Articles | Volume 18, issue 22
https://doi.org/10.5194/gmd-18-9149-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-18-9149-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Model description paper
| 
27 Nov 2025
Model description paper |
| 27 Nov 2025
| 27 Nov 2025
Matter (v1): an open-source MPM solver for granular matter
Institute for Geotechnical Engineering, ETH Zürich, 8093 Zurich, Switzerland
WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, Switzerland
Climate Change, Extremes, and Natural Hazards in Alpine Regions Research Center CERC, 7260 Davos Dorf, Switzerland
Johan Gaume
Institute for Geotechnical Engineering, ETH Zürich, 8093 Zurich, Switzerland
WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, Switzerland
Climate Change, Extremes, and Natural Hazards in Alpine Regions Research Center CERC, 7260 Davos Dorf, Switzerland
Related authors
Alessandro Cicoira, Daniel Tobler, Rachel Riner, Lars Blatny, Michael Lukas Kyburz, and Johan Gaume
Abstr. Int. Cartogr. Assoc., 9, 4, https://doi.org/10.5194/ica-abs-9-4-2025, https://doi.org/10.5194/ica-abs-9-4-2025, 2025
Alessandro Cicoira, Daniel Tobler, Rachel Riner, Lars Blatny, Michael Lukas Kyburz, and Johan Gaume
Abstr. Int. Cartogr. Assoc., 9, 4, https://doi.org/10.5194/ica-abs-9-4-2025, https://doi.org/10.5194/ica-abs-9-4-2025, 2025
Cited articles
Abramian, A., Staron, L., and Lagrée, P.-Y.: The Slumping of a Cohesive Granular Column: Continuum and Discrete Modeling, J. Rheol., 64, 1227–1235, https://doi.org/10.1122/8.0000049, 2020. a
Anura3D: Anura3D, GibHub [code], https://github.com/Anura3D (last access: 26 September 2025), 2017. a
Badetti, M., Fall, A., Hautemayou, D., Chevoir, F., Aimedieu, P., Rodts, S., and Roux, J.-N.: Rheology and Microstructure of Unsaturated Wet Granular Materials: Experiments and Simulations, J. Rheol., 62, 1175–1186, https://doi.org/10.1122/1.5026979, 2018. a
Bardenhagen, S. G. and Kober, E. M.: The Generalized Interpolation Material Point Method, Comput. Model. Eng. Sci., 5, 477–496, https://doi.org/10.3970/cmes.2004.005.477, 2004. a, b
Barker, T. and Gray, J. M. N. T.: Partial Regularisation of the Incompressible μ(I)-Rheology for Granular Flow, J. Fluid Mech., 828, 5–32, https://doi.org/10.1017/jfm.2017.428, 2017. a
Berger, N., Azéma, E., Douce, J.-F., and Radjai, F.: Scaling Behaviour of Cohesive Granular Flows, Europhys. Lett., 112, 64004, https://doi.org/10.1209/0295-5075/112/64004, 2015. a, b
Bingham, E.: Fluidity and Plasticity, McGraw-Hill, 1922. a
Blatny, L. and Gaume, J.: Matter, Zenodo [code], https://doi.org/10.5281/zenodo.15052337, 2025 (code also available at: https://github.com/larsblatny/matter/, last access: 26 September 2025). a, b
Blatny, L., Löwe, H., Wang, S., and Gaume, J.: Computational Micromechanics of Porous Brittle Solids, Comput. Geotech., 140, 104284, https://doi.org/10.1016/j.compgeo.2021.104284, 2021. a
Blatny, L., Löwe, H., and Gaume, J.: Microstructural Controls on the Plastic Consolidation of Porous Brittle Solids, Acta Materialia, 250, 118861, https://doi.org/10.1016/j.actamat.2023.118861, 2023. a, b
Blatny, L., Gray, J., and Gaume, J.: A Critical State μ(I)-Rheology Model for Cohesive Granular Flows, J. Fluid Mech., 997, A67, https://doi.org/10.1017/jfm.2024.643, 2024. a, b, c
Blatny, L. K. U.: Modeling the Mechanics and Rheology of Porous and Granular Media: An Elastoplastic Continuum Approach, PhD thesis, EPFL, Lausanne, https://doi.org/10.5075/EPFL-THESIS-10267, 2023. a, b, c
Brackbill, J., Kothe, D., and Ruppel, H.: Flip: A Low-Dissipation, Particle-in-Cell Method for Fluid Flow, Comput. Phys. Commun., 48, 25–38, https://doi.org/10.1016/0010-4655(88)90020-3, 1988. a
Bridson, R.: Fast Poisson Disk Sampling in Arbitrary Dimensions, ACM SIGGRAPH 2007 Sketches Program, https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-poissondisk.pdf (last access: 26 September 2025), 2007. a
Bruhns, O., Xiao, H., and Meyers, A.: Self-Consistent Eulerian Rate Type Elasto-Plasticity Models Based upon the Logarithmic Stress Rate, Int. J. Plastic., 15, 479–520, https://doi.org/10.1016/S0749-6419(99)00003-0, 1999. a
Chen, H., Zhao, S., and Zhao, J.: A Sparse-Memory-Encoding GPU-MPM Framework for Large-Scale Simulations of Granular Flows, Comput. Geotech., 180, 107113, https://doi.org/10.1016/j.compgeo.2025.107113, 2025. a
Christen, M., Kowalski, J., and Bartelt, P.: RAMMS: Numerical Simulation of Dense Snow Avalanches in Three-Dimensional Terrain, Cold Reg. Sci. Technol., 63, 1–14, https://doi.org/10.1016/j.coldregions.2010.04.005, 2010. a
Coombs, W. M. and Augarde, C. E.: AMPLE: A Material Point Learning Environment, Adv. Eng. Softw., 139, 102748, https://doi.org/10.1016/j.advengsoft.2019.102748, 2020. a
Cremonesi, M., Franci, A., Idelsohn, S., and Oñate, E.: A State of the Art Review of the Particle Finite Element Method (PFEM), Arch. Comput. Meth. Eng., 27, 1709–1735, https://doi.org/10.1007/s11831-020-09468-4, 2020. a
Dadvand, P., Rossi, R., and Oñate, E.: An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications, Arch. Comput. Meth. Eng., 17, 253–297, https://doi.org/10.1007/s11831-010-9045-2, 2010. a
Dagum, L. and Menon, R.: OpenMP: an industry standard API for shared-memory programming, IEEE Comput. Sci. Eng., 5, 46–55, 1998. a
Davison De St. Germain, J., McCorquodale, J., Parker, S., and Johnson, C.: Uintah: A Massively Parallel Problem Solving Environment, in: Proceedings the Ninth International Symposium on High-Performance Distributed Computing, IEEE Comput. Soc., Pittsburgh, PA, USA, 33–41, ISBN 978-0-7695-0783-5, https://doi.org/10.1109/HPDC.2000.868632, 2000. a
de Goes, F., Wallez, C., Huang, J., Pavlov, D., and Desbrun, M.: Power Particles: An Incompressible Fluid Solver Based on Power Diagrams, ACM T. Graph., 34, 1–11, https://doi.org/10.1145/2766901, 2015. a
de Vaucorbeil, A., Nguyen, V. P., and Hutchinson, C. R.: A Total-Lagrangian Material Point Method for Solid Mechanics Problems Involving Large Deformations, Comput. Meth. Appl. Mech. Eng., 360, 112783, https://doi.org/10.1016/j.cma.2019.112783, 2020a. a
de Vaucorbeil, A., Nguyen, V. P., Sinaie, S., and Wu, J. Y.: Material Point Method after 25 Years: Theory, Implementation, and Applications, in: Advances in Applied Mechanics, vol. 53, Elsevier, 185–398, ISBN 978-0-12-820989-9, https://doi.org/10.1016/bs.aams.2019.11.001, 2020b. a, b, c, d
de Vaucorbeil, A., Nguyen, V. P., and Nguyen-Thanh, C.: Karamelo: An Open Source Parallel C
Diakopoulos, D.: Tinyply, GitHub [code], https://github.com/ddiakopoulos/tinyply (last access: 26 September 2025), 2018. a
Drucker, D. and Prager, W.: Soil Mechanics and Plastic Analysis or Limit Design, Quart. Appl. Math., 10, 157–165, 1952. a
Dunatunga, S. and Kamrin, K.: Continuum Modelling and Simulation of Granular Flows through Their Many Phases, Journal of Fluid Mechanics, 779, 483–513, https://doi.org/10.1017/jfm.2015.383, 2015. a
Duverger, S., Duriez, J., Philippe, P., and Bonelli, S.: Critical Comparison of Motion Integration Strategies and Discretization Choices in the Material Point Method, Arch. Comput. Meth. Eng., https://doi.org/10.1007/s11831-024-10170-y, 2024. a
Fei, Y., Guo, Q., Wu, R., Huang, L., and Gao, M.: Revisiting Integration in the Material Point Method: A Scheme for Easier Separation and Less Dissipation, ACM T. Graph., 40, 1–16, https://doi.org/10.1145/3450626.3459678, 2021. a, b, c
Fu, C., Guo, Q., Gast, T., Jiang, C., and Teran, J.: A Polynomial Particle-in-Cell Method, ACM T. Graph., 36, 1–12, https://doi.org/10.1145/3130800.3130878, 2017. a
Gael, G. and Benoit, J.: Eigen, http://eigen.tuxfamily.org (last access: 26 September 2025), 2010. a
Gao, M., Wang, X., Wu, K., Pradhana, A., Sifakis, E., Yuksel, C., and Jiang, C.: GPU Optimization of Material Point Methods, ACM T. Graph., 37, 1–12, https://doi.org/10.1145/3272127.3275044, 2018. a
Gaume, J., Gast, T., Teran, J., van Herwijnen, A., and Jiang, C.: Dynamic Anticrack Propagation in Snow, Nat. Commun., 9, 3047, https://doi.org/10.1038/s41467-018-05181-w, 2018. a
GDR MiDi: On Dense Granular Flows, Eur. Phys. J. E, 14, 341–365, https://doi.org/10.1140/epje/i2003-10153-0, 2004. a, b
Harlow, F. H.: The Particle-in-Cell Computing Method for Fluid Dynamics, Meth. Comput. Phys., 3, 319–343, 1964. a
Heeres, O. M., Suiker, A. S. J., and De Borst, R.: A Comparison between the Perzyna Viscoplastic Model and the Consistency Viscoplastic Model, Eur. J. Mech. A, 21, 1–12, https://doi.org/10.1016/S0997-7538(01)01188-3, 2002. a
Herschel, W. H. and Bulkley, R.: Konsistenzmessungen von Gummi-Benzollösungen, Kolloid-Zeitschrift, 39, 291–300, https://doi.org/10.1007/BF01432034, 1926. a
Higo, Y., Oka, F., Kimoto, S., Morinaka, Y., Goto, Y., and Chen, Z.: A Coupled MPM-FDM Analysis Method for Multi-Phase Elasto-Plastic Soils, Soils Foundat., 50, 515–532, https://doi.org/10.3208/sandf.50.515, 2010. a
Higo, Y., Takegawa, Y., Zhu, F., and Uchiyama, D.: A Three-Phase Two-Point MPM for Large Deformation Analysis of Unsaturated Soils, Comput. Geotech., 177, 106860, https://doi.org/10.1016/j.compgeo.2024.106860, 2025. a
Hinks, T.: Tph_poisson, GitHub [code], https://github.com/thinks/poisson-disk-sampling (last access: 26 September 2025), 2018. a
Hoffman, W.: CMake, https://cmake.org/ (last access: 26 September 2025), 2000. a
Hu, Y., Fang, Y., Ge, Z., Qu, Z., Zhu, Y., Pradhana, A., and Jiang, C.: A Moving Least Squares Material Point Method with Displacement Discontinuity and Two-Way Rigid Body Coupling, ACM T. Graph., 37, 1–14, https://doi.org/10.1145/3197517.3201293, 2018a. a
Hu, Y., Fang, Y., Ge, Z., Qu, Z., Zhu, Y., Pradhana, A., and Jiang, C.: A Moving Least Squares Material Point Method with Displacement Discontinuity and Two-Way Rigid Body Coupling, ACM T. Graph., 37, 1–14, https://doi.org/10.1145/3197517.3201293, 2018b. a
Hu, Y., Li, T.-M., Anderson, L., Ragan-Kelley, J., and Durand, F.: Taichi: A Language for High-Performance Computation on Spatially Sparse Data Structures, ACM T. Graph., 38, 1–16, https://doi.org/10.1145/3355089.3356506, 2019. a
Iaconeta, I., Larese, A., Rossi, R., and Oñate, E.: A Stabilized Mixed Implicit Material Point Method for Non-Linear Incompressible Solid Mechanics, Computat. Mech., 63, 1243–1260, https://doi.org/10.1007/s00466-018-1647-9, 2019. a
Idelsohn, S., Oñate, E., and Pin, F. D.: The Particle Finite Element Method: A Powerful Tool to Solve Incompressible Flows with Free-Surfaces and Breaking Waves, Int. J. Numer. Meth. Eng., 61, 964–989, https://doi.org/10.1002/nme.1096, 2004. a
Jiang, C., Schroeder, C., Selle, A., Teran, J., and Stomakhin, A.: The Affine Particle-in-Cell Method, ACM T. Graph., 34, 1–10, https://doi.org/10.1145/2766996, 2015. a, b
Jiang, C., Schroeder, C., Teran, J., Stomakhin, A., and Selle, A.: The Material Point Method for Simulating Continuum Materials, in: ACM SIGGRAPH 2016 Courses, SIGGRAPH '16, Association for Computing Machinery, New York, NY, USA, ISBN 978-1-4503-4289-6, https://doi.org/10.1145/2897826.2927348, 2016. a
Jiang, C., Schroeder, C., and Teran, J.: An Angular Momentum Conserving Affine-Particle-in-Cell Method, J. Comput. Phys., 338, 137–164, https://doi.org/10.1016/j.jcp.2017.02.050, 2017. a
Jop, P., Forterre, Y., and Pouliquen, O.: Crucial Role of Sidewalls in Granular Surface Flows: Consequences for the Rheology, J. Fluid Mech., 541, 167, https://doi.org/10.1017/S0022112005005987, 2005. a
Jop, P., Forterre, Y., and Pouliquen, O.: A Constitutive Law for Dense Granular Flows, Nature, 441, 727–730, https://doi.org/10.1038/nature04801, 2006. a, b
Khamseh, S., Roux, J.-N., and Chevoir, F.: Flow of Wet Granular Materials: A Numerical Study, Phys. Rev. E, 92, 022201, https://doi.org/10.1103/PhysRevE.92.022201, 2015. a
Klár, G.: Simulation of Granular Media with the Material Point Method, PhD thesis, UCLA, 2016. a
Ku, Q., Zhao, J., Mollon, G., and Zhao, S.: Compaction of Highly Deformable Cohesive Granular Powders, Powder Technol., 421, 118455, https://doi.org/10.1016/j.powtec.2023.118455, 2023. a
Kumar, K., Salmond, J., Kularathna, S., Wilkes, C., Tjung, E., Biscontin, G., and Soga, K.: Scalable and Modular Material Point Method for Large-Scale Simulations, in: 2nd International Conference on the Material Point Method for Modeling Soil-Water-Structure Interaction, arXiv [preprint], https://doi.org/10.48550/ARXIV.1909.13380, 2019. a
Lee, E. H.: Elastic-Plastic Deformation at Finite Strains, J. Appl. Mech., 36, 1–6, https://doi.org/10.1115/1.3564580, 1969. a
Love, E. and Sulsky, D.: An Unconditionally Stable, Energy–Momentum Consistent Implementation of the Material-Point Method, Comput. Meth. Appl. Mech. Eng., 195, 3903–3925, https://doi.org/10.1016/j.cma.2005.06.027, 2006. a, b
Macaulay, M. and Rognon, P.: Viscosity of Cohesive Granular Flows, Soft Matter, 17, 165–173, https://doi.org/10.1039/D0SM01456G, 2021. a
Mandal, S., Nicolas, M., and Pouliquen, O.: Insights into the Rheology of Cohesive Granular Media, P. Natl. Acad. Sci. USA, 117, 8366–8373, https://doi.org/10.1073/pnas.1921778117, 2020. a
Mandal, S., Nicolas, M., and Pouliquen, O.: Rheology of Cohesive Granular Media: Shear Banding, Hysteresis, and Nonlocal Effects, Phys. Rev. X, 11, 021017, https://doi.org/10.1103/PhysRevX.11.021017, 2021. a
Moresi, L., Dufour, F., and Mühlhaus, H.-B.: A Lagrangian Integration Point Finite Element Method for Large Deformation Modeling of Viscoelastic Geomaterials, J. Comput. Phys., 184, 476–497, https://doi.org/10.1016/S0021-9991(02)00031-1, 2003. a
Nairn, J. A.: NairnMPM, GitHub [code], https://github.com/nairnj/nairn-mpm-fea (last access: 26 September 2025), 2015. a
Neto, E. A. d. S., Perić, D., and Owen, D. R. J.: Computational Methods for Plasticity: Theory and Applications, Wiley, Chichester, West Sussex, UK, ISBN 978-0-470-69452-7, 2008. a
Nguyen, V. P., de Vaucorbeil, A., and Bordas, S.: The Material Point Method: Theory, Implementations and Applications, Scientific Computation, Springer International Publishing, Cham, ISBN 978-3-031-24069-0, https://doi.org/10.1007/978-3-031-24070-6, 2023. a, b, c
Oliver, J., Cante, J. C., Weyler, R., González, C., and Hernandez, J.: Particle Finite Element Methods in Solid Mechanics Problems, in: Computational Plasticity, vol. 7, edited by: Oñate, E. and Owen, R., Springer Netherlands, Dordrecht, 87–103, ISBN 978-1-4020-6576-7, https://doi.org/10.1007/978-1-4020-6577-4_6, 2007. a
Ortiz, M. and Pandolfi, A.: A Variational Cam-clay Theory of Plasticity, Comput. Meth. Appl. Mech. Eng., 193, 2645–2666, https://doi.org/10.1016/j.cma.2003.08.008, 2004. a
Perić, D.: On a Class of Constitutive Equations in Viscoplasticity: Formulation and Computational Issues, Int. J. Numer. Meth. Eng., 36, 1365–1393, https://doi.org/10.1002/nme.1620360807, 1993. a, b
Perzyna, P.: The Constitutive Equations for Rate Sensitive Plastic Materials, Quart. Appl. Math., 20, 321–332, https://doi.org/10.1090/qam/144536, 1963. a
Perzyna, P.: Fundamental Problems in Viscoplasticity, in: Advances in Applied Mechanics, vol. 9, Elsevier, 243–377, ISBN 978-0-12-002009-6, https://doi.org/10.1016/S0065-2156(08)70009-7, 1966. a
Qu, Z., Li, M., De Goes, F., and Jiang, C.: The Power Particle-in-Cell Method, ACM Transactions on Graphics, 41, 1–13, https://doi.org/10.1145/3528223.3530066, 2022. a
Radjai, F. and Richefeu, V.: Bond Anisotropy and Cohesion of Wet Granular Materials, Philos. T. Roy. Soc. A, 367, 5123–5138, https://doi.org/10.1098/rsta.2009.0185, 2009. a
Radjai, F., Roux, J.-N., and Daouadji, A.: Modeling Granular Materials: Century-Long Research across Scales, J. Eng. Mech., 143, 04017002, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001196, 2017. a
Raymond, S. J., Jones, B., and Williams, J. R.: A Strategy to Couple the Material Point Method (MPM) and Smoothed Particle Hydrodynamics (SPH) Computational Techniques, Comput. Part. Mech., 5, 49–58, https://doi.org/10.1007/s40571-016-0149-9, 2018. a
Rognon, P. G., Roux, J.-N., Wolf, D., Naaïm, M., and Chevoir, F.: Rheophysics of Cohesive Granular Materials, Europhys. Lett., 74, 644–650, https://doi.org/10.1209/epl/i2005-10578-y, 2006. a
Rognon, P. G., Roux, J.-N., Naaïm, M., and Chevoir, F.: Dense Flows of Cohesive Granular Materials, J. Fluid Mech., 596, 21–47, https://doi.org/10.1017/S0022112007009329, 2008. a
Roscoe, K. H. and Burland, J. B.: On the Generalized Stress-Strain Behaviour of Wet Clay, in: Engineering Plasticity, Cambridge University Press, Cambridge, UK, 535–609, 1968. a
Sampl, P. and Zwinger, T.: Avalanche Simulation with SAMOS, Ann. Glaciol., 38, 393–398, https://doi.org/10.3189/172756404781814780, 2004. a
Schofield, A. N. and Wroth, P.: Critical State Soil Mechanics, McGraw-Hill, London, 1968. a
Simo, J. C.: Algorithms for Static and Dynamic Multiplicative Plasticity That Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory, Comput. Meth. Appl. Mech. Eng., 99, 61–112, https://doi.org/10.1016/0045-7825(92)90123-2, 1992. a
Sołowski, W. T., Berzins, M., Coombs, W. M., Guilkey, J. E., Möller, M., Tran, Q. A., Adibaskoro, T., Seyedan, S., Tielen, R., and Soga, K.: Material Point Method: Overview and Challenges Ahead, in: Advances in Applied Mechanics, vol. 54, Elsevier, 113–204, ISBN 978-0-323-88519-5, https://doi.org/10.1016/bs.aams.2020.12.002, 2021. a, b
Steffen, M., Kirby, R. M., and Berzins, M.: Analysis and Reduction of Quadrature Errors in the Material Point Method (MPM), Int. J. Numer. Meth. Eng., 76, 922–948, https://doi.org/10.1002/nme.2360, 2008a. a, b, c
Steffen, M., Wallstedt, P. C., Guilkey, J. E., Kirby, R. M., and Berzins, M.: Examination and Analysis of Implementation Choices within the Material Point Method (MPM), Comput. Model. Eng. Sci., 31, 107–128, https://doi.org/10.3970/cmes.2008.031.107, 2008b. a
Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A.: A Material Point Method for Snow Simulation, ACM T. Graph., 32, 1–10, https://doi.org/10.1145/2461912.2461948, 2013. a
Sulsky, D., Chen, Z., and Schreyer, H. L.: A Particle Method for History-Dependent Materials, Comput. Meth. Appl. Mech. Eng., 118, 179–196, https://doi.org/10.1016/0045-7825(94)90112-0, 1994. a
Sulsky, D., Zhou, S.-J., and Schreyer, H. L.: Application of a Particle-in-Cell Method to Solid Mechanics, Comput. Phys. Commun., 87, 236–252, https://doi.org/10.1016/0010-4655(94)00170-7, 1995. a, b
Tian, C.: The Ratio of Out-of-Plane to in-Plane Stresses for Plane Strain Problems, Meccanica, 44, 105–107, https://doi.org/10.1007/s11012-008-9168-9, 2009. a
Tonnel, M., Wirbel, A., Oesterle, F., and Fischer, J.-T.: AvaFrame com1DFA (v1.3): A Thickness-Integrated Computational Avalanche Module – Theory, Numerics, and Testing, Geosci. Model Dev., 16, 7013–7035, https://doi.org/10.5194/gmd-16-7013-2023, 2023. a
Tran, Q. A., Grimstad, G., and Ghoreishian Amiri, S. A.: MPMICE: A Hybrid MPM-CFD Model for Simulating Coupled Problems in Porous Media. Application to Earthquake-induced Submarine Landslides, Int. J. Numer. Meth. Eng., 125, e7383, https://doi.org/10.1002/nme.7383, 2024. a
Vacondio, R., Altomare, C., De Leffe, M., Hu, X., Le Touzé, D., Lind, S., Marongiu, J.-C., Marrone, S., Rogers, B. D., and Souto-Iglesias, A.: Grand Challenges for Smoothed Particle Hydrodynamics Numerical Schemes, Comput. Part. Mech., 8, 575–588, https://doi.org/10.1007/s40571-020-00354-1, 2021. a
Vo, T. T., Nezamabadi, S., Mutabaruka, P., Delenne, J.-Y., and Radjai, F.: Additive Rheology of Complex Granular Flows, Nat. Commun., 11, 1476, https://doi.org/10.1038/s41467-020-15263-3, 2020. a, b
von Mises, R.: Mechanik der festen Körper im plastisch- deformablen Zustand, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 582–592, 1913. a
Wallstedt, P. C.: MPM-GIMP, https://sourceforge.net/projects/mpmgimp/ (last access: 26 September 2025), 2011. a
Wallstedt, P. C. and Guilkey, J. E.: An Evaluation of Explicit Time Integration Schemes for Use with the Generalized Interpolation Material Point Method, J. Comput. Phys., 227, 9628–9642, https://doi.org/10.1016/j.jcp.2008.07.019, 2008. a
Wang, W. M., Sluys, L. J., and De Borst, R.: Viscoplasticity for Instabilities Due to Strain Softening and Strain-Rate Softening, Int. J. Numer. Meth. Eng., 40, 3839–3864, https://doi.org/10.1002/(SICI)1097-0207(19971030)40:20<3839::AID-NME245>3.0.CO;2-6, 1997. a
Wang, X., Qiu, Y., Slattery, S. R., Fang, Y., Li, M., Zhu, S.-C., Zhu, Y., Tang, M., Manocha, D., and Jiang, C.: A Massively Parallel and Scalable Multi-GPU Material Point Method, ACM T. Graph., 39, https://doi.org/10.1145/3386569.3392442, 2020. a
Wojciechowski, M.: A Note on the Differences between Drucker-Prager and Mohr-Coulomb Shear Strength Criteria, Studia Geotechnica et Mechanica, 40, 163–169, https://doi.org/10.2478/sgem-2018-0016, 2018. a
Wyser, E., Alkhimenkov, Y., Jaboyedoff, M., and Podladchikov, Y. Y.: A Fast and Efficient MATLAB-based MPM Solver: fMPMM-solver v1.1, Geosci. Model Dev., 13, 6265–6284, https://doi.org/10.5194/gmd-13-6265-2020, 2020. a
Xiao, H. and Chen, L. S.: Hencky's Elasticity Model and Linear Stress-Strain Relations in Isotropic Finite Hyperelasticity, Acta Mechanica, 157, 51–60, https://doi.org/10.1007/BF01182154, 2002. a
Yerro, A., Alonso, E., and Pinyol, N.: The Material Point Method for Unsaturated Soils, Géotechnique, 65, 201–217, https://doi.org/10.1680/geot.14.P.163, 2015. a
Yu, H.-S. (Ed.): Plasticity and Geotechnics, no. 13 in Advances in Mechanics and Mathematics, Springer, Boston, MA, ISBN 978-0-387-33597-1, https://doi.org/10.1007/978-0-387-33599-5, 2006. a
Zhang, X., Chen, Z., and Liu, Y.: The Material Point Method: A Continuum-Based Particle Method for Extreme Loading Cases, Elsevier and Tsinghua University Press Computational Mechanics Series, Academic Press, Amsterdam, the Netherlands, ISBN 978-0-12-407855-0, 2017. a
Zhao, Y., Choo, J., Jiang, Y., and Li, L.: Coupled Material Point and Level Set Methods for Simulating Soils Interacting with Rigid Objects with Complex Geometry, Comput. Geotech., 163, 105708, https://doi.org/10.1016/j.compgeo.2023.105708, 2023a. a
Zhao, Y., Jiang, C., and Choo, J.: Circumventing Volumetric Locking in Explicit Material Point Methods: A Simple, Efficient, and General Approach, Int. J. Numer. Meth. Eng., 124, 5334–5355, https://doi.org/10.1002/nme.7347, 2023b. a
Short summary
Matter is a new computer model that simulates granular media like sand, snow, and soil. These materials can behave like both solids and fluids, making their modeling difficult. Matter addresses this with a unified framework, using a numerical solver called MPM. Able to capture cohesion, density variations and complex terrains, it's particularly relevant for snow avalanches or landslides. Matter runs efficiently on standard computers, making advanced simulations more accessible.
Matter is a new computer model that simulates granular media like sand, snow, and soil. These...
