How robust is the virtual fields method with respect to experimental inhomogeneities for bulge inflation testing of hyperelastic materials?

Mechanical characterization of biological soft tissue can be a challenging process due to its inherent inhomogeneities. Constitutive model calibration based on the virtual fields method enables the use of full-field deformation and thickness data in order to obtain region-specific material parameters. However, for practical reasons, assumptions are often made in model calibration frameworks, e.g., by using the average sample thickness and deriving homogenized material parameters.

This study investigates the effect of these assumptions on the material parameters predicted by the virtual fields method. To this end, synthetic datasets of bulge inflation experiments were created using a finite element model and parameter identification was performed.

The ground truth parameters could be retrieved for a homogeneous sample with a high accuracy of 0.15%, even when only part of the full-field deformation data was known. For samples with a nonuniform thickness, the parameters could still be obtained with an error of 4% when taking into account the average sample thickness. However by including the region-specific thickness, parameters and stress responses closer to the ground truth were found, within 1% error. When samples showed inhomogeneous material properties spread throughout the sample, the obtained parameters resulted in a more homogenized stress response, eliminating the minimal and maximal stresses of the ground truth response. The ground truth stress response could not be obtained when the sample consisted of regions of different material properties. Further, only an incremental error of $0.6\text{\%}pt.$ was seen when decreasing the resolution in the parameter fitting framework by a factor 2.5 for both homogeneous samples and samples with a nonuniform thickness.

These results highlight the robustness of the virtual fields method and can be translated to other test types.