Hyperelasticity and the Failure of Averages

Hyperelastic constitutive models are frequently used to characterize the stress-strain response of highly flexible materials. Literature surveys reveal most researchers report statistical quantities (e.g. mean and standard deviation) to describe and summarize hyperelastic coefficient values. However, statistical quantities are not appropriate for describing and summarizing coefficient values of hyperelastic constitutive models. Average coefficient values do not produce average behaviors and evaluating a hyperelastic constitutive model within one standard deviation of the mean coefficient values can produce extreme behavior that is at times completely unrealistic. The purpose of this paper is to address this issue, providing the theoretical background for this problem as well as examples and recommendations for avoiding this common pitfall.