Reversible Adhesion: from Discrete to Continuum

We study a simple mechanical model whose aim is to reproduce basic physical mechanisms behind reversible surface attachment-detachment under quasi-static loading. At the micro level the adhesive layer is modeled as an elastic chain of particles interacting with a rigid foundation through breakable springs. This model can be viewed as prototypical for the description of a wide range of phenomena from peeling of polymeric tapes to rolling of cells, working of Gecko’s fibrillar structures and denaturation of DNA. We show that the model reproduces qualitatively the following experimentally observed effect: hysteretic transition from an incremental evolution of the adhesion front to a sudden decohesion of a macroscopic segment of the adhesion layer. We construct the rigorous continuum limit of our discrete model which captures both stable and metastable configurations. As the microscopic properties of the breakable elements change, the macroscopic behavior varies from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion hysteresis. At the micro-scale this corresponds to a transition from a ‘localized’ to a ‘diffuse’ structure of the decohesion front. The achieved parametric control of the microscopic mechanism can be used in the design of new biological inspired materials and reversible adhesion devices.