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Additively manufactured components often require temporary support material to prevent the component from collapsing or warping during fabrication. Whether these support materials are removed chemically as in the case of many polymer additive manufacturing processes, or mechanically as in the case of (for example) Direct Metal Laser Sintering, the use of sacrificial material increases total material usage, build time, and time required in post-fabrication treatments. The goal of this work is to embed a minimum allowable self-supporting angle within the topology optimization framework such that designed components and structures may be manufactured without the use of support material. This is achieved through a series of projection operations that combine a local projection to enforce minimum length scale requirements and a support region projection to ensure a feature is adequately supported from below. The magnitude of the self-supporting angle is process dependent and is thus an input variable provided by the manufacturing or design engineer. The algorithm is demonstrated on standard minimum compliance topology optimization problems and solutions are shown to satisfy minimum length scale, overhang angle, and volume constraints, and are shown to be dependent on the allowable magnitudes of these constraints.

Coral bleaching events vary in severity, however, to date, the hierarchy of susceptibility to bleaching among coral taxa has been consistent over a broad geographic range and among bleaching episodes. Here we examine the extent of spatial and temporal variation in thermal tolerance among scleractinian coral taxa and between locations during the 2010 thermally induced, large-scale bleaching event in South East Asia. Surveys to estimate the bleaching and mortality indices of coral genera were carried out at three locations with contrasting thermal and bleaching histories. Despite the magnitude of thermal stress being similar among locations in 2010, there was a remarkable contrast in the patterns of bleaching susceptibility. Comparisons of bleaching susceptibility within coral taxa and among locations revealed no significant differences between locations with similar thermal histories, but significant differences between locations with contrasting thermal histories (Friedman = 34.97; p<0.001). Bleaching was much less severe at locations that bleached during 1998, that had greater historical temperature variability and lower rates of warming. Remarkably, Acropora and Pocillopora, taxa that are typically highly susceptible, although among the most susceptible in Pulau Weh (Sumatra, Indonesia) where respectively, 94% and 87% of colonies died, were among the least susceptible in Singapore, where only 5% and 12% of colonies died. The pattern of susceptibility among coral genera documented here is unprecedented. A parsimonious explanation for these results is that coral populations that bleached during the last major warming event in 1998 have adapted and/or acclimatised to thermal stress. These data also lend support to the hypothesis that corals in regions subject to more variable temperature regimes are more resistant to thermal stress than those in less variable environments.

This article examines two intertwined topics on architected materials with imperfections—their mechanics and optimum design. We first discuss the main factors that control defect sensitivity along with a range of strategies for defect characterization. The potency of both as-designed and as-manufactured defects on their macroscopic response is highlighted with an emphasis on those caused by additive manufacturing technology. As a natural extension of defect sensitivity, we describe the design approaches for architected materials with particular focus on systematic tools of topology optimization. Recent extensions to formally incorporate imperfections in the optimization formulation are discussed, where the ultimate goal is to generate architectures that are flaw-tolerant and perform robustly in the presence of imperfections. We conclude with an outlook on the field, highlighting potential areas of future research.

Recurrent mass bleaching events threaten the future of coral reefs. To persist under climate change, corals will need to endure progressively more intense and frequent marine heatwaves, yet it remains unknown whether their thermal tolerance can keep pace with warming. Here, we reveal an emergent increase in the thermal tolerance of coral assemblages at a rate of 0.1 °C/decade for a remote Pacific coral reef system. This led to less severe bleaching impacts than would have been predicted otherwise, indicating adaptation, acclimatisation or shifts in community structure. Using future climate projections, we show that if thermal tolerance continues to rise over the coming century at the most-likely historic rate, substantial reductions in bleaching trajectories are possible. High-frequency bleaching can be fully mitigated at some reefs under low-to-middle emissions scenarios, yet can only be delayed under high emissions scenarios. Collectively, our results indicate a potential ecological resilience to climate change, but still highlight the need for reducing carbon emissions in line with Paris Agreement commitments to preserve coral reefs. Marine heatwaves and mass bleaching mortality events threaten the persistence of coral communities on tropical reefs. This study demonstrates that the thermal tolerance of coral communities in Palau has likely increased since the late 1980s. Such ecological resilience could reduce future bleaching impacts if global carbon emissions are cut down.

We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund ( Struct Multidiscip Optim 62:2211–2228, 2020a ), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions.

Spinal cord injury is a severely disabling neurological condition leading to impaired mobility, pain, and autonomic dysfunction. Most often, a single traumatic event, such as a traffic or recreational accident, leads to primary spinal cord damage through compression and laceration, followed by secondary damage consisting of inflammation and ischaemia, and culminating in substantial tissue loss. Patients need appropriate timely surgical and critical care, followed by neurorehabilitation to facilitate neuronal reorganisation and functional compensation. Although some neurological function might be regained, most patients with initially complete lesions have severe, irreversible neurological impairment. Cell-based and stem-cell-based therapies are recognised as promising candidates to promote functional recovery. However, no trials of these therapies in patients have yet provided reproducible evidence for clinical efficacy, challenged by small effect sizes, low immune suppression, and low sensitivity study designs. Nevertheless, in the past decade, clinical trials have shown the feasibility and long-term safety of cell transplantation into the injured spinal cord. This crucial milestone has paved the way to consider refinements and combined therapies, such as the use of biomaterials to augment the effects of cell transplantation. In the future, emerging cell types, scaffolding, and cell engineering might improve cell survival, integration, and therapeutic efficiency.

Length scale control in topology optimization is an important area of research with direct implications on numerical stability and solution manufacturability. Projection-based algorithms for continuum topology optimization have received considerable attention in recent years due to their ability to control minimum length scale in a flexible and computationally efficient manner. In this paper, we propose a new projection-based algorithm that embeds minimum length scale control on two material phases (e.g., solid and void) as well as optional maximum length scale on one material phase (e.g., solid or void) into the projection methodology used for material distribution approaches to topology optimization. The proposed algorithms are demonstrated on benchmark problems and are shown to satisfy the length scale constraints imposed.

A limited diversity of character states for reproductive traits and a robust phylogeny make scleractinian corals an ideal model organism with which to explore the evolution of life-history traits. Here, we explore systematic and biogeographical patterns in the reproductive biology of the Scleractinia within the context of a new molecular phylogeny and using reproductive traits from nearly 400 species. Our analyses confirm that coral sexuality is highly conserved, and mode of larval development is relatively plastic. An overabundance of species with autotrophic larvae in the eastern Pacific and Atlantic is most likely the result of increased capacity for long-distance dispersal conferred by vertical transmission of symbiotic zooxanthellae. Spawning records from diverse biogeographical regions indicate that multispecies spawning occurs in all speciose coral assemblages. A new quantitative index of spawning synchrony shows peaks at mid-tropical latitudes in the Indo-Pacific, influenced in part by two spawning seasons in many species on equatorial reefs.

This paper presents a technique for imposing maximum length scale on features in continuum topology optimization. The design domain is searched and local constraints prevent the formation of features that are larger than the prescribed maximum length scale. The technique is demonstrated in the context of structural and fluid topology optimization. Specifically, maximum length scale criterion is applied to (a) the solid phase in minimum compliance design to restrict the size of structural (load-carrying) members, and (b) the fluid (void) phase in minimum dissipated power problems to limit the size of flow channels. Solutions are shown to be near 0/1 (void/solid) topologies that satisfy the maximum length scale criterion. When combined with an existing minimum length scale methodology, the designer gains complete control over member sizes that can influence cost and manufacturability. Further, results suggest restricting maximum length scale may provide a means for influencing performance characteristics, such as redundancy in structural design.

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.