Identification of material parameters for FEM material models
As customer service, we first of all offer software tools for the identification of material parameters for (non-linear) material models within the field of FEM. The procedure used is applicable to:
- almost all typical material models and several more complex models for simulation of the mechanical behaviour of solid bodies.
- almost all typical FE programming packages
From comparison of results from laboratory tests and the corresponding FEM simulation calculations, an optimised set of parameters can be derived for a model of the material. The laboratory tests are concipated such that
- the exact material behaviour to be analysed is tested within an appropriate range of strain- and time-steps.
- in each individual laboratory test the forces applied to the sample and the two- or three-dimensional surface deformation are measured simultaneously, the latter being achieved by a contact-free optical measurement.
Interpolation of measured deformations in the FE mesh
Since comparison between experiment and simulation occurs via comparison of surface deformations, an FE model is constructed for each sample geometry and the forces measured at any moment in a run are introduced into corresponding times in the model. The surface deformations measured are likewise introduced by interpolation to the appropriate FE knot. Numerical calculation of the material parameter follows:
- based on the least squares method,
- by variation within the optimisation routine such that the difference between measured and simulated deformations in the weighted mean are minimised,
- by simultaneous variation of all material parameters.
The derivatives necessary within the routine are assessed numerically. The interface between the optimisation routine and the chosen FE software can be designed such that no modification of the FE software must be made.
- Parameter identification for a PUR-adhesive
Several experiments | Simultaneous variation of all parameters
The reason for deriving all parameters of a material model with several experiments by simultaneous variation of all parameters arises from several factors:
- an exhaustive amount of experimental data guarantees stable and clear estimates of material parameters.
- with a complete set of experimental data one can cover the entire spectrum of the material behaviour according to any given law.
- The optimisation process derives the material parameters with reference to various sources of error.
Restrictions only occur in as far as:
- the chosen material model is not able to describe the mechanical behaviour in a sufficiently comprehensive manner. One speaks here of model error.
- experimental data always contain error. Further scatter in data occurs due to variations in the test sample material itself.
Thus, the simultaneous variation of all parameters ensures an optimum set of parameters in the material model and an optimum fit to all experiments. Furthermore, the consideration of all experimental runs within an optimisation routine provides an improved fit of the simulation to the scatter in experimental data.
Inhomogeneous deformation fields | simulation reliability
In order to ensure simulation reliability, the material parameters derived are compared to those derived from laboratory tests. Here it is important to assess inhomogeneous deformations experimentally in order to compare indirect multi-axial distortion states.
- Tensile samples with holes can be used for example. Multi-axial distortions are thereby sufficiently characterised.
- Phenomena such as necking of ductile metallic or polymeric samples can also be accurately covered.
- Such data are measured during the entire test run and deliver far more meaningful results than the deformation fields of homogeneous tensile samples.
The simultaneous characterisation of different sample geometries, e.g. samples with holes and a side notch, can support this effect.
The following figure describes the verification of parameter identification for a compact PU-material. A parameter set was identified by the simutaneous consideration of two short-time tests and one long-term test on samples with holes. The total number of terms in the sum of the squares of errors was 322,480. Strain in two directions over 722 time steps were taken at 116 identification nodes for the identification.
- Verification of material parameters identified
Simultaneous consideration of short- and long-term behaviour
During the characterisation of material parameters for modular material laws, the parameters are commonly separated into different sets, which are then separately characterised experimentally. This means that, for example, in the case of viscoelastic materials, the previously identified elastic parameters are introduced into the identification of viscous relaxation as constants.
Often, however, viscoelastic materials such as rubber are subject to various short- and long-term strains simultaneously. It is therefore an important demand on the parameter optimisation that the material behaviour be covered over the entire time scale to be considered. In order to do this:
- a method with the simultaneous variation of all parameters from short- and long-term tests is used in which the parameters for different time scales need not be separated.
We have developed and apply a method for identification of material parameters based on the comparison of experimental and simulated deformation fields which delivers:
- an optimised and averaged agreement between experimental and simulated deformations for all experimental observations,
- time and cost savings due to shortened long-term experiments,
- optimisation routines which are compatible with generally available FE programmes.
The procedure is mobile in application, due to the contact-free non-destructive optical measurement setup used.