LSU Math Professor Robert Lipton Secures $1.25 Million MURI Award to Help Improve Materials Durability

Boomers may recall Timex's iconic slogan, "It takes a licking and keeps on ticking," from live commercials that "tortured" Timex watches with hammers to showcase their durability in the late 1960s. While later generations might have missed the watch-torture spectacle, they likely remember other examples of commercial products promising durability, highlighting a universal demand for long-lasting products and the pressing need for more resilient materials across various sectors.

What many don’t know is that mathematicians might hold the long-awaited formula for creating sturdier materials—or, in this case, equations.

"I'm interested in the dynamics of extreme deformation in material structures. And by extreme deformation, I mean ripping things apart and blowing things up," explains LSU Mathematics professor Robert Lipton. His research aims to enhance the understanding of damage propagation in heterogeneous materials.

"Even under fracture and severe damage conditions, you still need to know the behavior of your material. This understanding can be used to build more robust materials that can take on some punishment but still maintain their function. Much like a Timex watch."

The durability and robustness of materials is a crucial concern for the Department of Defense. "Predicting Performance Outcomes for Heterogeneous Materials Under Complex Loading" was among the 25 strategically important topic areas in the 2024 Multidisciplinary University Research Initiative (MURI) award competition. MURI awards support defense-related research with potential applications across military capabilities and commercial sectors alike and are a cornerstone of the DoD's basic research endeavors. Its primary goal is to address ongoing science and engineering challenges faced by society.

Professor Lipton and his team are set to receive $1.25 million over the next five years as part of their recently awarded MURI project titled "Complexity, Nonlocality, and Uncertainty in Heterogeneous Solids." The total grant award is $7.5 million, spread across five institutions including LSU’s Department of Mathematics, Carnegie Mellon University, the University of Chicago, the University of Colorado Boulder, and the University of Pennsylvania.

The successful MURI proposal reflects an integrated multidisciplinary effort between mathematical scientists, physicists, engineers, and experimentalists aimed at understanding the science of heterogeneous materials undergoing extreme damage.

"We will come up with new ways to create mathematical models during this truly dynamic situation in continuum mechanics, which is material deformation and damage," explains Lipton. 

"We will start with basic equations like Newton's laws for deforming objects, turning them into differential equations, and setting up initial conditions and boundary conditions. These will help us understand how forces and impacts can affect objects."

"It's also important to make sure these mathematical models reflect real physical laws and have solutions that make sense. Once we're sure of that, we can use computer programs to solve these problems. In other words, we are designing a problem that models physical reality as best it can and has a solution that we can find using a computer."

This is the third MURI award that Lipton has received. The highly competitive program received 276 white papers for the 2024 cycle, out of which an expert panel for full proposals selected 102. Ultimately, 25-30 projects were chosen for funding, including the one from Lipton and his team. 

"We had a very tight and intrinsic proposal, that has a synergistic interaction between the experimental sciences and the theoretical sciences," says Lipton. "All collaborators participated in the conception and writing of the project, and what is fun is that the experiments reinforce the theory, and the theory reinforces the experiments."

While funding for the new award begins this summer, Lipton’s current MURI award is set to conclude in August 2024. Titled "Predicting and Controlling the Response of Particulate Systems through Grain Scale Engineering," this project aims to enhance the understanding of continuum mechanics in granular materials, spanning from the macroscopic to microscopic scale. It involves collaboration with researchers from the California Institute of Technology, the University of Chicago, Northwestern University, and Carnegie Mellon University. Last year, the LSU team hosted collaborators on campus for a conference at the Lod Cook Conference Center on November 6 and 7, 2023, where researchers presented advances in modeling complex systems and particle engineering.