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


  • 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.