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We introduce a three dimensional model for interface failure of hierarchical materials adhering to heterogeneous substrates. We find that the hierarchical structure induces scale invariant detachment patterns, which in the limit of low interface disorder prevent interface failure by crack propagation (‘detachment fronts’). In the opposite limit of high interface disorder, hierarchical patterns ensure enhanced work of failure as compared to reference non-hierarchical structures. While the study of hierarchical adhesion is motivated by examples of fibrous materials of biological interest, our results indicate that hierarchical patterns can be useful in engineering scenarios in view of tuning and optimizing adhesion properties.

Statistical aspects of interface adhesion and detachment of hierarchically patterned structures