In order to improve the credibility of modern simulation tools, uncertainties of different
kinds have to be considered. This work is focused on epistemic uncertainties in the
framework of continuum mechanics, which are taken into account by fuzzy analysis. The
underlying min-max optimization problem of the extension principle is approximated by
-discretization,
resulting in a separation of minimum and maximum problems. To become more
universal, so-called quantities of interest are employed, which allow a general
formulation for the target problem of interest. In this way, the relation to parameter
identification problems based on least-squares functions is highlighted. The solutions
of the related optimization problems with simple constraints are obtained with a
gradient-based scheme, which is derived from a sensitvity analysis for the target
problem by means of a variational formulation. Two numerical examples
for the fuzzy analysis of material parameters are concerned with a necking
problem at large strain elastoplasticity and a perforated strip at large strain
hyperelasticity to demonstrate the versatility of the proposed variational
formulation.
Keywords
fuzzy analysis, $\alpha$-level optimization, quantities of
interest, optimization with simple constraints, large
strain elasticity, large strain elastoplasticity
