Gibson-soil-like materials achieve flaw-tolerant adhesion

Adhesion strength between two bonded solids is usually weakened by the interiacial flaws induced by surface roughness, impurities, contaminants, trapped air bubbles and so on. Minimizing the impact of the interiacial flaws on adhesion strength becomes a crucial problem for the design of robust adhesion. The optimal scenario that one can expect is to achieve the flaw tolerance state, in which a pre-existing crack does not propagate even as the material is stretched to failure near the theoretical adhesion strength. In this paper, we demonstrate in theory that Gibson soil, a type of incompressible material with linearly graded elastic modulus, can be designed to achieve flaw-tolerant adhesion. For general compressible materials, both theoretical analysis and numerical calculation indicate that flaw-tolerant adhesion also can be accomplished as long as an asymptotic design criterion on elasticity gradient is met. These results provide a theoretical foundation for the novel applications of functional graded materials in adhesion.