Ian Tobasco
University of Michigan, MI·Mathematics & Statistics·Early-career
A sheet of plastic wrap crumpled in your hand forms wrinkles and sharp folds. A sheet of paper cut in a repeating pattern, as in kirigami, can stretch and change shape in surprising ways.
- Fields
Mathematics & Statistics
Engineering
Materials Science
- Topics
calculus of variations
variational analysis
nonlinear elasticity
- Grants
- 1 known grant, through May 2027
What they work on
- Develop a variational model of the wrinkle-fold state seen in confined elastic shells, deriving an asymptotic description from fully nonlinear elasticity.
- Analyze stress focusing in confined shells and related one-dimensional elastic systems, using rigorous optimization to find extreme examples that guide a general theory of wrinkle and fold patterns.
- Characterize the effective deformations and emergent stress-strain laws of kirigami and other mechanical metamaterials by deriving weak limits and stored energy as the number of elastic bodies becomes infinite.
- Develop general techniques for designing load-bearing, shape-changing materials based on the derived limits of many-body elastic systems.
More about the research
This project uses mathematics to explain and predict such behavior. It applies the calculus of variations, which finds the shapes that minimize energy, along with optimization problems that have many competing solutions. The two topics are how stress concentrates when thin elastic sheets are confined, and how mechanical metamaterials behave as a whole. Mechanical metamaterials are structures whose overall properties come from many interacting elastic parts.
Why it matters
A general theory of where wrinkles and folds form in packed elastic sheets could help engineers predict and control how thin materials crumple. Methods for predicting how kirigami and other mechanical metamaterials respond to loads could support the design of load-bearing materials that change shape on demand.
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.
Carmen Lilley
University of Illinois Chicago, IL·Materials Science
Develop a machine-learning workflow that predicts elastic properties, stress-strain behavior and fracture strength of 2D lateral heterostructures with interface defects, at accuracy comparable to density functional theory (DFT).
Ranajay Ghosh
University of Central Florida, FL·Engineering·Early-career
Test whether concentrated salt solutions give green strength to oxide and nitride ceramic powder beds through ion transport and particle bridging during wetting and drying, using mechanical testing, microscopy and x-ray imaging.
The school
University of Michigan: 124 labs on PI Pages, $2.1B a year on research, 963 research doctorates a year.
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