This presentation was held at the 2020 NAFEMS UK Conference "Inspiring Innovation through Engineering Simulation". The conference covered topics ranging from traditional FEA and CFD, to new and emerging areas including artificial intelligence, machine learning and EDA.

Resource Abstract

Uncertainty is responsible for the difference between numerical simulation and experimental data. In most cases the differences can be pinpointed to modeling errors. Round robins are a nice example of uncertainty in numerical simulation. Participants are requested to predict an experimental outcome, while this outcome is withheld. In the end the findings of the participants are presented in combination with the result of the experiment. The differences can be large.

There are epistemic and aleatory uncertainties and the errors in instrumentation are typically of the second kind. A lot of testing will improve the accuracy and lower the error to order of 1%. On the other hand, epistemic uncertainty represents a lack of knowledge. The easy way out is to capture this deficiency in a statistical distribution with a mean value and a standard deviation. However, further study may fill the knowledge gap and the cause of this uncertainty can be eliminated.

It is very tempting to focus on the way of modeling. Finite Element Analysis (FEA) offers an extensive toolkit to simulate the experiment under consideration. The application of linear versus quadratic elements may have a large effect on the outcome, and not in the least, mesh size plays an important role. However, the results from the experiment are in most cases considered as a reference that represents the exact value.

The presentation addresses an experiment with a U-shaped plate. The legs are pulled apart, and strain gauges indicate the stresses in areas with unidirectional as well as biaxial stress states. The accuracy of the measurement is an important aspect of this experiment, and especially the measurement of principal stresses at locations with a biaxial stress state draws attention.

Rosettes initially measure changes in electrical resistance, and these changes are translated to strains. The next step is processing the results towards principal directions and from the strains follow principal stresses by constitutive equations. With each step in the process intrinsic errors (aleatory uncertainty) in measurement and material property accumulates.

The experiment is also simulated with FEA, and the influence of mesh refinement and element type is assessed. The variation in modeling gives confidence in the numerical result and relays the focus on the accuracy of the experiment. Besides the intrinsic error of the instrumentation the location of the measurements is important. Rosettes consist of three strain gauges, rotated over 45°, and this means that strains are not measured on exact the same spot. A closer look at the location of the three components of the rosette highlights the (epistemic) uncertainty in the measured strains.

The presentation focuses on the difference between test and simulation and assesses the underlying aspects.