Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design

• Published in: Structural and multidisciplinary optimization Vol. 60; no. 5; pp. 1887 - 1920
• Main Authors: Watts, Seth, Arrighi, William, Kudo, Jun, Tortorelli, Daniel A., White, Daniel A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019; Springer Nature B.V; Springer
• Subjects: Computational Mathematics and Numerical Analysis; Computer architecture; Density; elasticity; ENGINEERING; Engineering Design; Finite element method; finite element methods; materials science; Mathematical models; mathematics and computing; mechanical and civil engineering; Metamaterials; Modulus of elasticity; multiscale; Organic chemistry; Research Paper; surrogate model; Theoretical and Applied Mechanics; Three dimensional models; Topology; topology design; Trusses; Elasticity; Topology design; Surrogate model; Finite element methods; Multiscale
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-019-02297-5

Elastic meta-materials are those whose unique properties come from their micro-architecture, rather than, e.g., from their chemistry. The introduction of such architecture, which is increasingly able to be fabricated due to advances in additive manufacturing, expands the design domain and enables improved design, from the most complex multi-physics design problems to the simple compliance design problem that is our focus. Unfortunately, concurrent design of both the micro-scale and the macroscale is computationally very expensive when the former can vary spatially, particularly in three dimensions. Instead, we provide simple, accurate surrogate models of the homogenized linear elastic response of the isotruss, the octet truss, and the ORC truss based on high-fidelity continuum finite element analyses. These surrogate models are relatively accurate over the full range of relative densities, in contrast to analytical models in the literature, which we show lose accuracy as relative density increases. The surrogate models are also simple to implement, which we demonstrate by modifying Sigmund’s 99-line code to solve a three-dimensional, multiscale compliance design problem with spatially varying relative density. We use this code to generate examples in both two and three dimensions that illustrate the advantage of elastic meta-materials over structures with a single length scale, i.e., those without micro-architectures.