Parameter identification for constitutive models with error control

Other conference contribution, 2004

A recently proposed technique for the calibration of constitutive models, that is based on optimization with built-in error control, is applied to Norton's viscoelasticity model. In order to focus on the characteristic features, only the constitutive response for uniaxial stress is considered; however, the extension to multiaxial states and spatially non-homogeneous situations is quite straightforward although technically more complex. Essentially, the optimization strategy is based on Newton's method and consists of solving three linear problems running forwards in time and one linear problem (for the costate) running backwards in time. It is interesting to note that the same problem character is pertinent to the solution of the dual problem, which is the basis for the a posteriori error computation.