Robert Lipton
Louisiana State University, LA·Mathematics & Statistics
Predicting when and how materials crack is central to designing safe bridges, vehicles and energy systems. Yet mathematics still lacks a well-posed way to compute how fractures start and spread over time under changing loads.
- Fields
Mathematics & Statistics
Engineering
Materials Science
- Topics
fracture mechanics
dynamic fracture
quasistatic fracture
- Grants
- 1 known grant, through Aug 2029
What they work on
- Formulate fracture as a mathematically well-posed initial value problem, with displacement evolving under Newton's second law, so that damage and crack patterns emerge as the outcome of given starting displacements, velocities and time-varying boundary loads.
- Develop a blended fracture model that uses only the equation of motion for displacement, without the separate phase field equation of traditional models, to predict crack nucleation and growth with few material parameters.
- Build computational platforms for GPUs and high-performance computing clusters that compute solutions of the dynamic and quasistatic fracture problem.
More about the research
This collaborative project develops both the theory and the computer methods to do that, for fast-moving (dynamic) fracture and slowly loaded (quasistatic) fracture.
Why it matters
A predictive theory of how damage and cracks spread in complex structures under real-world loads could give engineers a better tool for designing infrastructure, transportation systems and energy production equipment. Methods that need few material parameters and run on GPU computing platforms could make such predictions more practical.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Christopher Larsen
Worcester Polytechnic Institute, MA·Mathematics & Statistics
Prove that equilibrium states exist satisfying a new variational principle for fracture, one that isolates crack propagation and remains compatible with all applied forces, including body loads such as gravity.
Mallikarjunaiah Muddamallappa
Texas A & M University-Corpus Christi, TX·Mathematics & Statistics
Formulate a regularized phase-field model of brittle fracture that uses strain-limiting constitutive relations, avoiding the unrealistic infinite strain predicted by linear models at crack tips.
Burak Aksoylu
Texas A&M University-San Antonio, TX·Mathematics & Statistics
Use machine learning to improve iterative local-to-nonlocal coupling, so that peridynamics models only the region where fracture occurs and cheaper local models handle the rest.
The school
Louisiana State University: 15 labs on PI Pages, $431M a year on research, 323 research doctorates a year.
Reach out
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