Error analysis for randomized uniaxial stretch test on high strain materials and tissues

Abstract

Many people have readily suggested different types of hyperelastic models for high strain materials and biotissues since the 1940’s without validating them. But, there is no agreement for those models and no model is better than the other because of the ambiguity. The existence of ambiguity is because the error analysis has not been done yet (Criscione, 2003). The error analysis is motivated by the fact that no physical quantity can be measured without having some degree of uncertainties. Inelastic behavior is inevitable for the high strain materials and biotissues, and validity of the model should be justified by understanding the uncertainty due to it. We applied the fundamental statistical theory to the data obtained by randomized uniaxial stretch-controlled tests. The goodness-of-fit test (2R) and test of significance (t-test) were also employed. We initially presumed the factors that give rise to the inelastic deviation are time spent testing, stretch-rate, and stretch history. We found that these factors characterize the inelastic deviation in a systematic way. A huge amount of inelastic deviation was found at the stretch ratio of 1.1 for both specimens. The significance of this fact is that the inelastic uncertainties in the low stretch ranges of the rubber-like materials and biotissues are primarily related to the entropy. This is why the strain energy can hardly be determined by the experimentation at low strain ranges and there has been a deficiency in the understanding of the exclusive nature of the strain energy function at low strain ranges of the rubber-like materials and biotissues (Criscione, 2003). We also found the answers for the significance, effectiveness, and differences of the presumed factors above. Lastly, we checked the predictive capability by comparing the unused deviation data to the predicted deviation. To check if we have missed any variables for the prediction, we newly defined the prediction deviation which is the difference between the observed deviation and the point forecasting deviation. We found that the prediction deviation is off in a random way and what we have missed is random which means we didn’t miss any factors to predict the degree of inelastic deviation in our fitting.