Uncovering the Fundamental Mechanisms Behind Toughening of Soft¨CHard Composites

Researchers use a minimal 3D model to obtain universal design rules for optimizing strength and fracture resistance

Soft¨Chard composite materials can overcome the inherent trade-off between strength and toughness, but the underlying mechanisms remain unclear. Recently, researchers from Japan and China developed a minimal three-dimensional composite model that eliminates nonlinear effects, isolating key design principles. This framework revealed how varying the mixing ratio of soft to hard materials leads to brittle-to-ductile transitions and identified the optimal ratio that maximizes toughness, offering insights for the development of next-generation structural and biomedical materials.

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 biological materials 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¨Chard composites¡ªfrom advanced dual-phase steels to specialized gels and reinforced rubbers¡ªthat demonstrate performance exceeding that of their individual components.

While artificial soft¨Chard composites have shown impressive performance in laboratory tests and real-world applications, 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 made available online on July 03, 2025, and published in Volume 122, Issue 27 of the journal PNAS on July 08, 2025, the researchers introduce a minimal three-dimensional soft¨Chard 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.

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¨Chard composite materials. This consistency emphasizes the fundamental principles underlying the toughening mechanisms in general soft¨Chard 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 regenerative medicine, 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 tissue engineering and medical devices, this research provides a powerful theoretical foundation for engineering materials that are both strong and tough.

Reference

Title of original paper:

Fundamental toughening landscape in soft¨Chard composites: Insights from a minimal framework

Journal

PNAS

DOI:

https://doi.org/10.1073/pnas.2506071122

Additional information for EurekAlert

Latest Article Publication Date

08 July 2025

Method of Research

Experimental study

Subject of Research

Not applicable

Conflicts of Interest Statement

The authors declare no competing interests.

About the University of Toyama, Japan

University of Toyama is a leading national university located in Toyama Prefecture, Japan, with campuses in Toyama City and Takaoka City. Formed in 2005 through the integration of three former national institutions, the university brings together a broad spectrum of disciplines across its 9 undergraduate schools, 8 graduate schools, and a range of specialized institutes. With more than 9,000 students, including a growing international cohort, the university is dedicated to high-quality education, cutting-edge research, and meaningful social contribution. Guided by the mission to cultivate individuals with creativity, ethical awareness, and a strong sense of purpose, the University of Toyama fosters learning that integrates the humanities, social sciences, natural sciences, and life sciences. The university emphasizes a global standard of education while remaining deeply engaged with the local community.

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About Professor Katsuhiko Sato from the University of Toyama, Japan

Dr. Katsuhiko Sato is a Specially Appointed Professor at the Program of Mathematics and Informatics, University of Toyama, Japan. His research interests lie in active matter, soft matter, mathematical modeling, cell movement, muscle contraction, and rheology. He has over 25 scientific publications credited to his name, with more than 300 citations and an h-index score of 10. He has been actively involved in facilitating research seminars.

Funding information

This work was supported by the Japan Society for the Promotion of Science (JSPS) International Research Fellow in Japan (grant no. 23KF0002) and JSPS KAKENHI (grant no. 22H04968, 22K21342, and 21H05310).

Media contact

Yumiko Kato

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