Estimate of Material Parameter Uncertainties in Calibrated Simulation Models

This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

In modern engineering design the representation of complex material behavior is often required. During the last decades a huge number of sophisticated constitutive formulations have been derived for different types of materials in different applications. Since the complexity of these models generally does not allow a direct determination of their constitutive parameters inverse strategies are applied to identify their parameter set. A common approach for this purpose is the minimization of the least squares error between measurements from experiments and the computed model responses. For materials behaving highly nonlinear, such as concrete and soils, the application of standard gradient-based optimization strategies often yields not to the optimal parameter set due to the complexity of the objective function containing several local minima. For such problems mainly global optimization strategies, such as genetic algorithms or particle swarm optimization, are utilized.



Since not all parameters of a material model can be identified equally well from one or more experimental setup, the additional assessment of their quality is required. In this paper an approach is proposed where the variation for each parameter is estimated based on the definition of uncertainties of the measurements. This study allows an efficient assessment of the parameter quality including the detection of their dependencies. Furthermore, this approach can be used to detect non-unique identification tasks, where different parameter combinations may lead to similar response values and thus to equivalent small deviations in the identification procedure.



The proposed approach is applied to two different calibration tasks. In one example the non-uniqueness is most dominant and an identification of the whole parameter set is not possible. In the second example, where the elastic and fracture parameters of concrete are identified, we will observe, that one parameter cannot be identified with the test setup. We will see, that two parameters which a have a more global influence on the measurement results can be identified very accurately and other parameter which have a more local or smaller influence can be identified less accurate.