Using Full Field Data to Produce a Single Indentation Test for Fully Characterising the Mooney Rivlin Material Model

Abstract

A theoretical testing method for fully characterising the Mooney-Rivlin three-parameter hyper-elastic material model is proposed by capturing full-field digital image correlation (DIC) data, namely displacement field and indentation force data. A finite element model with known parameters will act as the experimental model against which all data will be referenced (a preliminary test case). Going forward this stand-in model will be replaced with physical test data. This paper also introduces a new concept, the concept of hyperplanes. These hyperplanes represent regions in the force and displacement field data where all the objective function values are equal. The paper concludes that the Mooney-Rivlin material model can theoretically be fully characterised in a single indentation test. By applying the methods discussed in the paper when using full-field data operating under the assumption of hyper-planes.

A New Method for Improving Inverse Finite Element Method Material Characterization for the Mooney–Rivlin Material Model through Constrained Optimization

“…The research in this paper builds upon previous work by using a modified version of the hyperplane method described in [14]. In this study, we modified the method for characterizing the Mooney-Rivlin model, but the most significant difference is the use of new test data.…”

“…These factors motivated the research presented in this paper. The research presented here expands upon previous studies in [14] by exploring a modified version of the previous hyperplane method on data obtained from physical experiments as opposed to simulated experiments. In an effort to account for the curvature of the design space in areas with low error, the method was modified by replacing the intersecting planes with a constrained optimization approach.…”

“…Based on these findings, a method was developed to capture this rotation and isolate unique solutions for the Mooney-Rivlin material model. It should be noted that the results of the previous paper [14] were evaluated only on simulated data, and the method's applicability to physical data remains uncertain, which the research of this paper aims to resolve. Additionally, it was found that the lowerror regions were not perfectly flat but had a slight curvature, although assuming them to be flat near the optimal solution did produce low-error results.…”

“…In previous research [14], it was hypothesized that the non-unique solutions were caused by local minima scattered throughout the design space. To gain insight into the distribution of local minima, error functions between predicted and measured material behavior from a non-standard indentation load case (depicted in Figure 1) was used to sample different areas of the design space.…”

“…Comparing Figures 2b and 3b, it is clear that the two regions have different relationships with the constitutive model parameters. Further investigation revealed that these regions, which are referred to as hyperplanes in [14], rotate around the correct solution. The rotation was found to be dependent on the loading of the sample.…”