Unrealistic statistics: how average constitutive coefficients can produce non-physical results

The coefficients of constitutive models are frequently averaged in order to concisely summarize the complex, nonlinear, material properties of biomedical materials. However, when dealing with nonlinear systems, average inputs (e.g. average constitutive coefficients) often fail to generate average behavior. This raises an important issue because average nonlinear constitutive coefficients of biomedical materials are commonly reported in the literature. This paper provides examples which demonstrate that average constitutive coefficients applied to nonlinear constitutive laws in the field of biomedical material characterization can fail to produce average stress-strain responses and in some cases produce non-physical responses. Results are presented from a literature survey which indicates that approximately 90% of tissue measurement studies that employ a nonlinear constitutive model report average nonlinear constitutive coefficients. We suggest that reviewers and editors of future measurement studies discourage the reporting of average nonlinear constitutive coefficients. Reporting of individual coefficient sets for each test sample should be considered and discussed as designation for a "best practice" in the field of biomedical material characterization.