Mullins thresholds in context of the network alteration theories

Rubbers undergo a softening phenomenon in first cycles of loading where it is known this softening is more pronounced in filled rubbers. Existence of a clear physical interpretation for this phenomenon called Mullins effect is of great importance in development of constitutive relations and numerical simulations. In this paper, a recently proposed network alteration theory is extended to obtain a general form of evolution laws based on the physical description of the material molecular network. The resulting evolution laws are defined based on different measures to evaluate efficiency and accuracy of each measure in predicting the Mullins softening in context of the network alteration theories. Two experimental data sets on natural rubber are thoroughly investigated to determine a reliable threshold for this effect. It is concluded that, the maximum principal stretch and the Euler‒Almansi strain are not good thresholds for Mullins effect at all. Other investigated measures are relatively efficient at small stretches but they mostly become less and less accurate at large stretches. However, the stored strain energy preserves its accuracy at the whole stretch range.