Third party funded individual grant
Start date : 01.01.2016
End date : 31.01.2019
Many natural (biological) materials, but also engineered materials are characterized by hierarchical microstructures where load carrying elements are hierarchically grouped into modules, which in turn are grouped into modules of higher order (for a simple example, think of a wire rope). In biological load-carrying components many hierarchical levels may be nested in this manner (e.g. up to seven in the case of tendon). Hierarchical materials exhibit very high resilience against failure despite consisting of elementary components that may be highly unreliable and defected. It is our main conjecture that this resilience can be attributed to two aspects of the hierarchical architecture -- on the one hand a capability to efficiently re-distribute loads across the microstructure, which mitigates against failure by system-wide damage accumulation and damage percolation, on the other hand a capability to contain failure in single modules which mitigates against growth of localized cracks. This dualism between resilient system connectivity on the one hand and modular localization on the other hand is but one example of a generic type of behavior in systems with hierarchical modular architectures, which also encompass metabolic networks or brain networks as recently investigated by statistical physicists (see e.g. P. Moretti and M. Munoz, Nature Communications 4, 2013). In this project we aim at achieving a basic conceptual understanding of load-driven failure processes in materials with hierarchical microstructure that consist, on the smallest scale, of highly unreliable elements with a large scatter in failure strength. In particular we want to clarify whether failure in such materials occurs by system-wide breakdown (damage percolation) or by nucleation-and growth of localized flaws, and we want to understand the nature of the related precursor dynamics in view of the fundamental question whether failure prediction from precursors is possible or not in such systems. We also want to understand how the damage resilience of systems with hierarchical architecture compares with that of on-hierarchical reference systems, and how a system that is optimized in terms of failure stress or fracture energy might look like. The proposed investigation is posited on a conceptual level, we therefore focus on two types of generic models, namely (hierarchical) fiber bundle models and (hierarchical) random fuse models which can be thought of as concept models for real materials. The project as proposed should be understood as the proof-of-concept stage of a larger project, which in a second stage would include quantitative modelling of load bearing materials with engineered hierarchical microstructures through beam and finite element models, their manufacturing by additive manufacturing methods and subsequent testing, and their structural optimization.