An automated design framework for composite mechanical metamaterials and its application to 2D pentamode materials

• Published in: International journal of mechanical sciences 2024-08, Vol.276, p.109393, Article 109393
• Main Authors: Rodriguez, S.E., Calius, E.P., Khatibi, A., Orifici, A.C., Das, R.
• Format: Article
• Language: English
• Subjects: Bimode materials; CMA-ES; Composite structures; Evolutionary computing; Generative design; Heterogeneous structures; Mechanical metamaterials; Pentamode materials
• ISSN: 0020-7403
• DOI: 10.1016/j.ijmecsci.2024.109393

•An evolutionary design framework for mechanical metamaterials with heterogeneous, non-symmetric architectures is proposed.•Ensembles or populations of composite pentamode-like metamaterials are generated that include high-performing specimens.•During design evolution the initial variety of elastic moduli collapses, most often resulting in binary composites.•Less than a hundred generations are needed to evolve composite metamaterials with high bulk-to-shear modulus ratios.•The pentamode metamaterial designs eliminate point-like connections between lattice struts, reducing stress concentrations. Until relatively recently most mechanical metamaterial classes being studied have been composed of a single solid constituent phase and design has focused almost exclusively on structural geometry. Additional design dimensions can be introduced by accepting heterogeneity and varying materiality, i.e., allowing mechanical properties to vary across the metamaterial's unit cells or even from cell to cell in the metamaterial domain, creating composite metamaterials. This higher dimensionality significantly expands the effective property envelope, but the additional complexity also presents a significant hurdle. To overcome the design challenge, an automated design framework is proposed that leverages modern evolutionary computation techniques, combined with finite element analysis for fitness evaluation, to a discretized or voxelated design domain. However, this approach introduces stochastic and statistical aspects to the design process, which requires additional processing to successfully extract useful solutions. A case study is presented in which the proposed automated design framework is used to generate 2D structures that exhibit pentamode-like behavior. Pentamode metamaterials, which are best known for extreme bulk-to-shear modulus ratios (B/G), offer unique control over effective elastic properties and make for a particularly interesting test case. The evolutionary objective was defined as maximizing B/G over a voxelated square 2D domain. It was found that the evolutionary process converges to a solution relatively rapidly, generally in less that a hundred generations. B/G ratio values of 10,000 and more were obtained, largely exceeding those commonly found in the literature for experimental pentamode metamaterials. These generated designs feature reduced stress concentrations due to the elimination of point-like connections between lattice struts, which address