The Elasto-Adhesive-Capillary Length: An Emergent Length Scale in Soft, Sticky Materials

Surface effects in soft materials and soft-soft interfaces become of comparable magnitudes to bulk effects at certain, small length scales. These significant surface effects, such as adhesion and surface tension, in the presence of nonlinear, large deformations are challenges that present themselves in modeling the interfacial behavior of soft matter. Understanding the surface-driven interfacial failure of these materials is fundamental to harnessing their full potential in small-scale soft matter applications such as functional tissue-like design. Here, we develop an interface-enriched, size-dependent isogeometric finite element framework to quantify the separation mechanics of soft-hard and soft-soft interfaces endowed by low-dimensional energetics. The critical energy release rate, which dictates how much energy is needed to create a unit area of crack surface, is hypothesized to be a function of the surface tension of the material at these scales where surface effects are prominent. Through the developed numerical framework, we aim to characterize this dependence by defining a novel length-scale called the "elasto-adhesive-capillary length", reporting it for a wide range of material parameters and geometries. These numerical results will enable us to characterize the adhesive properties of soft materials at small scales, setting the stage for the design and assembly of miniaturized tissue-like structures.