Crack pattern in ceramics subject to thermal shock


Full length resume available for download here.


  • Ph.D. in Mathematics, Université Paris-Nord (France), 1998.
  • D.E.A. in Numerical Analysis, Université Paris-Nord (France), 1995.
  • Maîtrise in Applied Mathematics, Université Paris-Nord (France), 1994.



  1. Hossain, M. Z., Hsueh, C. J., Bhattacharya, K., Ravichandran, G., Bourdin, B. (2019) Systems and Methods for Determining the Effective Toughness of a Material and for Implementing Materials Possessing Improved Effective Toughness Characteristics. United States Patent No: US 10,190,955 granted Jan. 29, 2019. View on or download here



  1. Bourdin, B., Francfort, G. A., & Marigo, J.-J. (2008). The Variational Approach to Fracture. The Variational Approach to Fracture. Springer. DOI:10.1007/s10659-007-9107-3

Articles and reviewed conference proceedings

  1. Bourdin, B. (1998). Une méthode variationnelle en mécanique de la rupture, théorie et applications numériques (PhD thesis). Université Paris Nord, Institut Galilée, France. Download
  2. Bourdin, B. (1999). Image segmentation with a finite element method. M2AN Math. Model. Numer. Anal., 33(2), 229–244. DOI:10.1051/m2an:1999114 Download
  3. Bourdin, B., & Chambolle, A. (2000). Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numer. Math., 85(4), 609–646. DOI:10.1007/PL00005394 Download
  4. Bourdin, B., Francfort, G. A., & Marigo, J.-J. (2000). Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids, 48(4), 797–826. DOI:10.1016/S0022-5096(99)00028-9 Download
  5. Bourdin, B. (2001). Filters in topology optimization. Int. J. Num. Meth. Engng., 50, 2143–2158. DOI:10.1002/nme.116 Download
  6. Bourdin, B., & Kohn, R. V. (2002). Extremal Light-weight microstructures. In Proc of the 15th ASCE Eng. Mech. Conference. Columbia University, New York, NY. Download
  7. Bourdin, B., & Chambolle, A. (2003). Design-dependent loads in topology optimization. ESAIM Contr. Optim. Ca., 9, 19–48. DOI:10.1051/cocv:2002070 Download
  8. Kimn, J.-H., & Bourdin, B. (2006). Numerical Implementation of Overlapping Balancing Domain Decomposition Methods on Unstructured Meshes. In O. B. Widlund & D. E. Keyes (Eds.), Domain Decomposition Methods in Science and Engineering XVI (Vol. 55, pp. 309–315). Springer-Verlag. Download
  9. Bourdin, B., & Chambolle, A. (2006). The phase-field method in optimal design. In O. S. M.P. Bendsøe & N. Olhoff (Eds.), IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials (pp. 207–216). Springer. Download
  10. Bourdin, B. (2007). Numerical implementation of a variational formulation of quasi-static brittle fracture. Interfaces Free Bound., 9, 411–430. DOI:10.4171/IFB/171 Download
  11. Bourdin, B. (2007). The variational formulation of brittle fracture: numerical implementation and extensions. In R. de B. A. Combescure T. Belytschko (Ed.), IUTAM Symposium on Discretization Methods for Evolving Discontinuities (pp. 381–393). Springer. Download
  12. Bourdin, B., Francfort, G. A., & Marigo, J.-J. (2008). The Variational Approach to Fracture. J. Elasticity, 91(1-3), 1–148. DOI:10.1007/s10659-007-9107-3 Download
  13. Bourdin, B., & Kohn, R. V. (2008). Optimization of Structural Topology in the High-Porosity Regime. J. Mech. Phys. Solids, 56, 1043–1064. DOI:10.1016/j.jmps.2007.06.002 Download
  14. Bourdin, B., Bucur, D., & Oudet, É. (2009). Optimal Partitions for Eigenvalues. SIAM J. Sci. Comput., 31(6), 4100–4114. DOI:10.1137/090747087 Download
  15. Bourdin, B., Knepley, M., & Maurini, C. (2010). Secondary Thermal Cracks in EGS: a Variational Approach. In Proceedings of the 34th annual meeting of the Geothermal Resources Council. Sacramento, CA. Download
  16. Bourdin, B., Knepley, M., & Maurini, C. (2011). Numerical Simulation of Reservoir Stimulation – A Variational Approach. In Proceedings of the 37th Stanford Geothermal Workshop. Stanford University, CA. Download
  17. Bourdin, B., Larsen, C. J., & Richardson, C. (2011). A time-discrete model for dynamic fracture based on crack regularization. Int. J. Fracture, 168(2), 133–143. DOI:10.1007/s10704-010-9562-x Download
  18. Bourdin, B., & Francfort, G. A. (2011). Variational Models and Methods in Solid and Fluid Mechanics. In D. dell’Isola & S. Gavrilyuk (Eds.), . Springer Wien New York. DOI:10.1007/978-3-7091-0983-0_3 Download
  19. Bourdin, B., Chukwudozie, C., & Yoshioka, K. (2012). A Variational Approach to the Numerical Simulation of Hydraulic Fracturing. In Proceedings of the 2012 SPE Annual Technical Conference and Exhibition (Vol. SPE 159154). DOI:10.2118/159154-MS Download
  20. Mesgarnejad, A., Bourdin, B., & Khonsari, M. M. (2013). A variational approach to the fracture of brittle thin films under out of plane loading. J. Mech. Phys Solids, 61(11), 2360–2379. DOI:10.1016/j.jmps.2013.05.001 Download
  21. Chukwudozie, C., Bourdin, B., Yoshioka, K., Buchmann, T., & Connolly, P. (2013). A New Modeling Approach to Natural Fracturing Process. In 47th U.S. Rock Mechanics/Geomechanics Symposium. San Francisco, California: American Rock Mechanics Association. Download
  22. Bourdin, B., Chukwudozie, C., & Yoshioka, K. (2013). A Variational Approach To The Modeling And Numerical Simulation Of Hydraulic Fracturing Under In-Situ Stresses. In Proceedings of the 38th Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, CA. Download
  23. Maurini, C., Bourdin, B., Gauthier, G., & Lazarus, V. (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. Int. J. Fracture, 184(1-2), 75–91. DOI:10.1007/s10704-013-9824-5 Download
  24. León-Baldelli, A. A., Bourdin, B., Marigo, J.-J., & Maurini, C. (2013). Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a 1d variational model. Cont. Mech. Thermodyn., 25(2-4), 243–268. DOI:10.1007/s00161-012-0245-x Download
  25. Hossain, M. Z., Hsueh, C.-J., Bourdin, B., & Bhattacharya, K. (2014). Effective toughness of heterogeneous media. J. Mech. Phys. Solids, 71, 320–348. DOI:10.1016/j.jmps.2014.06.002 Download
  26. León-Baldelli, A. A., Babadjian, J.-F., Bourdin, B., Henao, D., & Maurini, C. (2014). A Variational Model For Fracture And Delamination Of Thin Films. J. Mech. Phys. Solids, 70, 15–32. DOI:10.1016/j.jmps.2014.05.020 Download
  27. Bourdin, B., Marigo, J.-J., Maurini, C., & Sicsic, P. (2014). Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks. Phys. Rev. Lett., 112(1), 014301. DOI:10.1103/PhysRevLett.112.014301 Download
  28. Mesgarnejad, A., Bourdin, B., & Khonsari, M. M. (2015). Validation simulations for the variational approach to fracture. Comp. Methods Appl. Mech. Engng., 290, 420–437. DOI:10.1016/j.cma.2014.10.052 Download
  29. León-Baldelli, A. A., & Bourdin, B. (2015). On the asymptotic derivation of Winkler-type energies from 3D elasticity. J. Elasticity, 121(2), 275–301. DOI:10.1007/s10659-015-9528-3 Download
  30. Yoshioka, K., & Bourdin, B. (2016). A variational hydraulic fracturing model coupled to a reservoir simulator. Int. J. Rock Mech. Min., 88, 137–150. DOI:10.1016/j.ijrmms.2016.07.020 Download
  31. Tanné, E., Li, T., Bourdin, B., Marigo, J.-J., & Maurini, C. (2018). Crack nucleation in variational phase-field models of brittle fracture. J. Mech. Phys. Solids, 110, 80–99. DOI:10.1016/j.jmps.2017.09.006 Download
  32. Hsueh, C.-J., Avellar, L., Bourdin, B., Ravichandran, G., & Bhattacharya, K. (2018). Stress fluctuation, crack renucleation and toughening in layered materials. J. Mech. Phys Solids, 120, 68–78. DOI:10.1016/j.jmps.2018.04.011 Download
  33. Chukwudozie, C., Bourdin, B., & Yoshioka, K. (2019). A variational phase-field model for hydraulic fracturing in porous media. Comp. Meth. Appl. Mech. Engng., 347, 957–982. DOI:10.1016/j.cma.2018.12.037 Download
  34. Dunkel, A., Bourdin, B., & Brandt, S. R. (2019). vDef-Web: A case-Study on building a science gateway around a research code. In Proceedings of the Gateways 2019 conference. San Diego, CA. Download
  35. Bourdin, B., & Francfort, G. A. (2019). Past and present of variational fracture. SIAM News, 52(9). Download
  36. Brach, S., Tanné, E., Bourdin, B., & Bhattacharya, K. (2019). Phase-field study of crack nucleation and propagation in elastic-perfectly plastic bodies. Comp. Meth. Appl. Mech. Engng., 353(15), 44–65. DOI:10.1016/j.cma.2019.04.027 Download
  37. Brach, S., Hossain, M. Z., Bourdin, B., & Bhattacharya, K. (2019). Anisotropy of the effective toughness of layered media. J. Mech. Phys. Solids, 131, 96–111. DOI:10.1016/j.jmps.2019.06.021 Download
  38. Brodnik, N. R., Hsueh, C.-J., Faber, K. T., Bourdin, B., Ravichandran, G., & Bhattacharya, K. (2020). Guiding and Trapping Cracks With Compliant Inclusions for Enhancing Toughness of Brittle Composite Materials. J. Appl. Mech., 87(3). DOI:10.1115/1.4045682 Download
  39. Kumar, A., Bourdin, B., Francfort, G. A., & Lopez-Pamies, O. (2020). Revisiting Nucleation in the Phase-Field Approach to Brittle Fracture. J. Mech. Phys. Solids, 104027. DOI:10.1016/j.jmps.2020.104027 Download
  40. Brodnik, N. R., Brach, S., Long, C. M., Ravichandran, G., Bourdin, B., Faber, K. T., & Bhattacharya, K. (2021). Fracture Diodes: Directional Asymmetry of Fracture Toughness. Phys. Rev. Lett., 126, 025503. DOI:10.1103/PhysRevLett.126.025503 Download
  41. Yoshioka, K., Zhang, Y., Lu, G., Bunger, A., Adachi, J., & Bourdin, B. (2022). Improving the Accuracy of Fracture Toughness Measurement in Burst Experiments. Rock Mech. Rock Engng. DOI:10.1007/s00603-022-03097-y
  42. Tanné, E., Bourdin, B., & Yoshioka, K. (2022). On the loss of symmetry in toughness dominated hydraulic fractures. Int. J. Fracture. DOI:10.1007/s10704-022-00623-5 Download
  43. Akerson, A., Bourdin, B., & Bhattacharya, K. (2022). Optimal Design of Responsive Structures. Struct. Multidiscip. O., 65(4). DOI:10.1007/s00158-022-03200-5
  44. Tran, N. V., & Bourdin, B. (2022). Minimum compliance with obstacle constraints: an active set approach. Struct. Multidiscip. O., 65(4). DOI:10.1007/s00158-022-03199-9
  45. Marazzato, F., & Bourdin, B. (2023). A DG/CR discretization for the variational phase-field approach to fracture. DOI:10.1007/s00466-023-02294-y

Open-source software

  1. mef90/vDef: a parallel scalable finite element implementation of the variational approach to fracture in fortran90, based on the variational phase field approach. mef90/vDef is also available as a docker container on docker hub. DOI:10.5281/zenodo.3242131
  2. snlp: a fork of Brian C. Fabien’s Sequential Non Linear Programing code, modified to interface with PETSc, and to include fortran90 bindings, using the iso_c_bindings module. DOI:10.5281/zenodo.3242159
  3. VPFHF: a structured parallel three-dimensional finite element hydro-mechanical reservoir simulator developed Chukwudi Chukwudozie and Keita Yoshioka. DOI:10.5281/zenodo.3242138
  4. partitions: the implementation of the algorithms of Bourdin, B., Bucur, D., & Oudet, É. (2009). Optimal Partitions for Eigenvalues. SIAM J. Sci. Comput., 31(6), 4100–4114.. DOI:10.5281/zenodo.3242188

Plenary and significant lectures

  • SIAM Conference on Mathematical Aspects of Materials Science (MS20), Bilbao, Spain. Plenary lecture, May 2021.
  • 5th Conference on Computational Modeling of Fracture and Failure of Materials and Structures (CFRAC 2017), Nantes, France. Plenary lecture, June 2017.
  • Mathematical Aspects of Continuum Mechanics CoMFos 2011 conference, Hiroshima Kokusai Gakuin University, Japan. Two plenary lectures, Oct. 2011.


  • Fonds France-Canada de Recherche (France-Canada Research Fund), “Morphologie des fissures et formes à durabilité optimale” with E. Bonnetier at Université Grenoble Alpes.
  • Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery program, “Variational phase-field models of fracture”. Awarded April 2022.
  • U.S. Office of Naval Research, Long Range BAA for Navy and Marine Corps Science and Technology program, “Phase Field Fracture Simulation Assessment”, with P. Voorhees at Northwestern University, and K. Bhattacharya and K.T. Faber at Caltech. Awarded July 2021.
  • U.S. NSF, Applied Mathematics Program: “Collaborative Research: Optimal Design of Responsive Materials and Structures”, DMS-2009303, awarded July 2020.
  • U.S. NSF, RII program: “Track-1: Louisiana Materials Design Alliance (LAMDA)” (senior investigator), OIA-1946231, awarded May 2020.
  • Asahi Glass Company (AGC), Japan: “Laser cutting of tempered and un-tempered glass”. Awarded May 2019, extended May 2020.
  • Chevron ETC: “Modeling and simulation of natural fracture networks in sedimentary rocks”. Awarded April 2020.
  • U.S. NSF, Applied Mathematics program: “Diffusion-Driven Fracture” (PI), DMS-1716763, awarded September 2017.
  • U.S. NSF, DMREF program: “Designing Microstructures for Engineering Toughness”, DMS-1535076, (Co-PI). Awarded September 2015.
  • U.S. NSF, Applied Mathematics program: “Variational Approaches to Defect Mechanics” (PI), DMS-1312739, awarded September 2013.
  • Chevron ETC: “Investigating Non-Linear Effects Within the Realm of the Variational Approach to Fracture” (PI). Awarded September 2014.
  • Corning Inc.: “The Variational Approach to Fracture” (PI) awarded May 2014.
  • Chevron ETC: “Coupling heat and mass transfer with the variational approach to fracture” (PI). Awarded December 2012.
  • LA Board of Regents, Enhancement program: “Geothermal Resources: Cross-Disciplinary Research and Student Training” (Co-PI). Awarded April 2011.
  • Chevron ETC, Division of Special Projects and Unconventional Resources: “Variational fracture for oil shale stimulation” (PI). Awarded 10/2010.
  • U.S. NSF, Division of Mathematical Sciences, Applied Mathematics program: “Applications of Variational Fracture: Enhanced Geothermal Systems” (PI). DMS-0908267, awarded August 2009
  • U.S. NSF, Division of Mathematical Sciences, Applied Mathematics program: “A Free Discontinuity Approach to Brittle Fracture Mechanics: Analysis and Numerical Implementation” (PI). DMS-0605320, awarded May 2006.
  • LA Board of Regents Enhancement Program. “Enhancement of Material Sciences in the LSU Mathematics Department” (Co-PI). Awarded May 2005.
  • U.S. NSF, Integrated Graduate Education, Research and Training. “IGERT on Multi-Scale Computational Fluid Dynamics” (Co-PI). DGE-0504507, awarded July 2005.
  • LSU Council on Research, Faculty Research Grant. “Numerical Simulation and Visualization of Three-dimensional Free-discontinuity Problems” (PI). Awarded August 2004.
  • LA Board of Regents, Research and Competitiveness Program. “Phase-Field Method in Optimal Design” (PI). Awarded May 2003.
  • LSU Council on Research, Summer Stipend Program (PI). Awarded July 2003.

  • Computing allocations on U.S and Canadian national supercomputing facilities since 2005.