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Minimal 3D model reveals fundamental mechanisms behind toughening of soft–hard composites

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Minimal 3D model reveals fundamental mechanisms behind toughening of soft–hard composites


Though relatively simple compared to previously used models, the proposed soft–hard composite (SH-com) framework developed in the study accurately reflects well-known physical phenomena observed in material systems. This image depicts the failure of a notched block for different combinations of soft and hard building blocks. Credit: Prof. Katsuhiko Sato from the University of Toyama, Japan Source Link: https://doi.org/10.1073/pnas.2506071122

Engineers have long grappled with a fundamental challenge: creating materials that are both strong and tough enough to resist deformation and prevent fractures. These two properties typically exist in opposition, as materials that excel in one area often fail in the other.

Nature, however, has elegantly solved this trade-off in like bone, teeth, and nacre, which strategically combine soft and hard components in multi-layered architectures. These blueprints have inspired scientists to develop artificial soft–hard composites—from advanced dual-phase steels to specialized gels and reinforced rubbers—that demonstrate performance exceeding that of their individual components.

While artificial soft–hard composites have shown impressive performance in and , the fundamental mechanisms behind their enhanced properties remain largely unclear. The inherent complexity of these materials, encompassing nonlinear behaviors, intricate internal structures, and multi-scale interactions, has made it difficult to isolate the essential design principles.

Specifically, scientists have struggled to understand how these materials transition from brittle-to-ductile (BTD) fracture behavior, and what the minimum requirements are for constituent components to achieve this toughening effect.

In this vein, a research team including Dr. Fucheng Tian and Professor Jian Ping Gong from the Faculty of Advanced Life Science, Hokkaido University, Japan, as well as Specially Appointed Professor Katsuhiko Sato from the Program of Mathematics and Informatics, University of Toyama, Japan, recently undertook a study to tackle this complex problem.

In their pioneering work published in the journal Proceedings of the National Academy of Sciences, the researchers introduce a minimal three-dimensional soft–hard composite (SH-com) framework. By eliminating complicated nonlinear effects and intricate network structures, their model enabled them to focus on the core underlying principles governing the toughening effect.







Evolution of crack patterns and damage morphologies in the pure hard system (ϕs = 0). Damaged hard elements are highlighted in orange. Credit: Proceedings of the National Academy of Sciences (2025). DOI: 10.1073/pnas.2506071122

The SH-com model uses randomly distributed linear-elastic soft and hard elements, each characterized by its elastic stiffness and the energy required for failure. Despite its simplicity, this model successfully reproduced several hallmark behaviors of tough composite materials, including mechanical hysteresis (the Mullins effect), sacrificial bond-driven toughening, and the critical BTD transition fracture behavior. Through systematic testing of different compositions, the team discovered that the BTD transition occurs when the soft and hard phases reach a specific mechanical equilibrium.

Moreover, they found that optimal toughening occurs at a specific ratio of soft to hard components, governed by a universal scaling relationship linked to the differences in fracture toughness between components. When an optimal composition is achieved, the composite can exceed the toughness of its individual constituents.

“Though the SH-com model is anchored in the fundamental linear-elastic regime, the outcomes exhibit compelling consistency with the experimental findings from nonlinear soft–hard composite materials. This consistency emphasizes the fundamental principles underlying the toughening mechanisms in general soft–hard composite materials,” remarks Dr. Fucheng.

Based on these insights, the team developed a “toughening phase diagram,” which serves as a practical guide illustrating the optimal combinations of stiffness and toughness between components to achieve superior material performance. Notably, the simplicity and universality of their model suggest that these principles can be applied broadly.

“Our study reveals the fundamental toughening mechanisms of SH-com systems, offering insights for designing tougher materials,” conclude the authors. “In fields such as , the development of tough gels is required, and we expect our study to contribute to those efforts.”

From the development of more resilient components for aerospace and automotive applications to advanced biomaterials for and , this research provides a powerful theoretical foundation for engineering materials that are both strong and tough.

More information:
Fucheng Tian et al, Fundamental toughening landscape in soft–hard composites: Insights from a minimal framework, Proceedings of the National Academy of Sciences (2025). DOI: 10.1073/pnas.2506071122

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The Best Cyber Monday Streaming Deals With a Convenient Roommate’s Email Address

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The Best Cyber Monday Streaming Deals With a Convenient Roommate’s Email Address


HBO knows you’re bored and cold. It wants you to Max and chill with Noah Wyle in scrubs. The company offers some of the best Cyber Monday streaming deals with a ridiculously low-priced $3/month offer for basic HBO Max (it’s the version with ads and 2K streaming, but still, super-cheap). Disney Plus and Hulu deals are bundled up for $5/month. Apple TV wants back in your life for $6.

Of course, this deal is only meant for new customers. Not boring ol’ existing customers. If you already have basic HBO Max, you’re already paying $11 for the same service, and HBO would like you to keep doing that. Streaming apps are banking on you being complacent and happy in your streaming life. Maybe they’re even taking you for granted.

Sometimes you can get the current deal just by threatening to cancel, or actually canceling, your account. Suddenly, you’re an exciting new customer again! Another method is by using an alternate email account (perhaps your spouse’s or roommate’s?) and alternate payment information as a new customer. If you do use a burner email (you did not hear this from me), check in on your favorite app’s terms of service to make sure you’re not in violation by re-enrolling with different emails. I’ll also issue the caveat that you lose all your viewing data and tailored suggestions if you sign up anew.

But times and wallets are tight! And $3 HBO Max sounds pretty good. After all, every middle-aged American man needs to rewatch The Wire once every five years or so—assuming he’s not the kind of middle-aged man who rewatches The Sopranos instead. Here are the current best streaming deals for Cyber Monday 2025.


Devon Maloney; ARCHIVE ID: 546772

Regular price: $80



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Hong Kong FWA services market set for 9.6% growth | Computer Weekly

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Hong Kong FWA services market set for 9.6% growth | Computer Weekly


Analysis from GlobalData is forecasting that fixed wireless access (FWA) service revenue in Hong Kong is expected to increase at a “healthy” compound annual growth rate (CAGR) of 9.6% between 2025 and 2030.

The latest Hong Kong Total Fixed Communications Forecast set out to quantify current and future demand and spending on mobile services for the special administrative region of China. It noted that growth was being driven by Hong Kong’s extensive 5G network coverage and could also be attributed to local operators’ efforts to expand FWA services and position it as an alternative to traditional fibre broadband services for both residential and commercial sectors, meeting growing demand for high-speed connectivity in areas where extending fibre lines is challenging.

“High-density urban and suburban centres of Hong Kong create a strong business case for FWA services due to their cost-effective and rapid deployments without the complex infrastructure and civil work required for extending fibre-optic lines to such locations,” said Neha Misra, senior analyst at GlobalData.

“Competitive, feature-rich plans from the operators will also help drive its adoption over the forecast period. For instance, HKBN’s 5G Home Broadband Plan provides unlimited 5G broadband data (subject to a 300GB with a fair-usage policy) for HKD118 per month on a 24-month contract, along with a seven-day trial guarantee. The plan also includes a waiver of the HKD28 monthly administration fee and complimentary access to the basic HomeShield security plan.”

In addition to HKBN, the study noted that operators such as 3 Hong Kong and HKT are also using their extensive 5G networks to offer home broadband services, particularly in areas with limited fibre infrastructure. It cited HKT as recently having successfully deployed mmWave-based FWA to deliver ultra-high-speed internet to rural areas and outlying islands.

“Growing demand for FWA provides operators a strong revenue opportunity by expanding home and SME broadband without the high capital intensity of fibre roll-out,” Misra added. “By leveraging nationwide 5G coverage, introducing competitively priced service plans and bundling digital home services, operators can unlock higher ARPU [average revenue per user], accelerate market penetration in underserved areas and diversify beyond traditional revenues.”

GlobalData believes the Hong Kong government’s smart city initiatives will also open new opportunities for FWA, especially 5G FWA, which can deliver high-speed internet to power applications such as the digital economy, digital governance and e-health services, while supporting the city’s dense urban environment and digital transformation goals under the Smart City Blueprint 2.0.

The original blueprint was set out in December 2017, outlining 76 initiatives under six smart areas, namely Smart Mobility, Smart Living, Smart Environment, Smart People, Smart Government and Smart Economy. Blueprint 2.0 puts forth more than 130 initiatives that continue to enhance and expand existing city management measures and services. The new initiatives aim to bring benefits and convenience to the public so that residents can better perceive the benefits of smart city innovation and technology.



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Prague’s City Center Sparkles, Buzzes, and Burns at the Signal Festival

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Prague’s City Center Sparkles, Buzzes, and Burns at the Signal Festival


And thanks to a mention in Dan Brown’s new novel, The Secret of Secrets, the festival has gained even more global recognition. Just a few weeks after the release of Brown’s new bestseller set in contemporary Prague, viewers were able to see for themselves what drew the popular writer to the festival, which is the largest Czech and Central European showcase of digital art. In one passage, the Signal Festival has a cameo appearance when the novel’s protagonist recalls attending an event at the 2024 edition.

“We’re happy about it,” festival director Martin Pošta says about the mention. “It’s a kind of recognition.” Not that the event needed promotion, even in one of the most anticipated novels of recent years. The organizers have yet to share the number of visitors to the festival this year, but the four-day event typically attracts half a million visitors.

On the final day, there was a long queue in front of the monumental installation Tristan’s Ascension by American video art pioneer Bill Viola before it opened for the evening, even though it was a ticketed event. In the Church of St. Salvator in the Convent of St. Agnes, visitors could watch a Christ-like figure rise upwards, streams of water defying gravity along with him, all projected on a huge screen.

The festival premiere took place on the Vltava River near the Dvořák Embankment. Taiwan’s Peppercorns Interactive Media Art presented a projection on a cloud of mist called Tzolk’in Light. While creators of other light installations have to deal with the challenges of buildings—their irregular surfaces, decorative details, and awkward cornices—projecting onto water droplets is a challenge of a different kind with artists having to give up control over the resulting image. The shape and depth of the Peppercorns’ work depended on the wind at any given moment, which determined how much of the scene was revealed to viewers and how much simply blown away. The reward, however, was an extraordinary 3D spectacle reminiscent of a hologram—something that can’t be achieved with video projections on static and flat buildings.

Another premiere event was a projection on the tower of the Old Town Hall, created for the festival by the Italian studio mammasONica. It transformed the 230-foot structure into a kaleidoscope of blue, green, red, and white surfaces. A short distance away, on Republic Square, Peppercorns had another installation. On a circular LED installation, they projected a work entitled Between Mountains and Seas, which recounted the history of Taiwan.





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