Wang, J., Zhou, G., Hillman, M., Madra, A., Bazilevs, Y., Du, J., Su, K. Consistent immersed volumetric Nitsche methods for composite analysis. Under Review. <Download preprint>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part I - Thermoelasticity. Computational Mechanics, In Press. <Download preprint>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, In Press. <Download preprint>
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, available online. <Download>
Baek, J., Chen, J.-S., Zhou, G., Arnett, K. P., Hillman, M., Hegemier, G., & Hardesty, S. (2021). A semi-Lagrangian RKPM with node-based shock algorithm for explosive welding simulation. Computational Mechanics, Vol. 67, pp. 1601-1627, 2021. <Download>
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, pp. 113448, 2021. <Download>
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>
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>
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>.
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>
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>
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>.
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part I - Thermoelasticity. Computational Mechanics, In Press. <Download preprint>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, In Press. <Download preprint>
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, available online. <Download>
Baek, J., Chen, J.-S., Zhou, G., Arnett, K. P., Hillman, M., Hegemier, G., & Hardesty, S. (2021). A semi-Lagrangian RKPM with node-based shock algorithm for explosive welding simulation. Computational Mechanics, Vol. 67, pp. 1601-1627, 2021. <Download>
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, pp. 113448, 2021. <Download>
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>
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>
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>.
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>
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>
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>.
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>