Parameter Identification in Continuum Mechanics: From Hand-Fitting to Stochastic Modelling

After a brief review on the development of three mathematical models in the history of mechanics, we outline today’s role of parameter identification within the process of model building. On this basis, parameter identification is illustrated as a direct method by hand-fitting for some simple mathematical structures from the early stages of mathematical modeling. The beginning of so called “advanced constitutive modeling” in the sixties of the twentieth century rendered parameter identification as a least-squares problem. For its solution evolution strategies and more efficient optimization algorithms have been introduced by several researchers. After addressing these developments, we will also outline some newer aspects such as inhomogeneous field problems and stochastic methods.