Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part I - Thermoelasticity. Computational Mechanics, accepted. <Download preprint>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, accepted. <Download preprint>
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, available online.
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, accepted.
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, Available Online. <Download preprint>
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 preprint>
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 preprint>
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 preprint>.
Gholizadeh-Vayghan, A., Rajabipour, F., Hillman, M., Characterization of Viscoelastic Behavior of Synthetic Alkali–Silica Reaction Gels, Cement and Concrete Composites, in press, available online.
Hillman, M., Lin, K.C., Madra, A., The Meshfree Explicit Galerkin Analysis (MEGA) Code. Proceedings, 14ème Colloque National en Calcul des Structures, May 13-17 2019, Presqu’île de Giens (Var). View on ResearchGate. <Downoad preprint>
Madra, A., 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, May 13-17 2019, Presqu’île de Giens (Var).
Hillman, M., Chen, J. S., Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods, Advances in Computational Plasticity, Vol. 46, pp.145-164, 2017, doi:10.1007/978-3-319-60885-3_7.
Chen, J. S., Liu, W. K., Hillman, M., Chi, S. W., Lian, Y., Bessa, M. A., Encyclopedia of Computational Mechanics, 2nd Edition, 2017, Editors: Erwin Stein, Renè de Borst and Tom Hughes, John Wiley & Sons, Ltd.
Liang, S., Chen, J. S., Li, J. , Lin, S. P., Roth, M. J., Heard, W., Hillman, M., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, 2017,doi:10.1061/(ASCE)EM.1943-7889.0001176.
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, 2017, doi:10.1007/s00466-017-1395-2.
Chen, J. S., Hillman, M., Chi, S. W., Meshfree methods: progress made after 20 years, 2017, Journal of Engineering Mechanics, doi:10.1061/(ASCE)EM.1943-7889.0001176. <Download self-archived preprint>
Hillman, M., Chen, J. S., An accelerated, convergent and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics, 2016, International Journal for Numerical Methods in Engineering, doi:10.1002/nme.5183. <Download self-archived preprint>
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, doi:10.1016/j.cma.2015.11.004. <Download self-archived preprint>
Hillman, M., Chen, J. S., An implicit gradient meshfree formulation for convection-dominated problems, Advances in Computational Fluid-Structure Interaction and Flow Simulation, Engineering and Technology Book Series, pp. 25-37, 2016, https://doi.org/10.1007/978-3-319-40827-9_3.
Wei, H., Chen, J. S., Hillman, M., A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fuid-saturated porous media, Computers and Fluids, 2015, doi:10.1016 /j.compfluid.2015.11.002.
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, doi:doi:10.1016/j.ijimpeng.2015.07.009.
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, doi:doi:10.1016/j.cma.2014.10.004.
Littlewood, D., Hillman, M., Yreux, E., Bishop, J., Chen, J.S., Implementation and verification of RKPM in the Sierra/SolidMechanics analysis code, Proceedings of ASME 2015 International Mechanical Engineering Congress & Exposition, doi:10.1115/IMECE2015-51939.
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, doi:10.1007/s40571-014-0024-5.
Ruter, M., Hillman, M., Chen, J. S., Corrected stabilized non-conforming nodal integration in meshfree methods, Lecture Notes in Computational Science and Engineering, Vol. 89, pp. 75-93, 2013, doi:10.1007/978-3-642-32979-1_5.
Chen, J. S., Hillman, M., Ruter, M., An arbitrary order variationally consistent method for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, Vol. 95, pp. 387-418, 2013, doi:10.1002/nme.4512. <Download self-archived preprint>
Hillman, M., Lin, K.C., Nodally integrated thermo-mechanical RKPM: Part II - Generalized thermoelasticity and hyperbolic finite-strain thermoplasticity. Computational Mechanics, accepted. <Download preprint>
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, available online.
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, accepted.
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, Available Online. <Download preprint>
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 preprint>
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 preprint>
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 preprint>.
Gholizadeh-Vayghan, A., Rajabipour, F., Hillman, M., Characterization of Viscoelastic Behavior of Synthetic Alkali–Silica Reaction Gels, Cement and Concrete Composites, in press, available online.
Hillman, M., Lin, K.C., Madra, A., The Meshfree Explicit Galerkin Analysis (MEGA) Code. Proceedings, 14ème Colloque National en Calcul des Structures, May 13-17 2019, Presqu’île de Giens (Var). View on ResearchGate. <Downoad preprint>
Madra, A., 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, May 13-17 2019, Presqu’île de Giens (Var).
Hillman, M., Chen, J. S., Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods, Advances in Computational Plasticity, Vol. 46, pp.145-164, 2017, doi:10.1007/978-3-319-60885-3_7.
Chen, J. S., Liu, W. K., Hillman, M., Chi, S. W., Lian, Y., Bessa, M. A., Encyclopedia of Computational Mechanics, 2nd Edition, 2017, Editors: Erwin Stein, Renè de Borst and Tom Hughes, John Wiley & Sons, Ltd.
Liang, S., Chen, J. S., Li, J. , Lin, S. P., Roth, M. J., Heard, W., Hillman, M., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, 2017,doi:10.1061/(ASCE)EM.1943-7889.0001176.
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, 2017, doi:10.1007/s00466-017-1395-2.
Chen, J. S., Hillman, M., Chi, S. W., Meshfree methods: progress made after 20 years, 2017, Journal of Engineering Mechanics, doi:10.1061/(ASCE)EM.1943-7889.0001176. <Download self-archived preprint>
Hillman, M., Chen, J. S., An accelerated, convergent and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics, 2016, International Journal for Numerical Methods in Engineering, doi:10.1002/nme.5183. <Download self-archived preprint>
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, doi:10.1016/j.cma.2015.11.004. <Download self-archived preprint>
Hillman, M., Chen, J. S., An implicit gradient meshfree formulation for convection-dominated problems, Advances in Computational Fluid-Structure Interaction and Flow Simulation, Engineering and Technology Book Series, pp. 25-37, 2016, https://doi.org/10.1007/978-3-319-40827-9_3.
Wei, H., Chen, J. S., Hillman, M., A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fuid-saturated porous media, Computers and Fluids, 2015, doi:10.1016 /j.compfluid.2015.11.002.
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, doi:doi:10.1016/j.ijimpeng.2015.07.009.
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, doi:doi:10.1016/j.cma.2014.10.004.
Littlewood, D., Hillman, M., Yreux, E., Bishop, J., Chen, J.S., Implementation and verification of RKPM in the Sierra/SolidMechanics analysis code, Proceedings of ASME 2015 International Mechanical Engineering Congress & Exposition, doi:10.1115/IMECE2015-51939.
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, doi:10.1007/s40571-014-0024-5.
Ruter, M., Hillman, M., Chen, J. S., Corrected stabilized non-conforming nodal integration in meshfree methods, Lecture Notes in Computational Science and Engineering, Vol. 89, pp. 75-93, 2013, doi:10.1007/978-3-642-32979-1_5.
Chen, J. S., Hillman, M., Ruter, M., An arbitrary order variationally consistent method for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, Vol. 95, pp. 387-418, 2013, doi:10.1002/nme.4512. <Download self-archived preprint>
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