Tuning parameters of the material model

IDIADA CZ is part of an international engineering company Applus IDIADA. In the Czech Republic, more than 200 experts deliver a portfolio of services from technical simulations and design proposals over conception designs up to design and series manufacture for automotive, aerospace, and other industries.

Challenge

In order to ensure good agreement between simulation and real part test, a robust material model must be available. Typically a tensile and creep sample tests are provided for calibration of the material model. Calibration of a material model is an iterative process of tuning several (typically around 10) parameters. After running the tensile and creep simulation using these parameters, a comparison to the original test data is made. Based on the correlation between simulation and the test data a new set of parameters is suggested.

Using standard simulation tools is time-costly proportionally to the number of parameters. Therefore it is desirable to decrease the number of iterations. This can be achieved by a smart analytical tool that can quickly recognize the optimal value of parameters.

This is what UptimAI’s solution excels at. Suggested algorithm decreased the number of iterations from thousands to several hundred. Furthermore, UptimAI has provided deep insight into parameter interaction.

For this study, the FEM structural solver Abaqus was used, allowing only a limited number of simulations within the timeframe of the project. Thus, the problem was described in a series of iteratively created surrogate models. In each iteration, a smaller section of the design space was selected in order to focus on ranges of parameters with a higher probability of a better match of material characteristics. Despite the surrogate model being built four times in total, the number of required computations dropped from thousands to hundreds.

Sample of the material under the virtual “testing” in Abaqus (picture: IDIADA CZ)

Solution

Coupling of Abaqus and UptimAI software was easy and straightforward. A standard approach was used, where input files required by Abaqus solver (these are text files in essence) were altered by UptimAI tool. After the simulation has finished, a unified post-processing python script produces resulting tensile and creep curves (in a form of a CSV table).

The UptimAI algorithm is used to process simulation results into the metamodel of agreement between measured and computed material characteristics. The level of agreement was defined as Normalised Mean Square Error (NMSE), observed separately for each material test (tensile test and three tests of creep – at stress 4MPa, 5MPa, and 6MPa). Results presented here are for the creep test at 4MPa.

The analysis of the metamodels began with the UptimAI sensitivity analysis. It revealed that in the first metamodel (the first iteration of the study) one parameter of the material model is dominant. Thus, the range of this parameter, C10, was reduced for the next iteration. There, other parameters showed their importance too, since local extremities they caused were more focused on now. Nevertheless, the effect of some parameters, like δς or δε, is still too negligible even for the last iteration created for the smallest input domain.

Sensitivity analysis – on a smaller domain, the mathematical model is able to describe the problem in more detail

The overall statistical properties of each metamodel were apparent from UptimAI histograms. It was found that the material model has a large overall variance, where any slight modification of the input parameters leads to significant changes in the accuracy of material characteristics. From the second iteration, it suggested the appearance of a distinct local extreme value. It also showed that interactions with parameters Sratio and n are responsible for this behaviour.

Contribution of the parameter Sratio to the statistical result

Position and origin of the extremity were later found on UptimAI total incremental plots. These depicted the sum of direct responses in the match of material curves to changes in particular input parameters and their combination. The figure allowed localizing the extremity with respect to ranges of material parameters, setting the base for the next iteration and reduction of the input domain.

Total incremental plot – sum of increments to the output based on changes in three interacting input parameters

New ranges of input parameters were set according to results of the UptimAI preliminary optimization tool. It used the statistical nature of the model to give recommendations leading to a new reduced input domain with a higher probability of a good match of material characteristics. This method also allows easy graphical comparison of proposed regions for multiple outputs. Here it has shown that model parameters affect all examined cases of creep behaviour (at 4MPa to 6MPa) in the same way. On the other hand, they are often contrary to the tensile behaviour, and thus, the iterative process was repeated again with the main focus on the tensile behaviour of the material.

Left: Example of proposed ranges of parameter Sratio inducing shift of output towards higher/lower values. Right: Adjusted probability distributions of NMSE values after all proposed input regions are applied.

Benefits

• Definition of influential parameters. The number of parameters could be reduced, since some of the inputs are negligible for the agreement of material characteristics.
• Lower computational time. Even though the process was iterative, the number of simulations required in total was cut significantly.
• Deeper insights into the task. Evaluation of the iterative process revealed the complex behaviour of the material model on a wide range of its input parameters.