Designing tough and strong quasi-brittle composites through multi-scale patterning – DURABLE

Living organisms have evolved hierarchical microstructures that confer remarkable strength and toughness to biomaterials. Transferring these properties to engineered materials could provide various sectors with high-performance, long-lasting composites. However, in a world where sustainability is multifaceted, maximizing durability through enhanced fracture resistance cannot be our only objective. French RE2020 standards has set CO2eq/m2 thresholds at the structural level, thereby imposing stringent requirements in terms of materials. The challenge, therefore, is to ensure optimal fracture properties even when resistance to failure is not the primary focus. Nature's blueprints, which result from evolutionary processes, may not be adequate to address sustainability concerns. DURABLE seeks to address a fundamental question: Can we engineer new multi-scale patterning strategies for the design of sustainable composite materials with enhanced fracture resistance, beyond biomimicry?

While crack growth can be described at the nanoscale from intrinsic failure mechanisms and at the macroscale from the structural response, a unified theory of quasi-brittle fracture, spanning the entire spectrum of scales, remains elusive. To bridge this nano-to-macroscale gap, our research project leverages a newly-derived perturbation theory of cohesive failure. The latter uniquely combines the size-dependency observed in traditional cohesive-zone models, with the remarkable analytical tractability and computational scalability of perturbation approaches in fracture mechanics. This theory makes us ideally positioned to investigate fracture processes in heterogeneous, both within and across scales.

The main goal of DURABLE is to offer unconventional multi-scale solutions for the design of fracture-resistant sustainable composites. This ambitious objective will be achieved through two methodological breakthroughs:
1. A consistent homogenization framework for tensile fracture properties. This analytical framework will be the fracture mechanics counterpart of traditional mean field theories for non-linear mechanical behavior. It will seamlessly upscale cohesive laws derived from the nanoscale using molecular dynamics simulations up to the macroscale, accounting for the presence of pervasive heterogeneities within and across scales. This ultimately permits to predict the effective tensile strength and fracture energy of the composite, from a statistical description of its microstructure at hierarchical length scales.
2. A novel numerical method for simulating fracture process in quasi-brittle composites with unparalleled computational efficiency. This method, called eXpanded Discontinuity-Displacement Method (XDDM), will allow simulating coplanar crack growth in 3D cohesive heterogeneous materials from only two 1D discretizations, based on an energetic formulation of cohesive failure.

To accommodate novel sustainability constraints and expand our focus beyond Nature’s own solutions, we will leverage our two assets for composite design through a dual-stage optimization strategy:
• In stage 1, we will build on the analytical tractability our homogenization theory and use it as a surrogate model to rapidly screen the high-dimensional compositional space of hierarchical composites. This will provide an initial design, in which inclusions are incorporated at multiple scales to promote fracture resistance under performance or sustainability constraints.
• In stage 2, we will refine this initial design, leveraging the computational scalability of XDDM. Namely, we will further enhance the toughening induced by microstructural details within each scale, through topological optimization, and account for the influence of concurrent heterogeneity scales, using direct numerical simulations.

Upon completion, DURABLE is expected to provide innovative multi-scale patterning solutions for the design of fracture-resistant sustainable composites.