Books
Belytschko, T., Chen, J. S., Hillman, M., Meshfree and Particle Methods: Fundamentals and Applications. Wiley: Hoboken, NJ, 2024. <Amazon>
Journal Articles
29. Groeneveld, A., Hillman, M., A new meshfree variational multiscale (VMS) method for essential boundary conditions, Computer Methods in Applied Mechanics and Engineering, Vol 427, p. 117081, 2024.
28. Cheng, H., Radlinska, A., Hillman, M., Liu, F., Wang, J., Modeling concrete deposition via 3D printing using reproducing kernel particle method, Cement and Concrete Research, Vol 181, p. 107526, 2024.
27. Wang, J., Hillman, M., Wilmes, D., Magallanes, J., Bazilevs, Y., Smoothed naturally stabilized RKPM for non-linear explicit dynamics with novel stress gradient update, Computational Mechanics, https://doi.org/10.1007/s00466-024-02494-0, 2024. <Download>
26. Wang, J., Hillman, M., Upwind reproducing kernel collocation method for convection-dominated problems. Computer Methods in Applied Mechanics and Engineering, Vol 420, p. 116711, 2024. <Download>
25. Wang, Y., Baek, J., Tang, Y., Du, J., Hillman, M., Chen, J. S. Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures. Computational Mechanics, https://doi.org/10.1007/s00466-023-02394-9, 2023. <Download>
24. Li, W., Moutsanidis, G., Behzadinasab, M., Hillman, M., Bazilevs, Y., 2022. Reduced quadrature for Finite Element and Isogeometric methods in nonlinear solids. Computer Methods in Applied Mechanics and Engineering, Vol 399, p. 115389, 2022. <Download>
23. Wang, J., Hillman, M., Temporal Stability of collocation, Petrov-Galerkin, and other non-symmetric methods in elastodynamics and an energy conserving time integration. Computer Methods in Applied Mechanics and Engineering, Vol 393, p. 114738, 2021. <Download>
22. Williams, B., Madra, A., Heard, W., Graham, S., Grotke, M., Hillman, M., Nie, X. Characterizing damage modes and size effects in high-strength concrete under hydrostatic and triaxial stress states using X-ray microtomography. Construction and Building Materials, Vol. 311, p. 125338, 2021. <Download>
21. Behzadinasab, M., Hillman, M. Bazilevs, Y. IGA-PD penalty-based coupling for immersed air-blast fluid–structure interaction: a simple and effective solution for fracture and fragmentation. Journal of Mechanics, Vol 37, pp. 680-692, 2021. <Download>
20. Wang, J., Zhou, G., Hillman, M., Madra, A., Bazilevs, Y., Du, J., Su, K. Consistent immersed volumetric Nitsche methods for composite analysis. Computer Methods in Applied Mechanics and Engineering, Vol. 385, p. 114042, 2021. <Download>
19. Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, Vol. 68, pp. 821-844, 2021. <Download>
18. Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part I - Thermoelasticity. Computational Mechanics, Vol 68, pp. 795-820, 2021. <Download>
17. Tang, Y., Su, K., Man, R., Hillman, M., Du, J., Investigation of internal cracks in epoxy-alumina using in situ mechanical testing coupled with micro-CT, JOM, Vol. 73, pp. 2452–2459. <Download>
16. Baek, J., Chen, J.-S., Zhou, G., Arnett, K. P., Hillman, M., Hegemier, G., & Hardesty, S. A semi-Lagrangian RKPM with node-based shock algorithm for explosive welding simulation. Computational Mechanics, Vol. 67, pp. 1601-1627, 2021. <Download>
15. Hillman, M., Lin, K.C., Consistent Weak Forms for Meshfree Methods: Full Realization of h-refinement, p-refinement, and a-refinement in Strong-type Essential Boundary Condition Enforcement, Computer Methods in Applied Mechanics and Engineering, Vol. 373, p. 113448, 2021. <Download>
14. Zhou, G., Hillman, M., Non-ordinary state-based Godunov-peridynamics Formulation for Strong Shocks in Solids, Computational Particle Mechanics, Vol. 7, pp. 365–375, 2020. <Download>
13. Hillman, M., Pasetto, M., Zhou, G., Generalized Reproducing Kernel Peridynamics: Unification of Local and Non-Local Meshfree Methods, and an Arbitrary-order Accurate Generalized State-Based Peridynamic Formulation. Computational Particle Mechanics, Vol. 7, pp. 435–469, 2020. <Download>
12. Huang, T.H., Wei, H., Chen, J.S., Hillman, M., RKPM2D: Open-Source Implementation of Nodally Integrated Reproducing Kernel Particle Method for Solving Partial Differential Equations. Computational Particle Mechanics, Vol. 7, pp. 393–433, 2020. <Download>.
11. Gholizadeh-Vayghan, A., Rajabipour, F., Hillman, M., Characterization of Viscoelastic Behavior of Synthetic Alkali–Silica Reaction Gels, Cement and Concrete Composites, Vol. 104, pp. 103359, 2019. <Download>.
10. Liang, S., Chen, J. S., Li, J. , Lin, S. P., Chi, S. W., Hillman, M., Roth, M. J., Heard, W., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, Vol. 208(1-2), pp. 97-113, 2017. <Download>
9. Bazilevs, Y., Moutsanidis, G., Bueno, J., Kamran, K., Kamensky, D., Hillman, M., Gomezc, H., Chen, J.S., A New Formulation for Air-Blast Fluid Structure Interaction Using an Immersed Approach. Part II: Coupling of IGA and Meshfree Discretizations, Computational Mechanics, Vol. 60, pp. 101-116, 2017. <Download>
8. Chen, J. S., Hillman, M., Chi, S. W., Meshfree methods: progress made after 20 years, Journal of Engineering Mechanics, Vol. 143(4), pp. 04017001, 2017. <Download>
7. Hillman, M., Chen, J. S., An accelerated, convergent and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics, International Journal for Numerical Methods in Engineering, Vol. 107, pp. 603-630, 2016. <Download>
6. Hillman, M., Chen, J. S., Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems, Computer Methods in Applied Mechanics and Engineering, Vol. 299, pp. 381-400, 2016. <Download>
5. Wei, H., Chen, J. S., Hillman, M., A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media, Computers and Fluids, Vol. 141, pp. 105-115, 2016. <Download>
4. Sherburn, J., Roth, M. J., Chen, J. S., Hillman, M., Meshfree modeling of concrete slab perforation using a reproducing kernel particle impact and penetration formulation, International Journal of Impact Engineering, Vol. 86, pp. 96-110, 2015. <Download>
3. Hillman, M., Chen, J. S., Bazilevs, Y., Variationally consistent domain integration for isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 284, pp. 521-540, 2015. <Download>
2. Hillman, M., Chen, J. S., Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems, Computational Particle Mechanics, Vol. 1, pp. 245-256, 2014. <Download>
1. Chen, J. S., Hillman, M., Rüter, M., An arbitrary order variationally consistent method for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, Vol. 95, pp. 387-418, 2013. <Download>
Encyclopedia Entries
1. Chen, J. S., Liu, W. K., Hillman, M., Chi, S. W., Lian, Y., Bessa, M. A., Reproducing kernel particle method for solving partial differential equations, In: Encyclopedia of Computational Mechanics Second Edition, Erwin Stein, Renè de Borst and Tom Hughes (Eds.), Volume 2, London: Wiley, 2018. <Download>
Book Chapters
3. Hillman, M., Chen, J. S., Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods, In: Advances in Computational Plasticity Vol. 46, Eugenio Oñate, Djordje Peric, Eduardo de Souza Neto, and Michele Chiumenti (Eds.), pp. 145-164, Cham: Springer, 2018. <Download>
2. Hillman, M., Chen, J. S., An implicit gradient meshfree formulation for convection-dominated problems, In: Advances in Computational Fluid-Structure Interaction and Flow Simulation, Yuri Bazilevs and Kenji Takizawa (Eds.), pp. 25-37, Cham: Springer, 2016. <Download>
1. Rüter, M., Hillman, M., Chen, J. S., Corrected stabilized non-conforming nodal integration in meshfree methods, In: Lecture Notes in Computational Science and Engineering VI, Michael Griebel and Marc Alexander Schweitzer (Eds.), pp. 75-93, Cham: Springer, 2013. <Download>
Proceedings
4. Chen, J. S., Baek, J., Huang, T.-H., Hillman, M. Accelerated and stabilized meshfree method for impact-blast modeling. Proceedings, 2020 ASCE Structures Congress, St. Louis, Missouri, April 5-8, 2020. <Download>
3. Hillman, M., Lin, K.C., Madra, A., The Meshfree Explicit Galerkin Analysis (MEGA) Code. Proceedings, 14ème Colloque National en Calcul des Structures, Presqu’île de Giens (Var), May 13-17, 2019. <Download>
2. Madra, A., K. Su., Du, J., Hillman, M., Multi-scale reduced-order model of composite microstructure based on X-ray micro-CT imaging. Proceedings, 14ème Colloque National en Calcul des Structures, Presqu’île de Giens (Var), May 13-17, 2019. <Download>
1. Littlewood, D., Hillman, M., Yreux, E., Bishop, J., Chen, J.S., Implementation and verification of RKPM in the Sierra/SolidMechanics analysis code, Proceedings, 2015 ASME International Mechanical Engineering Congress & Exposition, Houston, Texas, November 13-19, 2015. <Download>
Articles
3. Chen, J.S, Chi, S. W. , Hillman, M., Preface: Meshfree and particle methods for modeling extreme loadings, in memory of Steve Attaway, Computational Particle Mechanics, Vol. 7, pp. 173-176, 2020. <Download>
2. Hillman, M., Chen, J. S., Roth, M. J., Advanced computational methods to understand & mitigate extreme events, IACM Expressions Vol. 39, pp. 12-16, 2016. <Download>
1. Chen, J. S., Hillman, M., Rüter, M., Hu, H. Y., Chi, S. W., The role of quadrature in meshfree Methods: Variational consistency in Galerkin weak form and collocation in strong form, IACM Expressions Vol. 34. pp. 11-17, 2014. <Download>
User Manuals
4. KC-FEMFRE User Manual.
3. RKPM2D User Manual. <Download>
2. MEGA User Manual. <Download>
1. MEGA Technical Manual. <Download>
Belytschko, T., Chen, J. S., Hillman, M., Meshfree and Particle Methods: Fundamentals and Applications. Wiley: Hoboken, NJ, 2024. <Amazon>
Journal Articles
29. Groeneveld, A., Hillman, M., A new meshfree variational multiscale (VMS) method for essential boundary conditions, Computer Methods in Applied Mechanics and Engineering, Vol 427, p. 117081, 2024.
28. Cheng, H., Radlinska, A., Hillman, M., Liu, F., Wang, J., Modeling concrete deposition via 3D printing using reproducing kernel particle method, Cement and Concrete Research, Vol 181, p. 107526, 2024.
27. Wang, J., Hillman, M., Wilmes, D., Magallanes, J., Bazilevs, Y., Smoothed naturally stabilized RKPM for non-linear explicit dynamics with novel stress gradient update, Computational Mechanics, https://doi.org/10.1007/s00466-024-02494-0, 2024. <Download>
26. Wang, J., Hillman, M., Upwind reproducing kernel collocation method for convection-dominated problems. Computer Methods in Applied Mechanics and Engineering, Vol 420, p. 116711, 2024. <Download>
25. Wang, Y., Baek, J., Tang, Y., Du, J., Hillman, M., Chen, J. S. Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures. Computational Mechanics, https://doi.org/10.1007/s00466-023-02394-9, 2023. <Download>
24. Li, W., Moutsanidis, G., Behzadinasab, M., Hillman, M., Bazilevs, Y., 2022. Reduced quadrature for Finite Element and Isogeometric methods in nonlinear solids. Computer Methods in Applied Mechanics and Engineering, Vol 399, p. 115389, 2022. <Download>
23. Wang, J., Hillman, M., Temporal Stability of collocation, Petrov-Galerkin, and other non-symmetric methods in elastodynamics and an energy conserving time integration. Computer Methods in Applied Mechanics and Engineering, Vol 393, p. 114738, 2021. <Download>
22. Williams, B., Madra, A., Heard, W., Graham, S., Grotke, M., Hillman, M., Nie, X. Characterizing damage modes and size effects in high-strength concrete under hydrostatic and triaxial stress states using X-ray microtomography. Construction and Building Materials, Vol. 311, p. 125338, 2021. <Download>
21. Behzadinasab, M., Hillman, M. Bazilevs, Y. IGA-PD penalty-based coupling for immersed air-blast fluid–structure interaction: a simple and effective solution for fracture and fragmentation. Journal of Mechanics, Vol 37, pp. 680-692, 2021. <Download>
20. Wang, J., Zhou, G., Hillman, M., Madra, A., Bazilevs, Y., Du, J., Su, K. Consistent immersed volumetric Nitsche methods for composite analysis. Computer Methods in Applied Mechanics and Engineering, Vol. 385, p. 114042, 2021. <Download>
19. Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, Vol. 68, pp. 821-844, 2021. <Download>
18. Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part I - Thermoelasticity. Computational Mechanics, Vol 68, pp. 795-820, 2021. <Download>
17. Tang, Y., Su, K., Man, R., Hillman, M., Du, J., Investigation of internal cracks in epoxy-alumina using in situ mechanical testing coupled with micro-CT, JOM, Vol. 73, pp. 2452–2459. <Download>
16. Baek, J., Chen, J.-S., Zhou, G., Arnett, K. P., Hillman, M., Hegemier, G., & Hardesty, S. A semi-Lagrangian RKPM with node-based shock algorithm for explosive welding simulation. Computational Mechanics, Vol. 67, pp. 1601-1627, 2021. <Download>
15. Hillman, M., Lin, K.C., Consistent Weak Forms for Meshfree Methods: Full Realization of h-refinement, p-refinement, and a-refinement in Strong-type Essential Boundary Condition Enforcement, Computer Methods in Applied Mechanics and Engineering, Vol. 373, p. 113448, 2021. <Download>
14. Zhou, G., Hillman, M., Non-ordinary state-based Godunov-peridynamics Formulation for Strong Shocks in Solids, Computational Particle Mechanics, Vol. 7, pp. 365–375, 2020. <Download>
13. Hillman, M., Pasetto, M., Zhou, G., Generalized Reproducing Kernel Peridynamics: Unification of Local and Non-Local Meshfree Methods, and an Arbitrary-order Accurate Generalized State-Based Peridynamic Formulation. Computational Particle Mechanics, Vol. 7, pp. 435–469, 2020. <Download>
12. Huang, T.H., Wei, H., Chen, J.S., Hillman, M., RKPM2D: Open-Source Implementation of Nodally Integrated Reproducing Kernel Particle Method for Solving Partial Differential Equations. Computational Particle Mechanics, Vol. 7, pp. 393–433, 2020. <Download>.
11. Gholizadeh-Vayghan, A., Rajabipour, F., Hillman, M., Characterization of Viscoelastic Behavior of Synthetic Alkali–Silica Reaction Gels, Cement and Concrete Composites, Vol. 104, pp. 103359, 2019. <Download>.
10. Liang, S., Chen, J. S., Li, J. , Lin, S. P., Chi, S. W., Hillman, M., Roth, M. J., Heard, W., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, Vol. 208(1-2), pp. 97-113, 2017. <Download>
9. Bazilevs, Y., Moutsanidis, G., Bueno, J., Kamran, K., Kamensky, D., Hillman, M., Gomezc, H., Chen, J.S., A New Formulation for Air-Blast Fluid Structure Interaction Using an Immersed Approach. Part II: Coupling of IGA and Meshfree Discretizations, Computational Mechanics, Vol. 60, pp. 101-116, 2017. <Download>
8. Chen, J. S., Hillman, M., Chi, S. W., Meshfree methods: progress made after 20 years, Journal of Engineering Mechanics, Vol. 143(4), pp. 04017001, 2017. <Download>
7. Hillman, M., Chen, J. S., An accelerated, convergent and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics, International Journal for Numerical Methods in Engineering, Vol. 107, pp. 603-630, 2016. <Download>
6. Hillman, M., Chen, J. S., Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems, Computer Methods in Applied Mechanics and Engineering, Vol. 299, pp. 381-400, 2016. <Download>
5. Wei, H., Chen, J. S., Hillman, M., A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media, Computers and Fluids, Vol. 141, pp. 105-115, 2016. <Download>
4. Sherburn, J., Roth, M. J., Chen, J. S., Hillman, M., Meshfree modeling of concrete slab perforation using a reproducing kernel particle impact and penetration formulation, International Journal of Impact Engineering, Vol. 86, pp. 96-110, 2015. <Download>
3. Hillman, M., Chen, J. S., Bazilevs, Y., Variationally consistent domain integration for isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 284, pp. 521-540, 2015. <Download>
2. Hillman, M., Chen, J. S., Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems, Computational Particle Mechanics, Vol. 1, pp. 245-256, 2014. <Download>
1. Chen, J. S., Hillman, M., Rüter, M., An arbitrary order variationally consistent method for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, Vol. 95, pp. 387-418, 2013. <Download>
Encyclopedia Entries
1. Chen, J. S., Liu, W. K., Hillman, M., Chi, S. W., Lian, Y., Bessa, M. A., Reproducing kernel particle method for solving partial differential equations, In: Encyclopedia of Computational Mechanics Second Edition, Erwin Stein, Renè de Borst and Tom Hughes (Eds.), Volume 2, London: Wiley, 2018. <Download>
Book Chapters
3. Hillman, M., Chen, J. S., Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods, In: Advances in Computational Plasticity Vol. 46, Eugenio Oñate, Djordje Peric, Eduardo de Souza Neto, and Michele Chiumenti (Eds.), pp. 145-164, Cham: Springer, 2018. <Download>
2. Hillman, M., Chen, J. S., An implicit gradient meshfree formulation for convection-dominated problems, In: Advances in Computational Fluid-Structure Interaction and Flow Simulation, Yuri Bazilevs and Kenji Takizawa (Eds.), pp. 25-37, Cham: Springer, 2016. <Download>
1. Rüter, M., Hillman, M., Chen, J. S., Corrected stabilized non-conforming nodal integration in meshfree methods, In: Lecture Notes in Computational Science and Engineering VI, Michael Griebel and Marc Alexander Schweitzer (Eds.), pp. 75-93, Cham: Springer, 2013. <Download>
Proceedings
4. Chen, J. S., Baek, J., Huang, T.-H., Hillman, M. Accelerated and stabilized meshfree method for impact-blast modeling. Proceedings, 2020 ASCE Structures Congress, St. Louis, Missouri, April 5-8, 2020. <Download>
3. Hillman, M., Lin, K.C., Madra, A., The Meshfree Explicit Galerkin Analysis (MEGA) Code. Proceedings, 14ème Colloque National en Calcul des Structures, Presqu’île de Giens (Var), May 13-17, 2019. <Download>
2. Madra, A., K. Su., Du, J., Hillman, M., Multi-scale reduced-order model of composite microstructure based on X-ray micro-CT imaging. Proceedings, 14ème Colloque National en Calcul des Structures, Presqu’île de Giens (Var), May 13-17, 2019. <Download>
1. Littlewood, D., Hillman, M., Yreux, E., Bishop, J., Chen, J.S., Implementation and verification of RKPM in the Sierra/SolidMechanics analysis code, Proceedings, 2015 ASME International Mechanical Engineering Congress & Exposition, Houston, Texas, November 13-19, 2015. <Download>
Articles
3. Chen, J.S, Chi, S. W. , Hillman, M., Preface: Meshfree and particle methods for modeling extreme loadings, in memory of Steve Attaway, Computational Particle Mechanics, Vol. 7, pp. 173-176, 2020. <Download>
2. Hillman, M., Chen, J. S., Roth, M. J., Advanced computational methods to understand & mitigate extreme events, IACM Expressions Vol. 39, pp. 12-16, 2016. <Download>
1. Chen, J. S., Hillman, M., Rüter, M., Hu, H. Y., Chi, S. W., The role of quadrature in meshfree Methods: Variational consistency in Galerkin weak form and collocation in strong form, IACM Expressions Vol. 34. pp. 11-17, 2014. <Download>
User Manuals
4. KC-FEMFRE User Manual.
3. RKPM2D User Manual. <Download>
2. MEGA User Manual. <Download>
1. MEGA Technical Manual. <Download>