Phone:(508) 831-6124
Dept. Fax:(508) 831-5824
Office:109B Stratton Hall
US Mail:Department of Mathematical Sciences
Worcester Polytechnic Institute
100 Institute Road
Worcester, MA 01609

Upcoming conference at CIRM on Shape Optimization and Isoperimetric and Functional Inequalities, November, 2016.

Recent workshop on Advances in the mathematical analysis of material defects in elastic solids, June, 2016.

Recent workshop at the Banff International Research Station on Variational Models of Fracture, May, 2016.

Recent workshop at the Lorentz Center on Microstructure evolution in materials: defects, cracks, and interfaces. April, 2016.

Recent undergraduate course at Park City Mathematics Institute ~ Institute for Advanced Study on "variational methods for materials science," June-July, 2014. Abstract.

Video of IPAM lecture (December, 2012)

Lecture Notes for SISSA mini-course, "Mathematical Issues in Quasi-static and Dynamic Fracture Evolution" (March, 2013)

The main focus of my research has been on the interplay between bulk and surface energies in variational problems, motivated largely by questions in Materials Science (e.g., optimal design of composite materials, fracture mechanics, debonding of thin films). My current emphasis is on the evolution of damage and fracture, and in particular, on formulating and analyzing models for predicting damage sets and crack paths. The analysis requires (new) tools from the Calculus of Variations, Partial Differential Equations, and Geometric Measure Theory. Current support: NSF 1616197. Additional support provided by ERC Advanced Grant 290888.

Below are recent papers with abstracts, by topic.

Dynamic Fracture Evolution

Local Minimality and Material Defects (Fracture, Damage, and Plasticity)

Globally Minimizing Quasi-Static Evolution

Gamma Convergence

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Talks and Conferences | Undergraduate Projects | Links | Photos

My Math Genealogy
construction of a crack trajectory with
front for an arbitrary crack increment
(with M. Ortiz and C. Richardson)
fracture path through a laminate of two materials with constant fracture toughness but different elastic moduli (with K. Bhattacharya and B. Bourdin)
a level set method that naturally produces triple junctions (with C. Richardson and M. Sarkis)