Imperfect architected materials: Mechanics and topology optimization
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Introduction Research on lattices, origami and kirigami structures, and hybrid materials made of a range of solids is currently driving the development of architected materials with unique physical properties that promise to boost the performance of future technology. In the past few years, a wealth of unique functionalities has been pioneered, each tapping into the potential of material architecture, a term often loosely used to indicate the primary factor enabling their extreme performance. Pioneering works on architected materials (cellular materials in particular) primarily focus on the ideal state—a nominal architecture with defect-free geometry and homogenous base material.1–4 The main goal was to first understand the mechanisms of deformation that underpin their mechanics and structural properties. The focus then steered toward the realistic state, given that ideal conditions are seldom attained in a reallife setting, where structural deviations from the ideal target appear in both material and geometry. Due to manufacturing or damage, defects are not merely confined to a visual departure from the ideal state, but can also critically impact the mechanics and design of an architected material. Their influence can become even more acute in service conditions, when conventional assumptions on length-scale separation, periodicity, and boundary homogeneity typically break down or cannot be satisfied. Deviations from the ideal state might create disruptions in the expected mechanical and functional response at levels that
depend on the interplay between the base material and length scale of the constituent elements. Even when very small in amplitude, perturbations can generate a dramatic effect that can either serve to generate unprecedented responses, or jeopardize the function an architected material is designed for. For example, tiny perturbations in the architecture of elastomers have been exploited to generate a sequence of topological reconfigurations that are guided by buckling and self-contact between the elements of a metamaterial.5 For elastoplastic architectures, geometric defects can cause dramatic changes in the failure modes that are not visible in their defect-free counterparts.6 For brittle materials, the principle of reducing the characteristic feature size of the material architecture has been pursued to create large recoverable deformation in ceramics, and exceptional strength-to-density ratio in glassy carbon, among many others.7,8 In architected materials that are highly optimized, the deleterious effect of imperfections may be amplified even further. For example, the pursuit of lightweight materials with high stiffness and strength leads to architectures that are sparse and composed of thin members, potentially leading to nonredundant load paths and elements defined at a scale that may approach the scale of randomness. Such structures may perform well in a deterministic computational setting, but may fail under small load perturbations when tiny imperfections exist, thereby limiting their use
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