Fracture of Silicon-Based Metamaterials: Size Effects and Other Structurally Induced Anomalies

  • Kraschewski, Kevin (ETH Zurich)
  • Kochmann, Dennis (ETH Zurich)

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The failure behavior of beam-based linear-elastic architected materials, or metamaterials, is typically governed primarily by their topology, specifically the connectivity of constituent beams. Historically, research has focused on fracture initiation using boundary-layer analysis on domains spanning hundreds of beam-lengths in width and height [1]. However, comparisons with experimentally feasible tensile tests indicate that the domain sizes required to match boundary-layer predictions are up to an order of magnitude larger than typically assumed, particularly for prominent topologies like the Kagome lattice. Although simulations utilizing methods such as quasicontinuum approaches [2] can span millions of beams and billions of degrees of freedom, they are often restricted to fracture onset. In contrast, experiments on two-dimensional (2D) extruded structures are frequently constrained by sample size, fabrication imperfections, and material nonlinearities [3]. Here, we present a scalable simulation framework to predict crack propagation in beam lattices, enabling the investigation of size effects and revealing ductility and toughening mechanisms in 2D, linear-elastic and brittle metamaterials. We address validation limitations through an experimental setup that utilizes free-standing silicon-based wafer-scale metamaterials. These designs can contain millions of beams, are virtually defect-free, and exhibit purely brittle-elastic behavior [4]. This combination enables the prediction and verification of the fracture behavior of arbitrary 2D lattice structures, advancing the understanding of fracture in large-scale 2D metamaterials across length scales ranging from micrometer-sized beams to centimeter-scale structures. References [1] I. Schmidt and N.A. Fleck. Ductile fracture of two-dimensional cellular structures. International Journal of Fracture, October 2001. [2] Kevin Kraschewski, Gregory P. Phlipot, and Dennis M. Kochmann. A mixed-order quasicontinuum approach for beam-based architected materials with application to fracture. Computational Mechanics, August 2024. [3] Alessandra Lingua, Antoine Sanner, Franc¸ois Hild, and David S. Kammer. Breaking better: Imperfections increase fracture resistance in architected lattices, April 2025. arXiv:2504.08873. [4] Charles Dorn, Vignesh Kannan, Ute Drechsler, and Dennis M. Kochmann. Graded phononic meta-materials: Scalable design meets scalable microfabrication, July 2025. arXiv:2507.01874.