New Approaches to Modeling Failure and Fracture of Rubberlike Materials

In this chapter we review some recent approaches to modeling failure and fracture of soft materials. By failure we mean the onset of damage via material instability. By fracture we mean further localization of damage into cracks with their subsequent propagation. Mathematical description of failure is simple and it only requires some bounding of the strain energy density. The bounded strain energy automatically implies the bounded achievable stress, which is an indicator of material failure. By bounding the strain energy via energy limiters we show, for instance, how to explain cavitation, analyze strength of soft composites, and predict direction of possible cracks. Mathematical description of fracture is more involved because it requires regularized formulations suppressing the so-called pathological mesh sensitivity. Most existing approaches utilize purely formal regularization schemes that lack physical grounds. We discuss a more physically based approach rooted in the idea that bulk cracks are not a peaceful unzipping of adjacent atomic layers but rather a catastrophic explosion of bonds localized within a finite characteristic area.