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Abstract Spinodal architected materials with tunable anisotropy unify optimal design and manufacturing of multiscale structures. By locally varying the spinodal class, orientation, and porosity during topology optimization, a large portion of the anisotropic material space is exploited such that material is efficiently placed along principal stress trajectories at the microscale. Additionally, the bicontinuous, nonperiodic, unstructured, and stochastic nature of spinodal architected materials promotes mechanical and biological functions not explicitly considered during optimization (e.g., insensitivity to imperfections, fluid transport conduits). Furthermore, in contrast to laminated composites or periodic, structured architected materials (e.g., lattices), the functional representation of spinodal architected materials leads to multiscale, optimized designs with clear physical interpretation that can be manufactured directly, without special treatment at spinodal transitions. Physical models of the optimized, spinodal‐embedded parts are manufactured using a scalable, voxel‐based strategy to communicate with a masked stereolithography (m‐SLA) 3D printer. 

The distinction between “reinforcement” and “cloaking” has been overlooked in optimization-based design of devices intended to conceal a defect in an elastic medium. In the former, a so-called “cloak” is severely biased toward one or a few specific elastic disturbances, whereas in the latter, an “unbiased cloak” is effective under any elastic disturbance. We propose a two-stage approach for optimization-based design of elastostatic cloaks that targets true, unbiased cloaks. First, we perform load-case optimization to find a finite set of worst-case design loads. Then we perform topology optimization of the cloak microstructure under these worst-case loads using a judicious choice of the objective function, formulated in terms of energy mismatch. Although a small subset of the infinite load cases that the cloak must handle, these highly nonintuitive, worst-case loads lead to designs that approach perfect and unbiased elastostatic cloaking. In demonstration, we consider elastic media composed of spinodal architected materials, which provides an ideal testbed for exploring elastostatic cloaks in media with varying anisotropy and porosity, without sacrificing manufacturability. To numerically verify the universal nature of our cloaks, we compare the elastic response of the medium containing the cloaked defect to that of the undisturbed medium under many random load cases not considered during design. By using digital light processing additive manufacturing to realize the elastic media containing cloaked defects and analyzing their response experimentally using compression testing with digital image correlation, this study provides a physical demonstration of elastostatic cloaking of a three-dimensional defect in a three-dimensional medium. 

Topology optimization problems typically consider a single load case or a small, discrete number of load cases; however, practical structures are often subjected to infinitely many load cases that may vary in intensity, location and/or direction (e.g. moving/rotating loads or uncertain fixed loads). The variability of these loads significantly influences the stress distribution in a structure and should be considered during the design. We propose a locally stress-constrained topology optimization formulation that considers loads with continuously varying direction to ensure structural integrity under more realistic loading conditions. The problem is solved using an Augmented Lagrangian method, and the continuous range of load directions is incorporated through a series of analytic expressions that enables the computation of the worst-case maximum stress over all possible load directions. Variable load intensity is also handled by controlling the magnitude of load basis vectors used to derive the worst-case load. Several two- and three-dimensional examples demonstrate that topology-optimized designs are extremely sensitive to loads that vary in direction. The designs generated by this formulation are safer, more reliable, and more suitable for real applications, because they consider realistic loading conditions.