Phase-field modeling of fatigue-induced crack propagation in strain-hardening elastomers

Engineering materials and structures are often subject to repeated and cyclic loading during the entire life of a product.Prediction of fatigue failure under such loads has been a topic of interest in the scientific community for decades.In the context of the computational modeling of fracturing, the phase-field method has attracted great attention in the last years owing to its elegant way of modeling cracks within a continuum in the form of a scalar damage field.There is also growing literature where enhancements have been proposed to numerically model fatigue effects within the phase-field framework.However, most of the existing work concentrates on elastic and elasto-plastic behavior of metallic materials within the realm of small deformations.Fatigue formulations for polymers are also largely limited to Neo--Hookean models.In the present work, we propose a modeling framework that can be applied to the numerical simulation of fatigue crack growth of strain-hardening elastomeric materials, where the inextensibility of the polymeric chains is incorporated using a Gent-like material model.Numerical studies with increasing complexities are systematically performed to exemplify the striking features of the model.In addition, W\"ohler and Paris curves are simulatively generated under multiple deformation modes and compared with data from the literature.