Multiscale modeling and optimization of the mechanics of hierarchical metamaterials

D. M. Kochmann; J. B. Hopkins; L. Valdevit

MRS Bulletin 44 (2019) 773-781

We present a survey of modeling techniques used to describe and predict architected cellular metamaterials, and to optimize their topology and geometry toward tailoring their mechanical properties such as stiffness, strength, fracture toughness, and energy absorption. Architectures of interest include truss-, plate-, and shell-based networks with and without periodicity, whose effective mechanical behavior is simulated by tools such as classical finite elements, further scale-bridging techniques such as homogenization and concurrent scale-coupling, and effective continuum descriptions of the underlying discrete networks. In addition to summarizing advances in applying the latter techniques to improve the properties of metamaterials and featuring prominent examples of structure–property relations achieved this way, we also present recently introduced techniques to improve the optimization process toward a full exploitation of the available design space, accounting for both linear and nonlinear material behavior.