Towards shock absorbing hyperelastic metamaterial design (II): A prospective multiscale buckling-lattice computational model

Abstract

As a continuation of a previous work of the authors, on Computational Design of Shock-absorbing Metamaterials (Part I) (NunezLabielle et al. in Comput Methods Appl Mech Eng 393:114732, 2022), this work explores the potential of computational multiscale methods, in combination with massive buckling-lattice structures at the metamaterial core (meso/micro scale), to render a suitable framework for designing such a shock-absorbing metamaterials focusing on industrial applications. In this context, a prospective computational setting is considered under the hypothesis that, for a sufficiently complex microlattice topology, some localized regions might buckle within the lattice-structure core and propagate through it, giving rise to different loading-unloading paths, in such a way that hysteretic-like structural behaviours would take place, thus arising dissipative behaviours, even if the base material at the buckling micro-lattice behaves in a hyperelastic (thus intrinsically nondissipative) manner. Using the standard Hill-Mandel homogenization principle, and assuming that the necessary separation of scales holds, the homogenized body, now living in a classical solid-mechanics setting, displays a homogenized non-convex behaviour which, in agreement with the conclusions of Part (I) of the work, exhibits extrinsic dissipation and, thus, could be potentially used (at reduced computational cost) for shock absorbing metamaterials analysis and design purposes. A tentative industrial application, to a sneaker’s insole design, has been then considered as a work’s target for evaluation of the room offered by the explored setting in the context of shock-absorbing metamaterial design. Finally, remarks on the scope and limitations of the work, and its significance for further advances in the field are emphasized.