Identifying the properties of ultra-soft materials using a new methodology of combined specimen-specific finite element model and optimization techniques

Development of novel protective helmets requires a better understanding of the mechanical properties of brain tissues. In this paper, a new methodology was developed using a reverse engineering (RE) based approach to identify the material properties for ultra-soft materials, such as human brain tissues, that are very difficult to cut into an accurate geometric shape necessary for engineering measurements. The basic idea behind this method is to include geometric effects by using a sample-specific finite element model in conjunction with a set of optimization procedures that allows systematic adjustments of material parameters until the calculated responses matched the measured ones. The experimental component consists of conducting simple uniaxial compression tests at two different loading rates to obtain force–displacement relationships, instead of the less accurate stress–strain curves, that could be used directly to minimize an objective function. The Shepard-k-Nearest method was employed to establish an approximated model (i.e. a response surface) and a genetic algorithm was used to search the optimal design variables (i.e. material parameters) in the design space. The optimized parameters were then used to describe the material behavior in a third sample-specific FE model and the model-predicted force–deflection data were compared with experimental data at a third loading rate that were not used for optimizing material parameters. This new approach makes it possible to identify material constants of ultra-soft biological tissues and engineering materials (e.g. silicone gels and rubbers) without using a large number of test samples.