the set of optimization parameters have fewer parameters than a total number of coefficients in the first subset and the second subset; then the method can calculate optimum values of the optimization parameters to yield an optimum fit of the one or more models to the material test data, the optimum fit based on optimum material coefficients calculated from the calculated optimum values of the optimization parameters.