arXiv subjects

Leo de Waal

Publications and source records attributed to Leo de Waal.

4 recordsLinked to original sources

arXiv2026

Nonlinear Mechanics and Predictable Bifurcation of Multi-Cell Kresling Origami Chains

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

cond-mat.soft↗

arXiv2026

How Geometry Tames Disorder in Lattice Fracture

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.

cond-mat.mtrl-sci↗

arXiv2025

Architecting mechanisms of damage in topological metamaterials

Architecting mechanisms of damage in metamaterials by leveraging lattice topology and geometry poses a vital yet complex challenge, essential for engineering desirable mechanical responses. Of these metamaterials, Maxwell lattices, which are on the verge of mechanical stability, offer significant potential for advanced functionality. By leveraging their robust topological features, they enable precise control of effective elastic properties, manipulation of stress localisation and delocalisation across specific domains, and targeted global damage that follows local fracture events. In this work, we identify topology and geometry-dependent parameters that establish a simple, yet precise, framework for designing the behaviour of non-idealised Maxwell lattices and their damage processes. We numerically explore the underlying phenomenology to demonstrate how this framework can guide or arrest damage in lattices, both with and without domain walls and additional boundary constraints. Our approach uncovers a robust way to manipulate the mechanisms of damage and the path they follow in metamaterials, with further insight into crack arrest, diversion, and shielding.

cond-mat.soft↗

arXiv2025

Cracking Down on Fracture to Functionalise Damage

In this work we propose a novel relationship between topology and damage propagation in Maxwell lattices that redefines fracture as a functional design feature rather than mere degradation. We demonstrate that topologically protected modes, inherently robust against perturbations, localise along lattice discontinuities and govern the mechanical response. By precisely engineering the microstructure, we direct these modes to control stress distributions and trigger predictable, controlled damage. Our findings -- validated through comprehensive numerical simulations and experiments -- advance our understanding of nontrivial mechanical responses in Maxwell lattices and establish a clear framework for designing materials with improved fracture energy. This work paves the way for further exploration of topology-driven phenomena in mechanical systems and promises a new direction in the design of robust materials.

cond-mat.soft↗