Dynamic failure of meta-materials – METACRACK

During the past few years, there has been a growing interest for novel materials with architectured structures. Often inspired by nature, architectured materials with a “mesoscopic” heterogeneous structure (e.g. foams, honey combs) start to become a new standard in high performance engineering applications. These materials are also attractive for structural applications because their architecture could be optimized while a low weight is maintained. Architectured materials are usually structured but the scale separation between cracks and the material-structure is not always established. So, strong interactions occur between the crack and the structure of the material. The failure design of engineering structures using architectured materials is thus a complex issue. Under quasi-static loading, the driving force leading to the propagation of a crack is shown to be proportional to the crack length. This means that longer cracks are preferred for propagation and that a longer crack holds a higher risk level for a structure. Conversely, under transient loading, the crack driving force does not depend on the crack length but only on the load intensity. The probability for a crack to propagate under transient loading is thus independent on its size. The singularity at the crack tip, during transient loading, is established in the earliest stage of crack formation whereas the crack has to be longer in the case of quasi-static loading. In others words, under transient dynamics, the loading always contains short wave lengths which makes the crack behave as a long crack whatever its length. Depending on their wave length, elastic waves can interact with the structure of the material in the vicinity of the propagating crack tip. As a consequence, the interactions between a crack and the structure of the surrounding material may always be considered under transient loading. When architectured materials are used in the context of wave propagation (acoustic, photonic...), they are called meta-materials. Meta-materials have been shown to have great properties, such as being able to prevent a wave around a certain predefined wavelength to propagate, due to local vibration modes. This phenomenon is called a band gap. The range of the wave spectra within this band gap is defined by the geometry of the meta-material architecture. The long-term goal of this research project is to design materials that can avoid (or at least decrease the risk of) dynamic crack propagation by using the band gap capability of meta-materials. If the material architecture is designed for this band gap to stop the waves emitted from the crack tip then the crack could stop or at least its speed can decrease. In the METACRACK project, a unified framework including experiments, measurements, mechanical modelling and numerical simulations will be developed for this purpose. Using 3D prototyping, it is possible to produce samples of these materials rapidly and then to test them. High speed high resolution imaging will be used to analyse, by digital image correlation, the displacement at the scale of the unit cell of the material and the displacement at the macroscopic scale. The analysis of these displacements and their relationships will be used to validate the macroscopic mechanical model we chose (Cosserat continuum) for the specific material architecture we selected for the project (a quasi-periodic Penrose tilling). A fracture mechanics theory will be developed within this context. Two routes will be investigated: the first one based on fracture mechanics concepts like stress intensity factors and the other one based on a variational quasi-brittle model based on the Thick Level Set approach. This numerical method will be coupled to displacement field measurements by digital image correlation to validate the kinematic of macroscopic continuum model, and to identify the constitutive Cosserat parameters of the material and then the failure criterion.