Crack pattern in ceramics subject to thermal shock

Short Biography

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


Over 4,000 citations on google scholar, 2,000 on Publons/Web of Science . ESI highly cited articles in mathematics and in Engineering.


  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. 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
  2. Bourdin, B., & Francfort, G. A. (2019). Past and present of variational fracture. SIAM News, 52(9). Download
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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. Download
  22. 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
  23. 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
  24. 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
  25. Bourdin, B., Bucur, D., & Oudet, É. (2009). Optimal Partitions for Eigenvalues. SIAM J. Sci. Comput., 31(6), 4100–4114. DOI:10.1137/090747087 Download
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. Bourdin, B., & Chambolle, A. (2003). Design-dependent loads in topology optimization. ESAIM Contr. Optim. Ca., 9, 19–48. DOI:10.1051/cocv:2002070 Download
  33. 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
  34. Bourdin, B. (2001). Filters in topology optimization. Int. J. Num. Meth. Engng., 50, 2143–2158. DOI:10.1002/nme.116 Download
  35. 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/s002110000099 Download
  36. 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
  37. Bourdin, B. (1999). Image segmentation with a finite element method. M2AN Math. Model. Numer. Anal., 33(2), 229–244. Download
  38. Bourdin, B. (1998). Une méthode variationnelle en mécanique de la rupture, théorie et applications numériques (PhD thesis). Université Paris Nord, Institut Galilée, France. Download

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 2020.
  • 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.


Over $6M in research grants, including $1.5M as sole PI

  • Asahi Glass Company (AGC), Japan: “Laser cutting of tempered and un-tempered glass”. Awarded May 2019.
  • Chevron ETC: “Modeling and simulation of natural fracture networks in sedimentary rocks”. Awards pending (Apr. 2019).
  • NSF, Applied Mathematics program: “Diffusion-Driven Fracture” (PI), DMS-1716763, awarded 9/2017.
  • NSF, DMREF program: “Designing Microstructures for Engineering Toughness”, DMS-1535076, (Co-PI). Awarded 9/2015.
  • NSF, Applied Mathematics program: “Variational Approaches to Defect Mechanics” (PI), DMS-1312739, awarded 9/2013.
  • Chevron ETC: “Investigating Non-Linear Effects Within the Realm of the Variational Approach to Fracture” (PI). Awarded 9/2014.
  • Corning Inc.: “The Variational Approach to Fracture” (PI) awarded 05/2014.
  • NSF XSEDE: “Variational Approaches to Defect Mechanics” (PI), Awarded 2013.
  • LA Board of Regents, Enhancement program: “Geothermal Resources: Cross-Disciplinary Research and Student Training” (Co-PI). Awarded 04-2011.
  • Chevron ETC: “Coupling heat and mass transfer with the variational approach to fracture” (PI). Awarded 12/2012.
  • NSF-XSEDE: “Applications of variational fracture: thermal cracks, hydraulic stimulation and fracture in thin films” (PI). Awarded 2011.
  • Chevron ETC, Division of Special Projects and Unconventional Resources: “Variational fracture for oil shale stimulation” (PI). Awarded 10/2010.
  • NSF, Office of Cyberinitiative: Resource Allocation: “Variational approach to reservoir stimulation for Enhanced Geothermal Systems” (PI). TG-DMS060014, awarded 2010.
  • NSF, Division of Mathematical Sciences, Applied Mathematics program: “Applications of Variational Fracture: Enhanced Geothermal Systems” (PI). DMS-0908267, awarded 08/2009
  • NSF, Office of Cyberinitiative: Resource Allocation: “Multi-Scale Fracture Mechanics” (PI). TG-DMS060014, awarded 2008.
  • NSF, Office of Cyberinitiative: Medium Resource Allocation: “Numerical simulation of brittle fracture with the variational approach” (PI). TG-DMS060010N, renewed 12-2007.
  • NSF, Division of Mathematical Sciences, Applied Mathematics program: “A Free Discontinuity Approach to Brittle Fracture Mechanics: Analysis and Numerical Implementation” (PI). DMS-0605320, awarded 05-2006.
  • NSF, Office of Cyberinitiative: Medium Resource Allocation: “Crack Propagation in Brittle Media under Thermal Stresses” (PI). TG-DMS060010N, awarded 03-2006.
  • NSF, Office of Cyberinitiative: Development Allocation: “Crack Propagation in Brittle Media under Thermal Stresses: Scalability study” (PI). TG-DMS-060007T, awarded 12-2005.
  • LA Board of Regents Enhancement Program. “Enhancement of Material Sciences in the LSU Mathematics Department” (Co-PI). Awarded 05-2005.
  • NSF, Integrated Graduate Education, Research and Training. “IGERT on Multi-Scale Computational Fluid Dynamics” (Co-PI). DGE-0504507, awarded 07-2005.
  • LSU Council on Research, Faculty Research Grant. “Numerical Simulation and Visualization of Three-dimensional Free-discontinuity Problems” (PI). Awarded 08-2004.
  • LA Board of Regents, Research and Competitiveness Program. “Phase-Field Method in Optimal Design” (PI). Awarded 05-2003.
  • LSU Council on Research, Summer Stipend Program (PI). Awarded 07-2003.