The Mullins effect, mechanical preconditioning, and predictive power

Polymers and soft biological tissues are characterized by a damage mechanism known as the Mullins effect, which becomes apparent during mechanical testing upon unloading. It has been observed that further cyclic loading does not significantly alter the softened stress response as long as the magnitude of the cycle remains fixed. This so-called preconditioning is frequently used in experimental studies to isolate stable, albeit damaged material behavior. Similarly, it is not uncommon in constitutive modeling to disregard the initial stress response and instead to describe a pseudo-damaged material behavior using the preconditioned experimental data, without explicitly reproducing the Mullins effect. This contribution examines the aforementioned simplification in more detail. To this end, we define two material models: one that includes the softening effect and one that neglects it according to the simplification entailed by preconditioning. After calibrating both constitutive laws to the same experimental dataset in uniaxial extension, we compare their predictions in equibiaxial extension and torsion. We find significant deviations between both material models calling into question the predictive power of a pseudo-damaged stress response. The results prompt a more in-depth discussion of the underlying logic of mechanical preconditioning, particularly in regard to its implications for constitutive modeling.