Blaise
Bourdin
Professor, Mathematics and Statistics
Blaise Bourdin is a Professor of Mathematics at McMaster University and the Canada Research Chair in Mathematical and Computational Aspects of Solid Mechanics (tier 1).
After graduating from the Université Paris 13 (France) in 1998, Bourdin joined the Technical University of Denmark, California Institute of Technology and New York University as a Post-Doctoral Fellow. He joined the Department of Mathematics at Louisiana State University as an Assistant Professor in 2002 and raised to the ranks of Associate Professor, Full Professor, and A.K. & Shirley Barton Professor. B. Bourdin moved to the Department of Mathematics & Statistics at McMaster University in July 2021, and received the tier 1 Canada Research Chair in Mathematical and Computational Aspects of Solid Mechanics in July 2022.
Bourdin's formal training is at the confluence of solid mechanics, scientific computing, and applied mathematics. His main interest is on multi-disciplinary modeling, analysis, and numerical simulation in mechanical science with a specific focus on defect mechanics and optimal design. He pioneered the phase-field approach to brittle fracture, one today's most influential method in the field.
He is the recipient of research grants from the U.S. National Science Foundation, the Louisiana Board of Regents, the Natural Sciences and Engineering Research Council of Canada, and industry totalling over $6M. He is the author of one book and over 40 peer-reviewed publications, including three ESI highly cited papers in two disciplines (mathematics and engineering).
After graduating from the Université Paris 13 (France) in 1998, Bourdin joined the Technical University of Denmark, California Institute of Technology and New York University as a Post-Doctoral Fellow. He joined the Department of Mathematics at Louisiana State University as an Assistant Professor in 2002 and raised to the ranks of Associate Professor, Full Professor, and A.K. & Shirley Barton Professor. B. Bourdin moved to the Department of Mathematics & Statistics at McMaster University in July 2021, and received the tier 1 Canada Research Chair in Mathematical and Computational Aspects of Solid Mechanics in July 2022.
Bourdin's formal training is at the confluence of solid mechanics, scientific computing, and applied mathematics. His main interest is on multi-disciplinary modeling, analysis, and numerical simulation in mechanical science with a specific focus on defect mechanics and optimal design. He pioneered the phase-field approach to brittle fracture, one today's most influential method in the field.
He is the recipient of research grants from the U.S. National Science Foundation, the Louisiana Board of Regents, the Natural Sciences and Engineering Research Council of Canada, and industry totalling over $6M. He is the author of one book and over 40 peer-reviewed publications, including three ESI highly cited papers in two disciplines (mathematics and engineering).
- Contact Information
- PHONE: +1 905 525 9140 ext 27243
- EMAIL: bourdin
- Websites
Affiliations
- Faculty of Science, McMaster University
- Mathematics and Statistics (Internal), Faculty of Science
- Professor, Mathematics and Statistics, Faculty of Science
- Adjunct Professor, Department of Mechanical & Industrial Engineering, Louisiana State University
- Canada Research Chair in Mathematical and Computational Aspects of Solid Mechanics, McMaster University,
- A.K. and Shirley Barton Professor, Department of Mathematics, Louisiana State University
- Professor, Department of Mathematics, Louisiana State University
- Associate Professor, Department of Mathematics, Louisiana State University
- Visiting professor, Institut Jean le Rond d’Alembert, Université Pierre et Marie Curie
- Visiting Associate Professor, Department of Mechanical Engineering, California Institute of Technology
- Assistant Professor, Department of Mathematics, Louisiana State University
Research Areas
- Applied mathematics (RA)
- Numerical analysis (RA)
- Solid mechanics (RA)
- Theoretical and applied mechanics (RA)
- Affiliation
- Scholarly Activity
- Teaching
- Background
- Contact
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Affiliation
Scholarly Activity
selected scholarly activity
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books
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chapters
- Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach. 75-91. 2014
- Fracture. Courses and Lectures - International Centre for Mechanical Sciences. 107-161. 2011
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conferences
- A variational phase field model of hydraulic fracturing. ICF 2017 - 14th International Conference on Fracture. 1030-1031. 2017
- Crack initiation in variational phase field models of fracture. ICF 2017 - 14th International Conference on Fracture. 964-965. 2017
- A new modeling approach to natural fracturing process. 47th US Rock Mechanics / Geomechanics Symposium 2013. 2663-2672. 2013
- A Variational Approach to the Numerical Simulation of Hydraulic Fracturing. All Days. 1442-1452. 2012
- Secondary thermal cracks in EGS: A variational approach. Transactions - Geothermal Resources Council. 289-292. 2010
- Distributed fast marching methods. Proceedings of the 15th ACM Mardi Gras conference: From lightweight mash-ups to lambda grids: Understanding the spectrum of distributed computing requirements, applications, tools, infrastructures, interoperability, and the incremental adoption of key capabilities. 1-1. 2008
- The variational formulation of brittle fracture: numerical implementation and extensions. IUTAM Bookseries. 381-393. 2007
- The Phase-Field Method in Optimal Design. IUTAM Bookseries. 207-215. 2006
- 25 and de méthodes de champ de phase en mécanique de la rupture fragile
- A variational approach to the numerical simulation of hydraulic fracturing under in-situ stresses
- Advanced discretization schemes for phase-field fracture
- Advanced discretization schemes for phase-field fracture
- Fracture in heterogeneous brittle materials
- NUMERICAL SIMULATION OF RESERVOIR STIMULATION - A VARIATIONAL APPROACH
- Phase-field approach to diffusion-driven fracture
- Phase-field approximation of diffusion-driven fracture
- Phase-field models of sharp interfaces in fluids and solids
- Rebuilding mef90
- vDef-Web: A Case-Study on Building a Science Gateway Around a Research Code
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journal articles
- A DG/CR discretization for the variational phase-field approach to fracture. Computational Mechanics. 72:693-705. 2023
- Improving the Accuracy of Fracture Toughness Measurement in Burst Experiments. Rock Mechanics and Rock Engineering. 56:427-436. 2023
- On the loss of symmetry in toughness dominated hydraulic fractures. International Journal of Fracture. 237:189-202. 2022
- Phase-field approaches to fracture in the 3rd millennium. International Journal of Fracture. 237:1-2. 2022
- Minimum compliance with obstacle constraints: an active set approach. Structural and Multidisciplinary Optimization. 65. 2022
- Optimal design of responsive structures. Structural and Multidisciplinary Optimization. 65. 2022
- Fracture Diodes: Directional Asymmetry of Fracture Toughness. Physical Review Letters. 126:025503. 2021
- Revisiting nucleation in the phase-field approach to brittle fracture. Journal of the Mechanics and Physics of Solids. 142:104027-104027. 2020
- Guiding and Trapping Cracks With Compliant Inclusions for Enhancing Toughness of Brittle Composite Materials. Journal of Applied Mechanics, Transactions ASME. 87. 2020
- Anisotropy of the effective toughness of layered media. Journal of the Mechanics and Physics of Solids. 131:96-111. 2019
- Phase-field study of crack nucleation and propagation in elastic–perfectly plastic bodies. Computer Methods in Applied Mechanics and Engineering. 353:44-65. 2019
- A variational phase-field model for hydraulic fracturing in porous media. Computer Methods in Applied Mechanics and Engineering. 347:957-982. 2019
- Stress fluctuation, crack renucleation and toughening in layered materials. Journal of the Mechanics and Physics of Solids. 120:68-78. 2018
- Crack nucleation in variational phase-field models of brittle fracture. Journal of the Mechanics and Physics of Solids. 110:80-99. 2018
- A variational hydraulic fracturing model coupled to a reservoir simulator. International Journal of Rock Mechanics and Minings Sciences. 88:137-150. 2016
- On the Asymptotic Derivation of Winkler-Type Energies from 3D Elasticity. Journal of Elasticity. 121:275-301. 2015
- Validation simulations for the variational approach to fracture. Computer Methods in Applied Mechanics and Engineering. 290:420-437. 2015
- Effective toughness of heterogeneous media. Journal of the Mechanics and Physics of Solids. 71:15-32. 2014
- A variational model for fracture and debonding of thin films under in-plane loadings. Journal of the Mechanics and Physics of Solids. 70:320-348. 2014
- Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks. Physical Review Letters. 112:014301. 2014
- A variational approach to the fracture of brittle thin films subject to out-of-plane loading. Journal of the Mechanics and Physics of Solids. 61:2360-2379. 2013
- Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach. International Journal of Fracture. 184:75-91. 2013
- Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model. Continuum Mechanics and Thermodynamics. 25:243-268. 2013
- A time-discrete model for dynamic fracture based on crack regularization. International Journal of Fracture. 168:133-143. 2011
- Optimal Partitions for Eigenvalues. SIAM Journal on Scientific Computing. 31:4100-4114. 2010
- The Variational Approach to Fracture. Journal of Elasticity. 91:5-148. 2008
- Optimization of structural topology in the high-porosity regime. Journal of the Mechanics and Physics of Solids. 56:1043-1064. 2008
- Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces and Free Boundaries. 9:411-430. 2007
- Numerical Implementation of Overlapping Balancing Domain Decomposition Methods on Unstructured Meshes. Lecture Notes in Computational Science and Engineering. 55:309-315. 2007
- Design-dependent loads in topology optimization. ESAIM - Control, Optimisation and Calculus of Variations. 9:19-48. 2003
- Filters in topology optimization. International Journal for Numerical Methods in Engineering. 50:2143-2158. 2001
- Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numerische Mathematik. 85:609-646. 2000
- Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids. 48:797-826. 2000
- Image segmentation with a finite element method. ESAIM: Mathematical Modelling and Numerical Analysis. 33:229-244. 1999
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preprints
- Systematic design of compliant morphing structures: a phase-field approach 2024
- A DG/CR discretization for the variational phase-field approach to fracture 2022
- Fracture Diodes: Directional asymmetry of fracture toughness 2021
- Optimal Design of Responsive Structures 2021
- Phase-field study of crack nucleation and propagation in elastic - perfectly plastic bodies 2018
- On the asymptotic derivation of Winkler-type energies from 3D elasticity 2014
- Morphogenesis and propagation of complex cracks induced by thermal shocks 2013
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presentations
- Recent developments in variational and phase-field models of brittle fracture 2023
- Crack nucleation in variational phase-field models of brittle fracture 2023
- Variational and phase-field models of brittle fracture: Past successes and current issues 2023
- Fracture in heterogeneous brittle materials 2023
- Phase-field approaches to topology optimization and fracture: recent developments
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software
Teaching
teaching activities
- Engineering Mathematics IV - MATH 2ZZ3, Instructor 2024
- Engineering Mathematics IV - MATH 2ZZ3, Instructor 2024
- Engineering Mathematics IV - MATH 2ZZ3, Instructor 2024
- Methods of Applied Mathematics I - MATH 741, Instructor 2023
- Graduate Level Topics in Mathematics - MATH 5GT3, Instructor 2023
- Fourier Analysis - MATH 724, Instructor 2023
- Graduate Level Topics in Mathematics - MATH 5GT3, Instructor 2023
- Calculus for Math and Stats I - MATH 1X03, Instructor 2022
- Calculus for Math and Stats I - MATH 1X03, Instructor 2022
- Topics in Differential Equations - MATH 4FT3, Instructor 2022
- Topics in Differential Equations - MATH 6FT3, Instructor 2022
Background
education and training
- Doctorate, Université Paris 13 1995 - 1998
- Diplôme d'Études Approfondies, Université Paris 13 1994 - 1995
- Maîtrise, Université Paris 13 1993 - 1994
- License, Université Paris 13 1992 - 1993
- Diplôme d'Études Universitaires Générales, Université Paris 13 1990 - 1992
- California Institute of Technology , Postdoctoral fellow 2000 - 2002
Contact
full name
- Blaise Bourdin
mailing address
-
McMaster University
Department of Mathematics & Statistics
1280 Main Street West
Hamilton
ON
L8S 4L8
Canada