Elastic characterization of membranes with a complex shape using point indentation measurements and inverse modelling

The elasticity parameters of membranes can be obtained from tensile experiments on strips if adequate quantities of the material are available. For biomedical specimens, however, it is not always possible to harvest strips of uniform and manageable geometry suitable for tensile tests. A typical example is the human tympanic membrane. This small structure has a complex conical shape. In such case, elasticity parameters need to be measured in situ.A possible way to determine elasticity parameters of complex surfaces is the use of point indentation measurements. In this paper, this characterization procedure was applied on a scaled phantom model of the tympanic membrane. The model was built of natural latex rubber.In the characterization procedure, a point indentation is carried out on the membrane surface while forces and three-dimensional shapes are measured. Afterwards, a finite element simulation of the experiment is performed and parameters are found using an optimization routine. For validation purposes, the rubber was also subjected to a uniaxial tensile test.Several hyperelastic constitutive models are available to describe rubber-like behaviour. Among these, Mooney-Rivlin and Ogden models are the most popular. We used a low order Mooney-Rivlin and a higher order Ogden model to describe our experiments.Results show that there is a reasonable agreement between the tensile experiments output and the output of the inverse modelling of the indentation experiments.