# How Soft Polymers Cope with Cracks and Notches
## 1 Introduction  
A class of materials, which are relevant from the point of view of advanced applications, is represented by the so-called soft or highly deformable materials, such as elastomeric polymers, colloids, liquid-crystals polymers, gels, foams, as well as biological materials--such as soft tissues--that are roughly governed by the same mechanical principles [1]. Typically, these materials have mechanical properties falling within the following range; elastic modulus of 0.1-1.5 MPa, tensile strengths of 1-10 MPa, ultimate tensile strains up to 2000%, and fracture energy of 100-1000 J/m\({}^{2}\). Soft materials are endowed with unique features and mechanical properties, explaining the great attention that they have been receiving from the scientific community in the last decades. In natural systems, soft tissues are a fertile source of inspiration for advanced applications, with mechanics and biology going hand-in-hand to formulate the underlying mechanical principles and develop new optimized structural materials [2; 3; 4; 5; 6]. The peculiar properties exhibited by soft materials are a direct consequence of their complex and entangled molecular structure, which involves millions or billions of atoms forming linear chains. We owe the fundamentals of the chemical- and physics-based mechanical behavior of this class of materials to the research work of [PERSON] and [PERSON] [7; 8; 9]. In fully amorphous materials, the structure at the nanoscale level consists of a three-dimensional network of polymer chains, linked together at several discrete points identified as cross-links. The mechanical response of these materialsat the meso- or macroscale is heavily affected by the amount of entanglement and the number of existing cross-links per unit volume, rather than by the bonding strength existing between the atoms, as happens in fully crystalline materials (e.g., metals, ceramics, etc.). Upon the application of load, the deformation induces an alignment and unentanglement of the polymeric chains, with the initial amorphous conformation turned into a semicrystalline-like one. Such a phenomenon usually occurs at quite large deformation, thanks to the highly-oriented arrangement of the chains along the tensile direction [10; 11; 12]. This so-called strain-induced crystallization is responsible for the typical stiffening behavior which is noticed in the stress-strain curve of polymers at high strain levels [13; 14]. Soft materials normally can deform several times their original length, without being damaged or ruptured. If macroscopic flaws are introduced in the form of cuts, cracks or notches, the stretchability can be affected in different measure, depending on the flaw sensitivity of the material. The concept of a material length scale, separating flaw-sensitive from flaw-insensitive rupture, has been initially proposed for hard materials [15] and later extended to soft polymers [16]. Differently from traditional crystalline solids, rupture of soft polymers occurs at large deformation, when the rearrangement of the polymeric chains leads to flaw reshaping and strengthening around the highest strained region. In particular, an existing initial sharp crack blunts significantly before propagation, with the effect of relieving the strain concentration around the tip [17; 18; 19]. The resulting feature is an enhanced defect tolerance, with some tough soft materials showing an insensitivity to flaws up to a few millimeters long, in contrast to the typical nanometer scale for hard brittle solids [20]. For instance, biological tissues such as skin are known for their extreme resistance to flaws, which makes virtually impossible to propagate tearing in a stretched sample. Experimental observations on rabbit skin showed that a small notch does not propagate but progressively blunts, due to straightening and stretching of the collagen fibers [21]. However, other soft materials, such as the so-called hydrogels, are often prone to premature fracture and have low fatigue resistance.