Christopher Larsen
Worcester Polytechnic Institute, MA·Mathematics & Statistics
Predicting when materials and structures crack and fail matters for everything from bridges to defense systems. Those predictions rest on mathematical and computational models, and both should be rigorous and physically sound.
- Fields
Mathematics & Statistics
Engineering
- Topics
fracture mechanics
variational methods
calculus of variations
- Grants
- 1 known grant, through Aug 2028
What they work on
- 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.
- Show existence of quasi-static fracture evolutions, meaning cracks that grow slowly as loads change, under the new variational principle, avoiding the unphysical nucleation forced by energy minimization.
- Formulate fracture models that combine the new propagation principle with completely independent strength criteria for nucleation, and establish existence of evolutions satisfying both.
- Improve the link between phase-field fracture implementations and sharp-fracture models by studying the new spatially local variational principle with Gamma-convergence, then build better computational models.
More about the research
Mathematics has improved fracture simulation a great deal over the past 25 years, but gaps remain: most results cannot handle applied forces, and some models tangle together two distinct events, nucleation (when a crack first appears) and propagation (how an existing crack grows).
Why it matters
Accurate failure prediction underpins the design of civil infrastructure and defense structures. Firmer mathematical foundations for fracture could yield simulations that predict cracking more faithfully when realistic forces act on a structure, giving engineers better tools for judging when materials and structures will break.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
Robert Lipton
Louisiana State University, LA·Mathematics & Statistics
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.
Yingchao Yang
University of Missouri-Columbia, MO·Materials Science·Early-career
Synthesize single-layer and multilayer two-dimensional high entropy materials containing at least five elements, using solid-state reaction and chemical vapor deposition.
The school
Worcester Polytechnic Institute: 6 labs on PI Pages, $72M a year on research, 69 research doctorates a year.
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