Exploring novel mechanical metamaterials: Unravelling deformation mode coupling and size effects through second-order computational homogenisation

• Published in: International journal of solids and structures Vol. 292; p. 112724
• Main Authors: dos Santos, Wanderson F., Rodrigues Lopes, Igor A., Andrade Pires, Francisco M., Proença, Sergio P.B.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15-04-2024
• Subjects: Architected materials; Coupling deformation mechanisms; Finite strains; Multi-scale modelling; Size effects; Multi-scale modelling; Size effects; Finite strains; Architected materials; Coupling deformation mechanisms
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2024.112724

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.
•A multi-scale second-order homogenisation method is used to explore metamaterials.•A second gradient continuum theory is combined with first-order continuum mechanics.•An assessment is conducted through coupled multi-scale numerical simulations.•Novel metamaterials are investigated for diverse loading conditions.•Higher-order deformation modes, coupling mechanisms and size effects are captured.