In a groundbreaking study, Chase Hartquist, Shu Wang, Bolei Deng headed up by Prof. Xhuane Zhao at MIT have developed a universal law governing network fracture energy, providing a unifying framework for understanding material toughness across a wide range of material types. This research offers critical insights into the fundamental mechanisms that dictate fracture resistance, with applications spanning healthcare, automotive, and aerospace industries.
Follow the main authors here:
- Chase Harquist MIT profile | Linkedin
- Shu Wang MIT profile | Linkedin
- Bolei Deng | Linkedin
- Prof. Xhuane Zhao MIT profile | Linkedin
A link to the related news report, which provides additional context for this interview, can be found here. The following 3 papers are related to the research direction and are great for more indepth understanding:
Hartquist, C., Wang, S., Cui, Q., Matusik, W., Deng, B., & Zhao, X. (2025). Scaling Law for Intrinsic Fracture Energy of Diverse Stretchable Networks. Physical Review X, 15(1), 011002. https://doi.org/10.1103/PhysRevX.15.011002
Hartquist, C. M., Wang, S., Deng, B., Beech, H. K., Craig, S. L., Olsen, B. D., Rubinstein, M., & Zhao, X. (2025). Fracture of polymer-like networks with hybrid bond strengths. Journal of the Mechanics and Physics of Solids, 195, 105931. https://doi.org/10.1016/J.JMPS.2024.105931
Deng, B., Wang, S., Hartquist, C., & Zhao, X. (2023). Nonlocal Intrinsic Fracture Energy of Polymerlike Networks. Physical Review Letters, 131(22), 228102. https://doi.org/10.1103/PhysRevLett.131.228102
As part of our in-depth exploration of this discovery, previously covered in our news feature, we spoke with Chase Hartquist to gain further insights into the methodology, applications, and future directions of this research.
The following interview is presented unedited to preserve Hartquist’s original responses, offering readers an in-depth, unfiltered understanding of how this universal law could transform material design and engineering.
Acknowledgement From Chase Hartquist:
Support for this project was provided in part by the National Institutes of Health (Grants No. 1R01HL153857-01 and No. 1R01HL167947-01), Department of Defense Congressionally Directed Medical Research Programs (Grant No. PR200524P1), and the National Science Foundation (Grant No. EFMA1935291). The authors further acknowledge the MIT SuperCloud and Lincoln Laboratory Supercomputing Center for providing HPC resources that contributed to their research results.
Could you explain the key principles of the universal law governing network fracture energy and how it provides a unifying framework for understanding material toughness across various material types?
The scaling law provides a framework that directly relates the large-scale failure resistance of a material to the small-scale components that make up its structure. It states that the intrinsic fracture energy is directly proportional to two quantities describing the strands that encompass the underlying network: the length and force at which they break when highly stretched. This means that networks can be made tougher by making their strands longer or resistant to higher forces. The law also provides insights into how architecture impacts failure performance. It provides that connecting the strands into topologies with larger loop sizes can further increase the toughness. Since networks across material types can be described by the mechanical behavior and connectivity of their strands, this result can be leveraged to better understand and design against failure in a breadth of candidate materials.
What experimental methodologies or tools were critical in uncovering this law, and how did the team validate its applicability across different material classes such as polymers, biological tissues, and synthetic networks?
The key advancement necessary to uncover this law was the development of our lattice-like computational model: a simulation platform with the capacity to study failure behavior in networks with a variety of mechanical responses. The tunability and scalability of the model enabled us to directly parametrize the mechanical behaviors of individual strands and the assembly details of diverse architectures. We could then directly measure the response of materials in each network class based on the key input variables that define their structure.
Based on insights from simulations, we validated the scaling law experimentally on architected materials and polymer gels containing strands ranging from the nanoscale to the macroscale. Notably, we created soft, stretchable 2D networks by cutting ribbon-shaped strands out of thin plastic sheets that could unwind and stretch well past their initial lengths. We also constructed a massive 3D architected network of spring-shaped strands by 3D- printing the structural design using a rubber-like material. We then measured intrinsic fracture energy through a set of classic experiments by cutting large cracks into the networks and mechanically loading them until failure.
How does this universal law contribute to the prediction and engineering of fracture resistance in complex materials? Could you provide examples of materials where this has been successfully applied?
By boiling down the fracture resistance of networks to a few key variables, the scaling law provides a roadmap that links the macroscopic performance to the microscopic structure. Now, by dialing the knobs controlling these variables while designing networks, engineers and scientists alike can directly manipulate and tune the performance of the resulting materials they create. There are numerous incredible natural examples of this process in action. Many biological materials, for example, rely on networks of biopolymers like collagen for mechanical integrity, which are highly extensible and can withstand relatively large forces before breaking.
What role does the molecular architecture of a network (e.g., crosslink density, chain length) play in determining its fracture energy, and how does the new law incorporate these variables?
Each of these molecular details describing polymer networks relates to one of the parameters included in the scaling law. Chain length, for instance, is included as a strand-level variable. The scaling law shows that networks with longer chain lengths display a larger fracture energy. Crosslink density is included as a topological variable. It manifests in the network architecture because it controls the size of loops connecting adjacent strands. The scaling law provides that networks with larger loops in their structural design have larger fracture energy. These factors—along with many others common in polymers—each relate to some element of the scaling law and each play an important role in describing the fracture performance of a given material.
How could this breakthrough impact material design in industries such as healthcare, automotive, and aerospace? Are there any specific real-world applications currently under development?
These findings shed light on the fundamental principles that dictate the toughness of engineered materials. Many advanced products in modern industrial applications require tough, soft, and stretchable materials for optimum performance. In practice, the scaling law provides a guide that could lead to injury-resistant artificial tissues for improved healthcare treatment, fatigue-resistant rubbers for more durable automotive tires, and fatigue-resistant lattices for innovative aerospace structures. The scaling law could accelerate developments like these being made across each of these disciplines.
What challenges did the team face in reconciling the diverse behaviors of materials under stress with a single universal framework? How were these challenges addressed?
One key problem in reconciling the fundamentals driving mechanical behavior is dealing with a range of length scales. Most computational frameworks have narrow limits to the sizes they can simulate before becoming too complex, especially when studying highly nonlinear phenomena like large deformations and fracture. We conquered this by implementing a coarse-grained approach within our stretchable lattice model, which enabled us to study networks with thousands of repeating layers in a fraction of the time. By drastically increasing efficiency, we could parametrize our model to study a wide variety of network types.
Looking forward, what are the next steps in the research? Are there plans to extend this law to other types of materials or explore its limitations in practical applications?
There are plenty of exciting avenues for exploration in this research. For instance, there remain plenty of unanswered fundamental questions regarding the nature of crack growth in network materials. One unique feature of our computational model is its ability to track and map the failure process within the network. We have since tested this functionality to visualize how cracks grow and progress in heterogeneous networks with varying ratios of both strong and weak strands (link to Journal of the Mechanics of Physics and Solids paper). We hope to leverage this capability to better understand the qualitative picture behind crack propagation in material failure. Our discovery also directly impacts the emerging field of architected materials, whose inherent structures drive their unique performance characteristics. The scaling law provides insights into how these materials can be toughened even further. By studying and optimizing performance in this class of materials, we can better understand the extent to which this law can apply generally in cutting-edge material design for many practical applications.
