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

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–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 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 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.

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 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.