Exploring novel mechanical metamaterials: Unravelling deformation mode coupling and size effects through second-order computational homogenisation
Wanderson Ferreira dos Santos, Igor A. Rodrigues Lopes, F.M. Andrade Pires, Sérgio Persival Baroncini Proença
Abstract
Architected materials and mechanical metamaterials are known for their unique macroscopic properties and complex behaviour that often defy conventional continuum mechanics. Therefore, in this contribution, a recent multi-scale second-order computational homogenisation method (Dos Santos et al., 2023) is employed to explore these materials under finite strains. The approach combines a second gradient continuum theory at the macro-scale and a representative volume element (RVE) with classical first-order continuum mechanics at the micro-scale. The Method of Multi-scale Virtual Power ensures a consistent scale transition. The predictive capability and applicability of the second-order computational strategy are evaluated through coupled multi-scale numerical simulations. These simulations involve two- and three-dimensional problems, with a strong focus on the development of novel metamaterials, while also accounting for diverse loading conditions, such as tension/compression-induced undulation, bending, and compression-induced torsion. Comparisons with first-order homogenisation and Direct Numerical Simulations validate the approach. Analysis of homogenised consistent tangents reveals valuable insights into macroscopic properties. Overall, the results highlight the capability of the second-order strategy to capture significant phenomena, including second-order deformation modes, coupling deformation mechanisms, and size effects.