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Parameter Identification


Finite Element based simulations are used for a variety of industrial and scientific purposes, whether it is the optimisation of existing products, the development of new prototypes or some other objective which requires a predictive simulation. All thermo-mechanically consistent FE-simulations are based on a material law representing some specific material behaviour. Hence, the user must not only choose a material model which represents the material under consideration (quality), but must also determine a suitable set of material parameters (quantity). Since material parameter sets for thermodynamically consistent material models are usually not published in literature,  the ability to perform a parameter identification is vital for any predictive simulation. In the past twenty years several papers have been dedicated to the concept of parameter identification for purely mechanical material models. However, if temperature effects are to be considered, a thermo-mechanically coupled material model must be used. This requires the identification of calorical quantities alongside the mechanical material parameters. Furthermore, the convection or conduction coefficients defining the thermal boundary conditions are usually unknown as well. These have to be determined to enable an accurate simulation.

The aim of this project is to provide a suitable setup for the identification of mechanical and calorical material parameters. It includes the development of the numerical framework in c++ with interfaces to the fully parallelised c++ in-house FEM-code and to commercial FEM software, as well as the performance of suitable experiments using DIC and thermography systems. Furthermore, an appropriate material model must be chosen and implemented before its material parameters can be identified.

Solution technique

There are a multitude of different approaches to the solution of the so-called inverse problem. The most intuitive, however, is certainly the Finite-Element-Model-Updating method. The main idea of this technique is to minimise the difference between experimental data and the respective simulation results, e.g. by definition of an error square function. This objective function is in the simplest case defined as the error square in displacements (experimental - computed), but can easily be extended to account for other measurable quantities such as forces or temperatures.

The used framework of the parameter identification is a self-developed C++ routine and the numerical results are generated by means of a fully parallelised in-house FEM C++ code, though any commercial FE software could be used as well.


Apart from the numerical framework, experimental data is the essential part of every identification. Not only must an experiment be chosen which allows an identification of all sought material parameters, but these experiments have to be performed with an adequate accuracy to avoid erroneous results. Whereas simple material models can be fitted by means of data from a strain gauge, more complex models require further information as input for a parameter identification. For this reason, a DIC-System is used to measure the displacement field during the experiments.

Figure: Experimental equipment. Aramis system from GOM, tensile
        and torsion machine from W&B, ImageIR from InfraTech.

The temperature field is simultaneously obtained by means of a thermography system. Current experiments feature elastic cooling and plastic heating while the specimen is loaded, followed by a cooling down phase of the specimen during which the displacements are held constant.


Figure: Experimental displacement along the tensile axis. 


Figure: Experimental temperature distribution.


Lars Rose, M.Sc.