Resources
Documentation
This verification and validation manual presents a compilation of benchmark tests simulated using the Hybrid Optimization Software Suite.
Download PDFBooks & Book Chapters

Rougier, E., Knight, E.E. & Munjiza, A. Special issue titled “combined finite discrete element method and virtual experimentation”. Comp. Part. Mech. 7, 763 (2020). https://doi.org/10.1007/s40571-020-00364-z

A. Munjiza, E. Rougier, E. E. Knight, Z. Lei. Discrete Element and Particle Methods. Encyclopedia of Continuum Mechanics, 2018. https://doi.org/10.1007/978-3-662-53605-6_16-1

Chen, L., Hyman, J.D., Lei, Z., Min, T., Kang, Q., Rougier, E. and Viswanathan, H. (2018). Effect of Fracture Density on Effective Permeability of Matrix‐Fracture System in Shale Formations. In Geological Carbon Storage (eds S. Vialle, J. Ajo‐Franklin and J.W. Carey). https://doi.org/10.1002/9781119118657.ch6
Peer Reviewed Journal Articles
2020
E. Rougier, A. Munjiza, J. Munjiza. Distributed intelligence and the equivalence of matter and information. Computational Particle Mechanics, 7(5):1073–1080, 2020. https://doi.org/10.1007/s40571-020-00340-7
E.E. Knight, E. Rougier, Z. Lei, B. Euser, V. Chau, S.H. Boyce, K. Gao, K. Okubo, M. Froment. HOSS: an implementation of the combined finite-discrete element method. Computational Particle Mechanics, 7(5):765–787, 2020. https://doi.org/10.1007/s40571-020-00349-y
Froment, M., Rougier, E., Larmat, C., Lei, Z., Euser, B., Kedar, S., et al. (2020). Lagrangian‐based simulations of hypervelocity impact experiments on Mars regolith proxy. Geophysical Research Letters, 47, e2020GL087393. https://doi.org/10.1029/2020GL087393
K. Gao, R.A. Guyer, E. Rougier, P.A. Johnson. Plate motion in sheared granular fault system. Earth and Planetary Science Letters, 548:116481, 2020. https://doi.org/10.1016/j.epsl.2020.116481
Boyce, S., Lei, Z., Euser, B. et al. Simulation of mixed-mode fracture using the combined finite–discrete element method. Comp. Part. Mech. 7, 1047–1055 (2020). https://doi.org/10.1007/s40571-020-00341-6
Okubo, K., Rougier, E., Lei, Z. et al. Modeling earthquakes with off-fault damage using the combined finite-discrete element method. Comp. Part. Mech. 7, 1057–1072 (2020). https://doi.org/10.1007/s40571-020-00335-4
Lei, Z., Rougier, E., Euser, B. et al. A smooth contact algorithm for the combined finite discrete element method. Comp. Part. Mech. 7, 807–821 (2020). https://doi.org/10.1007/s40571-020-00329-2
K. Larkin, E. Rougier, V. Chau, G. Srinivasan, A. Abdelkefi, A. Hunter. Scale Bridging Damage Model for Quasi-Brittle Metals Informed with Crack Evolution Statistics. Journal of the Mechanics and Physics of Solids, 103921. 2020. https://doi.org/10.1016/j.jmps.2020.103921
Munjiza, A., Rougier, E., Lei, Z. et al. FSIS: a novel fluid–solid interaction solver for fracturing and fragmenting solids. Comp. Part. Mech. 7, 789–805 (2020). https://doi.org/10.1007/s40571-020-00314-9
Chau, V., Rougier, E., Lei, Z. et al. Numerical analysis of flyer plate experiments in granite via the combined finite–discrete element method. Comp. Part. Mech. 7, 1005–1016 (2020). https://doi.org/10.1007/s40571-019-00300-w
E. Rougier, A. Munjiza, Z. Lei, V.T. Chau, E.E. Knight, A. Hunter, G. Srinivasan. 2020. The combined plastic and discrete fracture deformation framework for finite‐discrete element methods. International Journal for Numerical Methods in Engineering, 121(5), 1020-1035. https://doi.org/10.1002/nme.6255
2019
Okubo, K., Bhat, H.S., Rougier, E., Marty, S., Schubnel, A., Lei, Z., Knight, E.E., & Klinger, Y. 2019. Dynamics, Radiation, and Overall Energy Budget of Earthquake Rupture with Coseismic Off‐Fault Damage. Journal of Geophysical Research: Solid Earth, 124, 11771– 11801. https://doi.org/10.1029/2019JB017304
N. Vaughn, A. Kononov, B. Moore, E. Rougier, H. Viswanathan, A. Hunter. 2019. Statistically informed upscaling of damage evolution in brittle materials. Theoretical and Applied Fracture Mechanics. 102, 210-221. https://doi.org/10.1016/j.tafmec.2019.04.012
Lei, Z., Rougier, E., Munjiza, A., Viswanathan, H., & Knight, E.E. 2019. Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite‐discrete element method. Int J Numer Anal Methods Geomech. 43, 1724-1743. https://doi.org/10.1002/nag.2929
Euser, B., Rougier, E., Lei, Z., Knight, E.E., Frash, L., Carey, J.W., Viswanathan, H., & Munjiza, 2019. Simulation of fracture coalescence in granite via the combined finite-discrete element method. Rock Mech Rock Eng. 52(9), 3213-3227. https://doi.org/10.1007/s00603-019-01773-0
Gao, K., Guyer, R.A., Rougier, E., Ren, C.X., & Johnson, P. 2019. From Stress Chains to Acoustic Emission. Physical Review Letters. 123(4), 048003. https://doi.org/10.1103/PhysRevLett.123.048003
Gao, K., Rougier, E., Guyer, R.A., Lei, Z., Johnson, P. 2019. Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method. Ultrasonics. 98, 51-61. https://doi.org/10.1016/j.ultras.2019.06.003
Mudunuru, M.K.; Panda, N.; Karra, S.; Srinivasan, G.; Chau, V.T.; Rougier, E.; Hunter, A.; Viswanathan, H.S. Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials. Appl. Sci. 2019, 9, 2706. https://doi.org/10.3390/app9132706
S. Rahimi-Aghdam, V.-T. Chau, H. Lee, H. Nguyen, W. Li, S. Karra, E. Rougier, H. Viswanathan, G. Srinivasan, and Z.P. Bažant. Branching of Hydraulic Cracks in Gas or Oil Shale with Closed Natural Fractures: How to Master Permeability. Proceedings of the National Academy of Sciences, 116(5):1532-1537, 2019. https://doi.org/10.1073/pnas.1818529116
M. Schwarzer, B. Rogan, Y. Ruan, Z. Song, D.Y. Lee, A.G. Percus, V.T. Chau, B.A. Moore, E. Rougier, H.S. Viswanathan, G. Srinivasan. 2019. Learning to fail: Predicting fracture evolution in brittle material models using recurrent graph convolutional neural networks. Computational Materials Science. 162, 322-332. https://doi.org/10.1016/j.commatsci.2019.02.046
A. Hunter, B.A. Moore, M. Mudunuru, V. Chau, R. Tchoua, C. Nyshadham, S. Karra, D. O’Malley, E. Rougier, H. Viswanathan, G. Srinivasan. 2019. Reduced-order modeling through machine learning and graph-theoretic approaches for brittle fracture applications. Computational Materials Science. 157, 87-98 https://doi.org/10.1016/j.commatsci.2018.10.036
H.C. Godinez, E. Rougier, D. Osthus, Z. Lei, E. Knight, G. Srinivasan. 2019 Fourier amplitude sensitivity test applied to dynamic combined finite‐discrete element methods–based simulations. International Journal for Numerical and Analytical Methods in Geomechanics. 43, 30–44. https://doi.org/10.1002/nag.2852
2018
G. Srinivasan, J.D. Hyman, D.A. Osthus, B.A. Moore, D. O’Malley, S. Karra, E. Rougier, A.A. Hagberg, A. Hunter, H.S. Viswanathan. 2018. Quantifying topological uncertainty in fractured systems using graph theory and machine learning. Scientific reports. 8(1). https://doi.org/10.1038/s41598-018-30117-1
Gao, K., Euser, B., Rougier, E., Guyer, R.A., Lei, Z., Knight, E.E., Carmeliet, J., & Johnson, P. 2018. Modeling of stick‐slip behavior in sheared granular fault gouge using the combined finite‐ discrete element method. Journal of Geophysical Research: Solid Earth. 123(7), 5774-5792. https://doi.org/10.1029/2018JB015668
Klinger, Y., Okubo, K., Vallage, A., Champenois, J., Delorme, A., Rougier, E., Lei, Z., Knight, E.E., Munjiza, A., Satriano, C., Baize, S., Langridge, R., & Bhat, Harsha S. 2018. Earthquake Damage Patterns Resolve Complex Rupture Processes. Geophysical Research Letters, 45(19), 10,279-10,287. https://doi.org/10.1029/2018GL078842
B.A. Moore, E. Rougier, D. O’Malley, G. Srinivasan, A. Hunter and H. Viswanathan. 2018. Predictive modeling of dynamic fracture growth in brittle materials with machine learning. Computational Materials Science. 148, 46-53. https://doi.org/10.1016/j.commatsci.2018.01.056
J.D. Hyman, S. Karra, C.W. Gable, H. Viswanathan, J.W. Carey, E. Rougier, Z. Lei. 2018. Discontinuities in effective permeability due to fracture percolation. Mechanics of Materials. 119, 25-33. https://doi.org/10.1016/j.mechmat.2018.01.005
D. Osthus, H.C. Godinez, E. Rougier, G. Srinivasan. Calibrating the stress-time curve of a combined finite-discrete element method to a Split Hopkinson Pressure bar experiment. International Journal of Rock Mechanics and Mining Sciences, 106:278-288, 2018. https://doi.org/10.1016/j.ijrmms.2018.03.016
2017 & Older
Lei, Z., Rougier, E., Knight, E.E., Frash, L., Carey, J.W., & Viswanathan, H. 2016. A non- locking composite tetrahedron element for the combined finite discrete element method. Engineering Computations. 33(7), 1929-1956. https://doi.org/10.1108/EC-09-2015-0268
Lei, Z., Rougier, E., Knight, E.E., Munjiza, A., & Viswanathan, H. 2016. A generalized anisotropic deformation formulation for geomaterials. Comp. Part. Mech 3, 215-228. https://doi.org/10.1007/s40571-015-0079-y
Carey, J.W., Lei, Z., Rougier, E., Mori, H. & Viswanathan, H.S. 2015. Fracture-permeability behavior of shale. J. Unconventional Oil and Gas Resources, 11, 27-43. https://doi.org/10.1016/j.juogr.2015.04.003
Jordan, A., Stauffer, P., Knight, E. et al. Radionuclide Gas Transport through Nuclear Explosion-Generated Fracture Networks. Sci Rep 5, 18383 (2015). https://doi.org/10.1038/srep18383
A. Zubelewicz, E. Rougier, M. Ostoja-Starzewski, E.E. Knight, C. Bradley, H.S. Viswanathan. A mechanisms-based model for dynamic behavior and fracture of geomaterials. Intl. J. Rock Mech. & Min. Sci. 72, 277-282 (2014). https://doi.org/10.1016/j.ijrmms.2014.09.015
Lei, Z., Rougier, E., Knight, E.E., & Munjiza, A. 2014. A Framework for Grand Scale Parallelization of the Combined Finite Discrete Element Method in 2D. Comp. Part. Mech. 1, 307-319. https://doi.org/10.1007/s40571-014-0026-3
Rougier, E., Knight, E.E., Broome, S.T., Sussman, A.J. & Munjiza, A. 2014. Validation of a three-dimensional Finite-Discrete Element Method using experimental results of the Split Hopkinson Pressure Bar test. Intl. J. of Rock Mechanics and Mining Sciences, 70, 101-108. https://doi.org/10.1016/j.ijrmms.2014.03.011
Munjiza, A., Lei, Z., Divic, V. & Peros, B. 2013. Fracture and fragmentation of thin shells using the combined finite–discrete element method. Int. J. Numer. Meth. Eng. 95(6), 478–498. https://doi.org/10.1002/nme.4511
Ning, Y.J., Yang, J., Ma, G.W. & Chen, P.W. 2011. Modeling Rock Blasting Considering Explosion Gas Penetration using Discontinuous Deformation analysis. Rock Mech. Rock Eng., 44, 483-490. https://doi.org/10.1007/s00603-010-0132-3
Rougier, E., Patton, H. J., Knight, E. E., and Bradley, C. R. (2011), Constraints on burial depth and yield of the 25 May 2009 North Korean test from hydrodynamic simulations in a granite medium, Geophys. Res. Lett., 38, L16316. https://doi.org/10.1029/2011GL048269
Rougier, E., Munjiza, A. and Latham, J.P. (2004), "Shape selection menu for grand scale discontinua systems", Engineering Computations, Vol. 21 No. 2/3/4, pp. 343-359. https://doi.org/10.1108/02644400410519820
Munjiza, A. & Andrews, K.R.F. 2000. Penalty function method for in combined finite-discrete element systems comprising large number of separate. Int. J. Num. Meth. Eng., 49, 1377-96. https://doi.org/10.1002/1097-0207(20001220)49:11<1377::AID-NME6>3.0.CO;2-B
Munjiza, A., Owen, D.R.J. & Bicanic, N. 1995. A combined finite-discrete element method in transient dynamics of fracturing solids. Int. J. of Engineering Computation, 12, 145-174. https://doi.org/10.1108/02644409510799532