On a staggered iFEM approach to account for friction in compression testing of soft materials

An inverse finite element method (iFEM) to estimate material parameters from compression tests of soft materials is presented, where alginate hydrogel was used as a phantom material. The method applies if the boundary conditions at the loaded surfaces are not ideal, i.e. neither free of friction nor fully constrained, as it may be the case in most realistic testing set-ups. Assuming a linear friction law, the friction coefficient μ was considered unknown and estimated in a first step by minimising the difference between the contours of the sample, obtained by optical measurements, and the simulated shape. Force-displacement data were used in a second step to determine the parameters of the constitutive law. Staggering these two steps, both friction and material parameters were identified by optimisation. Skipping the first step and predefining μ instead, a unique parameter set could only be clearly identified if the deviations of the contours were considered in addition to the deviations in the force-displacement data. Finally, forward FEM calculations with differently shaped specimens were used to verify the goodness of the obtained parameter sets.