Wing Kam Liu - Walter P. Murphy Professor
 
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Publications

(For most recent publication list, you may also visit: http://www.cestagi.com/?Wing_Kam_Liu)

-- Selected --

An Introduction to Computational Nano Mechanics and Materials
Wing Kam Liu, Karpov EG, Zhang S, Park HS
Computer Method in Applied Mechanics and Engineering 193 (17-20), 1529-1578, 2004.

Three Reliability Methods for Fatigue Crack Growth
W. K. Liu, Y. J. Chen, T. Belytschko, and Y. J. Lua
INVITED, Engineering Fracture Mechanics, Vo. 53-5, pp. 733-752, 1996.

Reproducing Kernel Particle Methods
W. K. Liu, Jun, S., and Zhang, Y. F.
International Journal for Numerical Methods in Fluids, vol. 20, pp. 1081-1106, 1995.

Reproducing Kernel Particle Methods for Structural Dynamics
W. K. Liu, S. Jun, S. Li, J. Adee, and T. Belytschko
International Journal for Numerical Methods in Engineering, vol. 38, pp. 1655-1679, 1995.

Formulation of Dynamic Stability of Fluid-Filled Shells
K. Tsukimori, W. K. Liu and R. A. Uras
Nuclear Engineering and Design, Vol. 142, pp. 267-297, 1993.

Elastic Interactions of a Fatigue Crack with a Micro-Defect by Mixed Boundary Integral Equation Method
Lua, Y. J.and W. K. Liu
International Journal of Numerical Methods, Vol. 36, pp. 2743-2759, 1993.

Adaptive ALE Finite Elements with Particular Reference to External Work Rate on Frictional Interface
W. K. Liu, Y. F. Zhang, T. Belytschko and J. S. Chen
Computer Methods in Applied Mechanics and Engineering, Vol. 93, 189-216, 1991.

Multi-Scale Finite Element Methods
W. K. Liu, Y. F. Zhang and M. R. Ramirez
International Journal for Numerical Methods in Engineering, vol. 32, pp. 969-990, 1991.

Viscous Flow with Large Free Surface Motion
A. Huerta and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, Vol. 69, pp. 277-324, 1988.

Random Field Finite Elements
W. K. Liu, T. Belytschko and A. Mani
International Journal for Numerical Methods in Engineering, Vol. 23, pp. 1831-1845, 1986.

-- 2012 --

Two-scale mechanism-based theory of nonlinear viscoelasticity
Shan Tang, M. Steven Greene, Wing Kam Liu
Journal of the Mechanics and Physics of Solids, 60 (2012) 199\96226.

A renormalization approach to model interaction in microstructured solids: Application to porous elastomer
Shan Tang, M. Steven Greene, Wing Kam Liu
Comput. Methods Appl. Mech. Engrg. 217\96220 (2012) 213\96225.

Nanoparticle Geometrical Effect on Structure, Dynamics and Anisotropic Viscosity of Polyethylene Nanocomposites
Ying Li, Martin Kr\F6ger, Wing Kam Liu
Macromolecules 2012, 45, 2099-2112.

Review: Electric Field Guided Assembly of One-dimensional Nanostructures for High Performance Sensors
Devon Brown, Jong-hoon Kim, Hyun-boo Lee, Gareth Fotouhi, Kyong-hoon Lee, Wing Kam Liu, Jae-hyun Chung
Sensors 12, 5725-5751, 2012.

DNA Nanotube Formation Based on Normal Mode Analysis
PengFei Qian, Sangjae Seo, Junghoon Kim, Seungjae Kim, Byeong Soo Lim, Wing Kam Liu, Bum Joon Kim, Thomas Henry LaBean, Sung Ha Park, and Moon Ki Kim
Nanotechnology, 23, 105704 2012.

Computational microstructure characterization and reconstruction for stochastic multiscale material design
Yu Liu, M. Steven Greene, Wei Chen, Dmitriy A. Dikin, Wing Kam Liu
Computer-Aided Design, 2012.

The Immersed Molecular Finite Element Method
Adrian M. Kopacz, Neelesh A. Patankar, Wing K. Liu
Comput. Methods Appl. Mech. Engrg. 233\96236 (28\9639) 2012.

Nanoscale Sensor Analysis using Immersed Molecular Electrokinetic Finite Element Method
Adrian M. Kopacz, Woon-Hong Yeo, Jae-Hyun Chung, and Wing Kam Liu
5189-5194 (4), Nanoscale, 2012.

Archetype-blending continuum theory
Khalil I Elkhodary, Michael S Greene, Shan Tang, Ted Belytschko, Wing K Liu
Submitted to Computer Methods in Applied Mechanics and Engineering, 2012.

-- 2011 --

Prediction of Anisotropic Behavior of Nano/Micro Composite Based on Damage Mechanics with Cell Modeling
Dock-Jin Lee, Young-Jin Kim, Moon-Ki Kim, Jae-Boong Choi, Yoon-Suk Chang, and Wing Kam Liu
Journal of Nanoscience and Nanotechnology, Vol 11, 619-623, 2011

Conforming Local Meshfree Method
Rong Tian, Albert C. To, Wing Kam Liu
Int. J. Numer. Meth. Engng, 2011; 86:335\96357.

Atomistic Simulation and Measurement of pH dependent Cancer Therapeutic Interactions with Nanodiamond Carrier
Adnan, Ashfaq; Lam, Robert; Chen, hanning; Lee, Jessica; Schaffer, Daniel; Barnard, Amanda; Schatz, George; Ho, Dean; Liu, Wing Kam
Molecular Pharmaceutics, 2011, 8 (2), pp 368\96374, DOI: 10.1021/mp1002398.

Enhancing endothelial cell retention on ePTFE constructs by siRNA-mediated SHP-1 gene silencing
Tefft BJ, Kopacz AM, Liu WK, Liu SQ (2011)
Journal of Nanotechnology in Engineering and Medicine, 2(1): 011007-1-011007-6.

Denoising methods for thermomechanical decomposition for quasi-equilibrium molecular dynamics simulations
To, Albert, Fu, Y., and Liu, W. K.
Comput. Methods Appl. Mech. Engrg. 200 (2011) 1979\961992

Characterization of heterogeneous solids via wave methods in computational microelasticity
S. Gonella, M.S. Greene, W.K. Liu, (2011)
Journal of the mechanics and Physics of Solids, Vol. 59 n. 5, pp. 959-974.

Multiscale framework for biomedical simulation from molecular dynamics to continuum mechanics
W. K. Liu, T.R. Lee, A. M. Kopacz, H. Kim, W. Stroberg, H. B. Man, D. Ho, M.K. Kim, J.H. Chung, P. Decuzzi
Journal of the Serbian Society for Computational Mechanics, 2011, Vol. 5, No. 2, pp. 61-80.

Computational Uncertainty Analysis in Multiresolution Materials via Stochastic Constitutive Theory
Greene M.S., Liu, Y., Chen, W., Liu, W.K.
Journal of Computer Methods in Applied Mechanics and Engineering, (2011), 200, pp.309-325.

Primitive chain network study on uncrosslinked and crosslinked cis-polyisoprene polymers
Ying Li, Martin Kr\F6ger, Wing Kam Liu
Polymer (2011).

A variable constraint tube model for size effects of polymer nano-structures
Shan Tang, M. Steven Greene, and Wing Kam Liu
APPLIED PHYSICS LETTERS 99, 191910 (2011).

Transformative research issues and opportunities in energy efficiency
Yip-Wah Chung, Jane Wang, Oyelayo Ajayi, Girma Biresaw, Jian Cao, Diann Hua, Walter Lapatovich, Wing K. Liu, Arun Majumdar, Farrukh Qureshi, Dong Zhu
Current Opinion in Solid State and Materials Science 15 (2011) 16\9619.

-- 2010 --

Multiresolution Continuum Modeling of Micro-void Assisted Dynamic Adiabatic Shear Band Propagation
Cahal McVeigh, Wing Kam Liu
J. Mech. Phys. Solids, Volume 58, Issue 2, February 2010, Pages 187-205.

Design of Nanodiamond Based Drug Delivery Patch for Cancer Therapeutics and Imaging Applications
Wing Kam Liu, Ashfaq Adnan, Adrian M Kopacz, Michelle Hallikainen, Dean Ho, Robert Lam, Jessica Lee, Ted Belytschko, George Schatz, Yonhua (Tommy) Tzeng, Young-Jin Kim, Seunghyun Baik, Moon Ki Kim, Taesung Kim, Junghoon Lee, Eung-Soo Hwang, Seyoung Im, Eiji Osawa, Amanda Barnard, Huan-Cheng Chang, Chia-Ching Chang, Eugenio O\F1ate
Nanodiamonds: Applications in Biology and Nanoscale Medicine. 249-284, Springer US, 2010.

An Efficient Elastic Displacement Analysis Procedure for Simulating Transient Conformal-Contact Elastohydrodynamic Lubrication Systems
Shangwu Xiong, Chih Lin, Yansong Wang, Wing Kam Liu, and Q. Jane Wang
Transactions of the ASME, Journal of Tribology, April 2010, vol.132, issue 2, pp.021502-1~021502-9.

Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum
Wing Kam Liu, Dong Qian, Stefano Gonella, Shaofan Li, Wei Chen, and Shardool Chirputkar
Int. J. Numer. Meth. Engng 83:1039\961080 (2010).

A Level-Set Approach for Optimal Design of Smart Energy Harvesters
Shikui Chen, Stefano Gonella, Wei Chen, Wing Kam Liu
Comput. Methods Appl. Mech. Engrg., 199(37-40),2532-2543, 2010,

Mechano-Kinetic Coupling Approach for Materials with Dynamic Internal Structure
Eudard Karpov, Semyon Chaichenets, Wing Kam Liu, and Dong Qian
Philophical Magazine Letters, Vol. 90, No. 7, pp. 471-480, July 2010.

A Multiscale Design Methodology for Hierarchical Systems With Random Field Uncertainty
Wei Chen, Xiaolei Yin, Sanghoon Lee, Wing Kam Liu
Journal of Mechanical Design, APRIL 2010, Vol. 132 / 041006-1.

A Multiresolution Continuum Simulation of the Ductile Fracture Process
Rong Tian, Stephanie Chan, Shan Tang, Adrian M. Kopacz, Jian-Sheng Wang, Herng-Jeng Jou, Larbi Siad, Lars-Erik Lindgren, Gregory B. Olson, Wing Kam Liu
Journal of the Mechanics and Physics of solids, 58 (2010) 1681\961700.

Yield Design Homogenization Method for Compaction of Monosized Spherical Powders
Benabbes Anouar, Siad Larbi, and Wing Kam Liu
International Journal of Applied Mechanics, Vol. 2, No. 3 (2010) 457\96488.

Precise spring constant assignment in elastic network model for identification of vibration frequency and modeshape
Mingwen Hu, Sharad Raj, Byung Kim, Wing Kam Liu, Seunghyun Baik, Taesung Kim, Byeong-Soo Lim and Moon Ki Kim
Journal of Mechanical Science and Technology, vol. 24, no. 9, pp.1771-1780, 2010.

A domain-reduction approach to bridging-scale simulation of one-dimensional nanostructures
Dong Qian, Manas Phadke, Eduard Karpov, and Wing Kam Liu
Computational Mechanics, vol. 47, 1. 31-47, 2010.

-- 2009 --

Multiresolution modeling of ductile reinforced brittle composites
McVeigh,C.,Liu,W.K.
J. Mech. Phys. Solids, 57 244-267, 2009.

Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting
Gonella, S., To, A., and Liu, W. K.
J. Mech. Phys. Solids 57 (2009), 621-633.

Efficient Random Field Uncertainty Propagation in Design using Multiscale Analysis
Yin, X., Lee, S., Chen, W., Liu, W. K., Horstemeyer, M.F.
ASME Journal of Mechanical Design, 131(2), 2009.

Thermal effects in 10 keV Si PKA cascades in 3C-SiC
D.E. Farrell, Noam Bernstein, and Wing Kam Liu
J. Nucl. Mater. 385, pp. 572-581, (2009).

Molecular dynamics study of surface effect on martensitic cubic-to-tetragonal transformation in Ni\96Al alloy
Ken-ichi Saitoh and Wing Kam Liu
Computational Materials Science, 46 (2009) 531\96544.

Complexity science of multiscale materials via stochastic computations
Wing Kam Liu, Larbi Siad, Rong Tian, Sanghoon Lee, Dockjin Lee, Xiaolei Yin, Wei Chen, Stephanie Chan, Gregory B. Olson, Lars-Erik Lindgen, Mark F. Horstemeyer, Yoon-Suk Chang, Jae-Boong Choi and Young Jin Kim
International Journal for Numerical Methods in Engineering, Volume 80, Issue 6, 5 - 12 November 2009, Pages: 932-978, 2009.

Multi-length scale micromorphic process zone model
Franck Vernerey, Wing Kam Liu, Brian Moran, and Greg Olson
Computational mechanics, Volume 44 (3), August 2009, pp. 433-445.

On Computational Issues of Immersed Finite Element Methods
X. Wang, L.T. Zhang, and W.K. Liu
Journal of Computational Physics, 228, pp. 2535-2551, 2009.

Multi-scale solid oxide fuel cell materials modeling
Ji Hoon Kim, Wing Kam Liu, and Christopher Lee
Computational Mechanics, Volume 44(5), October, 2009, PP. 683-704.

Numerical Simulation of a Nanoparticle Focusing Lens in a Microfluidic Channel by Using Immersed Finite Element Method
Tae-Rin Lee, Yoon-Suk Chang, Jae-Boong Choi, Wing Kam Liu, and Young-Jin Kim
Journal of Nanoscience and Nanotechnology, Vol.9, 1\965, 2009.

Explicit numerical study of softening in porous ductile solids
Siad, L., Liu, W. K., and Benables, A.
Mechanics Research Communications 36 (2), pp. 236-245, 2009.

Multiresolution Mechanics for Nano/Micro-Structured Materials
Franck J. Vernerey, Wing Kam Liu, Elisa Budyn, Ji Hoon Kim, and Albert To
Computational Mechanics, 2009, Part 1, 1-9.

-- 2008 --

The immersed/fictitious element method for fluid-structure interaction: Volumetric consistency, compressibility and thin members
Wang, H.; Chessa, J.; Liu, W. K.; Belytschko, T.
International Journal for Numerical Methods in Engineering, 74, 32-55, 2008.

Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting
Gonella, S., To, A., and Liu, W. K.
J. Mech. Phys. Solids 2008.

Concurrent quantum/continuum coupling analysis of nanostructures
Dong Qian, Wing Kam Liu, Qingjin Zheng
Comput. Methods Appl. Mech. Engrg. Volume 197, Issues 41-42, Pages 3291-3323, 2008.

Statistical volume element method for predicting microstructure-constitutive property relations
Xiaolei Yin, Wei Chen, Albert To, Cahal McVeigh, Wing Kam Liu
Comput. Methods Appl. Mech. Engrg. 197 3516-3529, 2008.

A finite temperature continuum theory based on interatomic potential in crystalline solids
Albert C. To, Wing Kam Liu, Adrian Kopacz
Computational Mechanics, Volume 42, Number 4, September, pp. 531-541, 2008.

A micromorphic model for the multiple scale failure of heterogeneous materials
F. J. Vernerey, W. K. Liu, B. Moran, G.B. Olson
Journal of the Mechanics and Physics of solids, 56(4), 1320-1347, 2008.

Linking microstructure and properties through a predictive 3 multiresolution continuum
Cahal McVeigh, Wing Kam Liu
Comput. Methods Appl. Mech. Engrg. 197 3268–3290, 2008.

Materials integrity in microsystems: a framework for a petascale predictive-science-based multiscale modeling and simulation system
Albert C. To, Wing Kam Liu, Gregory B. Olson, Ted Belytschko, Wei Chen, Mark S. Shephard, Yip-Wah Chung, Roger Ghanem, Peter W. Voorhees, David N. Seidman, Chris Wolverton, J. S. Chen, Brian Moran, Arthur J. Freeman, Rong Tian, Xiaojuan Luo, Eric Lautenschlager, A. Dorian Challoner
Computational Mechanics, Volume 42, Number 4, September, 2008, pp. 485-510.

Manipulation of nanoparticles and biomolecules by electric field and surface tension
Yaling Liu, Kieseok Oh, John G. Bai, Cheng-Ling Chang, Woonhoog Yeo, Jae-Hyun Chung, Kyong-Hoon Lee, Wing Kam Liu
Computer Methods in Applied Mechanics and Engineering, 197(25-28), 2156-2172, 2008.

Predictive multiscale theory for design of heterogeneous materials
Wing Kam Liu, Cahal McVeigh
Computational Mechanics, 42(2), 147-170, 2008.

Multiple time scale method for atomistic simulations
Sergey N. Medyanik and Wing Kam Liu
Computational Mechanics, Volume 42, Number 4, September, pp. 569-577, 2008.

A micromorphic model for the multiple scale failure of heterogeneous materials
Franck J. Vernerey, Wing Kam Liu, Brian Moran and Gregory Olson
Journal of the Mechanics and Physics of Solids, 56(4), 1320-1347, 2008.

Simulation and prediction of endothelial cell adhesion modulated by molecular engineering
Adrian Marcin Kopacz, Wing Kam Liu, Shu Q. Liu
Computer Methods in Applied Mechanics and Engineering, 197(25-28), 2340-2352, 2008.

-- 2007 --

Fluid flow-assisted dielectrophoretic assembly of nanowires
K. Oh, J. Chung, J. Riley, Y. Liu, and W.K. Liu
Langmuir, 23 (23), 11932 -11940, 2007.

Immersed electrokinetic finite element method
Yaling Liu, Wing Kam Liu, Ted Belytschko, Neelesh Patankar, Albert C. To, Adrian Kopacz, Jae-Hyun Chung
International Journal for Numerical Methods in Engineering 71:379-405, 2007.

Implementation Aspects of the Bridging Scale Method and Application to Intersonic Crack Propagation
D.E. Farrell, H.S. Park and W.K. Liu
International Journal for Numerical Methods in Engineering 71:583-605, 2007.

Multi-Scale Micromorphic Theory for Hierarchical Materials
Franck Vernerey, Wing Kam Liu, Brian Moran
Journal of the Mechanics and Physics of Solid, 55(12), 2603-2651, 2007.

Extrinsic Meshfree Approximation Using Asymptotic Expansion for Interfacial Discontinuiy of Derivative
Do Wan Kim, Y. C. Yoon, W. K. Liu and T. Belytschko
Journal of Computational Physics, 221(1):370-394, 2007.

An Interactive Microvoid Shear Localization Mechanism in High Strength Steels
Cahal McVeigha, Franck Vernerey, Wing Kam Liu, Brian Morana, Gregory Olson
Journal of the Mechanics and Physics of Solids, 55(2):225-224, 2007.

On criteria for dynamic adiabatic shear band propagation
Sergey N.Medyanika, Wing Kam Liua, Shaofan Lib
Journal of the Mechanics and Physics of Solids, 55(7):1439-1461, 2007.

Meshfree point collocation method with intrinsic enrichment for interface problems
Do Wan Kim, Wing Kam Liu, Young-Cheol Yoon, Ted Belytschko, Sang-Ho Lee
Accepted to Computational Mechanics, 2007.

Mathematical foundations of the immersed finite element method
Wing Kam Liu, Do Wan Kim, and Shaoqiang Tang
Computational Mechanics, Vol. 39, No. 3, 2007.

A phonon heat bath approach for the atomistic and multiscale simulation of solids
Karpov EG, Park HS, Liu WK
International Journal for Numerical Methods in Engineering, 70:3, pp. 351-378, 2007.

-- 2006 --

The 3-D computational modeling of shear-dominated ductile failure in steel
Franck J. Vernerey, Cahal McVeigh, Wing Kam Liu, Brian Moran, Deepti Tewari, David M. Parks, Gregory B. Olson
Journal of The Minerals, Metals and Materials Society, pp. 45-51, December 2006.

Rheology of red blood cell aggregation by computer simulation
Y. Liu and W.K. Liu
Journal of Computational Physics, 220(1):139-154, 2006.

Immersed Electrokinetic Finite Element Method
Y. Liu, W.K. Liu, N. Patankar, and T. Belytschko
International Journal for Numerical Methods in Engineering, accepted 2006.

Stent modeling using immersed finite element method
M. Gay, L. Zhang, W.K. Liu
Computer Methods in Applied Mechanics and Engineering, 195:33-36, pp. 4358-4370, 2006.

Multiscale boundary conditions in crystalline solids: theory and application to nanoindentation
Karpov, E. G., Yu, H., Park, H. S., Liu, W. K., Wang Q. and Qian D.
International Journal of Solids and Structures, in press 2006.

Domain Reduction Method for Atomistic Simulations
Sergey N. Medyanika, Eduard G. Karpova, Wing Kam Liu
Journal title: Journal of Computational Physics, 218:2, pp. 836-859, 2006.

Domain Reduction Approach to Molecular Mechanics Simulations of Carbon Nanostructures
Medyanik SN, Karpov EG, Liu WK
Journal of Computational Physics, accepted 2006.

Approaching on the mixed elastohydrodynamic lubrication of smooth journal-bearing system with low viscosity and rotating speed
S.W.Xiong, Q.J.Wang, W.K.Liu, Q.M.Yang, K.Vaidyanathan, D.Zhu and C.Lin
Tribology Transactions, 49, 598-610, 2006.

Predictions and Observations of Multiple Slip Modes in Atomic-Scale Friction
Sergey N. Medyanik, Wing Kam Liu, In-Ha Sung, and Robert W. Carpick
Physical Review Letters, Vol. 97, No. 13, 2006.

Dielectrophoretic Assembly of Nanowires
Yaling Liu, Jae-Hyun Chung, Wing Kam Liu and Rodney S. Ruoff
Journal of Physical Chemistry B, 110, 14098-14106, 2006.

Multiresolution analysis for material design
Cahal McVeigh, Franck Vernerey, Wing Kam Liu and L. Cate Brinson
Computer Methods in Applied Mechanics and Engineering, Volume 195, Issues 37-40, Pages 5053-5076, 2006.

Maximum principle and convergence analysis for the meshfree point collocation method
Do Wan Kim, Wing Kam Liu
SIAM J. Numer. Anal. Vol. 44, No. 2, pp. 515–539, 2006.

A Pseudo-Spectral Multiscale Method: Interfacial Conditions and Coarse Grid Equations
Shaoqiang Tang, Thomas Y. Hou, and Wing Kam Liu
Journal of Computational Physics, 213- , pp. 57-85, 2006.

Immersed Finite Element Method and its Applications to Biological Systems
Wing Kam Liu, Yaling Liu, David Farrell, Lucy Zhang, X. Sheldon Wang, Yoshio Fukui, Neelesh Patankar, Yongjie Zhang et al.
Computer Methods in Applied Mechanics and Engineering, 195(1722-1749), 2006.

Bridging scale methods for nanomechanics and materials
Liu, W.K.; Park, H.S.; Qian, D.; Karpov, E.G.; Kadowaki, H.; Wagner, G.J.
Computer Methods in Applied Mechanics and Engineering, Volume 195, Issue 13-16, 1, Pages 1407-1421 February 2006.

Mathematical foundations of the Immersed Finite Element Method
Wing Kam Liu, Do Wan Kim and Shaoqiang Tang
Computational Mechanics, 1 - 12, December 2006.

A Mathematical Framework of the Bridging Scale Method
Shaoqiang Tang, Thomas Y. Hou, Wing Kam Liu
International Journal for Numerical Methods in Engineering, 65, 1688-1713, 2006.

Prediction of Central Bursting during Axisymmetric Cold Extrusion of a Metal Alloy containing Particles
Cahal McVeigh, Wing Kam Liu
International Journal of Solids and Structures, 43:10, 3087-3105, 2006

-- 2005 --

Treatment of Discontinuity in the Reproducing Kernel Element Method
Hongsheng Lu, Do Wan Kim, Wing Kam Liu
International Journal for Numerical Methods in Engineering
Volume 63, Issue 2, Pages 241-255, 2005

Computational Nanomechanics of Materials
W. K. Liu, S. Jun, and D. Qian
Accepted for publication in "Handbook of Theoretical and Computational Nanotechnology" edited by M. Rieth and W. Schommers, American Scientific Publishers, Stevenson Ranch, CA, 2005.

Bridging Scale Methods for Computational Nanotechnology
W. K. Liu and H. S. Park
To appear in Handbook of Theoretical and Computational Nanotechnology, edited by M. Rieth and W. Schommers, American Scientific Publishers, 2005.

A multiscale approach for the micropolar continuum model
Hiroshi Kadowaki and Wing Kam Liu
Computer Modeling in Engineering & Sciences, Vol. 7, No. 3, pp. 269-282, 2005.

The Bridging Scale for Two-Dimensional Atomistic/Continuum Coupling
H.S. Park, E.G. Karpov, W.K. Liu and P.A. Klein
Philosophical Magazine, 85 (1): 79-113, 2005.

Simulation of Bulk Metal Forming Processes using the Reproducing Kernel Particle Method
Shangwu Xiong, Wing Kam Liu, Jian Cao, C. S. Li, J. M. C. Rodrigues and P. A. F. Martins
Computers & Structures, 83, 574-587, 2005.

A Green's Function Approach to Deriving Non-Reflecting Boundary Conditions in Molecular Dynamics Simulations
E. G. Karpov¤, G. J. Wagnery and Wing Kam Liu
International Journal for Numerical Methods in Engineering 62(9), 1250-1262, 2005.

Non-reflecting Boundary Conditions for Atomistic, Continuum and Coupled Atomistic/Continuum Simulations.
Park HS, Karpov EG, Klein PA, Wing Kam Liu
International Journal for Numerical Methods in Engineering, 64:237-259, 2005.

Three-Dimensional Bridging Scale Analysis of Dynamic Fracture
H.S. Park, E.G. Karpov, P.A. Klein and W.K.Liu
Journal of Computational Physics, 207(2), 588-609, 2005.

-- 2004 --

An Introduction to Computational Nano Mechanics and Materials
Wing Kam Liu, Karpov EG, Zhang S, Park HS
Computer Method in Applied Mechanics and Engineering 193 (17-20), 1529-1578, 2004.

Microforming–Experimental Investigation of the Extrusion Process for Micropins and its Numerical Sim. Using RKEM
J. Cao, N. Krishnan, Z. Wang, H. Lu, W. K. Liu
Accepted, the Journal of Manufacturing Science and Engineering, March, 2004.

Adaptive Enrichment Meshfree Sim. and Experiment on Buckling and Post-buckling Analysis in Sheet Metal Forming
H. Lu, H. S. Cheng, J. Cao, and W. K. Liu
Accepted, Computer Methods in Applied Mechanics and Engineering, 2004.

Bridging Scale Methods
W.K. Liu, L.T. Zhang, E.G. Karpov, H. Kadowaki and H.S Park
Submitted to Springer Lecture Notes in Computational Science and Engineering, editors T. Barth, M. Griebel, D.E. Keyes, R.M. Nieminen, D. Roose and T. Schlick, 2004.

Modelling of Chaotic Thermal Motion in Solids
Karpov EG, Park HS, Wing Kam Liu, et al.
Submitted to Applied Physics Letters, 2004.

Molecular Dynamics Boundary Conditions Incorporating Non-Nearest Neighbor Interactions
H.S. Park, E.G. Karpov and W.K. Liu
Submitted to International Journal for Numerical Methods in Engineering, 2004.

Multiscale Boundary Conditions in Crystalline Solids
E.G. Karpov, H. Yu, H.S. Park, W.K. Liu, J. Wang and D. Qian
Submitted to Physical Review, 2004.

Bridging Scale Mechanics and Materials
W. K. Liu, H. S. Park, E. G. Karpov, H. Kadowaki, G. J. Wagner, D. Qian, and S. Li
International Center for Numerical Methods and Engineering (CIMNE), ISBN: 84-95999-49-8, 72-88, 2004.

Experimental and molecular dynamics simulation studies of friction behavior of hydrogenated carbon films
Sulin Zhanga, Greg Wagnera, Sergey N. Medyanika, Wing-Kam Liua, Yuan-Hsin Yub and Yip-Wah Chung
Surface and Coating Technology 177, 518-523, 2004.

Molecular Dynamics Boundary Conditions for Regular Crystal Lattices
Wagner GJ, Karpov EG, Wing Kam Liu
Computer Method in Applied Mechanics and Engineering 193 (17-20), 1579-1601, 2004.

An Introduction and Tutorial on Multiple Scale Analysis in Solids
H.S. Park, W.K. Liu
Computer Methods in Applied Mechanics and Engineering, 193 1733-1772, 2004.

Extended immersed boundary method using FEM and RKPM
Xiaodong Wang and Wing Kam Liu
Computer Methods in Applied Mechanics and Engineering, Volume 193, Issues 12-14, 26, Pages 1305-1321, March 2004.

Finite Element Method for Mixed Elastohydrodynamic Lubrication of Journal-Bearing Systems
Wing Kam Liu, Shangwu Xiong, Yong Guo, Q. Jane Wang, Yansong Wang, Qingmin Yang, Kumar Vaidyanathan
International Journal for Numerical Methods in Engineering, 60(10): 1759-1790, 2004.

Molecular Dynamics Boundary Conditions for Regular Crystal Lattices
Wagner GJ, Karpov EG, Wing Kam Liu
Computer Method in Applied Mechanics and Engineering 193 (17-20), 1579-1601, 2004.

Bridging Multi-Scale Method for Localization Problems
Hiroshi Kadowaki and Wing Kam Liu
Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 30-32 , 30 July 2004, Pages 3267-3302
Presented at 7th U.S. National Congress on Computational Mechanics, July 28-30, 2003, Albuquerque, New Mexico.

Special issue on Multiple Scale Methods for Nanoscale Mechanics and Materials
Liu WK, Qian D, and Horstemeyer MF
Computer Methods in Applied Mechanics and Engineering, 193(17-20): III-V 2004.

Bridging Multi-Scale Method for Localization Problems
Hiroshi Kadowaki and Wing Kam Liu
Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 30-32, 30 July 2004, Pages 3267-3302.

A Multiscale Projection Method for the Analysis of Carbon Nanotubes
Qian D, Wagner GJ, and Liu WK
Computer Methods in Applied Mechanics and Engineering, 193(17-20): 1603-1632 2004.

Modeling and Simulation of Intersonic Crack Growth
Su Hao, Wing Kam Liu, Patrick A. Klein, Ares J. Rosakis
International Journal for Solids Structure, v.41, p1773, 2004.

Multi-scale Constitutive Model and Computational Framework for the Design of Ultra-high Strength, High ...
Su Hao, Wing Kam Liu, Brian Moran, Franck Vernerey,Gregory B. Olson
Computer Methods in Applied Mechanics and Engineering, v.193, p.1865, 2004.

Moving Particle Finite Element Method with Global Smoothness
Su Hao, Wing Kam Liu and Ted Belytschko
International Journal for Numerical Methods in Engineering, 59:1007–1020 (DOI: 10.1002/nme.999), 2004.

Cohesive Solutions of Intersonic Moving Dislocations
Su Hao and Wing Kam Liu, J. Weertman
Philosophical Magazine A, v.84, p.1067, 2004.

An Introduction and Tutorial on Multiple Scale Analysis in Solids
H.S. Park and W.K. Liu
Computer Methods in Applied Mechanics and Engineering 2004; 193: 1733-1772.

An Introduction to Computational Nanomechanics and Materials
W.K. Liu, E.G. Karpov, S. Zhang, H.S. Park
Computer Methods in Applied Mechanics and Engineering, 193 (2004) 1529–1578.

Experimental and Molecular Dynamics studies of friction between Nano-Scale Carbon Coatings
S. Zhang, G. J. Wagner, Y. -H. Yu, W. K. Liu, S. N. Medyanik and Y. W. Chung
Surface and Coating Technology 177, 518-523, 2004.

A Temperature Equation for Coupled Atomistic/Continuum Simulations
H.S. Park, E.G. Karpov and W.K. Liu
Computer Methods in Applied Mechanics and Engineering, 193: 1713-1732, 2004.

Reproducing Kernel Element Method Part IV. Globally Conforming Cn(n >1) Triangular Hierarchy
D. C. Simkins, S. Li, H. Lu, and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, 193: 1013–1034, 2004.

Reproducing Kernel Element Method Part III. Generalized Enrichment and Applications
H. Lu, S. Li, D. C. Simkins, W. K. Liu, and J. Cao
Computer Methods in Applied Mechanics and Engineering, 193: 989–1011, 2004.

Reproducing Kernel Element Method, Part II Globally Conforming Im/Cn Hierarchies
S. Li, H. Lu, W. Han and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, 193: 953–987, 2004.

Reproducing Kernel Element Method, Part I Theoretical Formulation
W. K. Liu, W. Han, H. Lu and S. Li
Computer Methods in Applied Mechanics and Engineering, 193: 933–951, 2004.

Flexible Piecewise Approximations Based on Partition of Unity
Weimin Han and Wing Kam Liu
Advances in Computational Mathematics, Kluwer Academic Publishers. Printed in the Netherlands. 0: 1–9, 2004.

Atomistic Simulations of Double-Walled Carbon Nanotubes (DWCNTs) as Rotational Bearings
Sulin Zhang, Wing Kim Liu, and Rodney S. Ruoff
Nano Letters 4, 293-297, 2004.

Immersed Finite Element Method
Lucy Zhang, Axel Gerstenberger, Xiaodong Wang, and Wing Kam Liu
Computer Methods in Applied Mechanics and Engineering, Volume 193, Issues 21-22, Pages 2051-2067 May 2004.

A Hierarchical Multi-Physics Constitutive Model for Design of High Toughness Steels
S. Hao, B. Moran, W. K. Liu, G. B. Olson
J. Computer-aided Materials Design, 10(2): 99-142, 2003.

On the Utilization of the Reproducing Kernel Particle Method for the Numerical Simulation of Plane Strain Rolling
Xiong Shangwu, Wing Kam Liu, Jian Cao, J. M. C. Rodrigues and P. A. F. Martins
International Journal of Machine Tools and Manufacture. 43(1):89-102, 2003.

Stress Generation Mechanisms in Carbon Thin Films Grown by Ion-Beam Deposition
Sulin Zhang, Harley T. Johnson, Gregory J. Wagner, Wing Kam Liu, K. Jimmy Hsia
Acta Materialia 51, 5211-5222, 2003.

Coupling of Atomistic and Continuum Simulations using a Bridging Scale Decomposition
Gregory J. Wagner, Wing Kam Liu
Journal of Computational Physics, 190, 249–274, 2003.

Initial Tension in Randomly Disordered Periodic Lattices
E.G. Karpov, N.G. Stephen,Wing Kam Liu
International Journal of Solids and Structures, Volume 40, Issue 20, October 2003, Pages 5371-5388.

Multiscale Analysis and Design in Heterogeneous Systems
Wing Kam Liu, Su Hao, Franck J. Vernerey, Hiroshi Kadowaki, Harold Park, Dong Qian
Presented at VII International Conference on Computational Plasticity (COMPLAS VII).

Load Transfer Mechanism in Carbon Nanotube Ropes
Dong Qian, Wing Kam Liu, Rodney S. Ruoff
Composites Science and Technology, Volume 63, Issue 11, Pages 1561-1569, August 2003.

On the Utilization of the Reproducing Kernel Particle Method for the Numerical Simulation of Plane Strain Rolling
Xiong Shangwu, Wing Kam Liu, Jian Cao, J. M. C. Rodrigues and P. A. F. Martins
International Journal of Machine Tools and Manufacture, 43(1), 89-102, 2003.

Particulate Flow Simulations Using Lubrication Theory Solution Enrichment
G.J. Wagner, S. Ghosal, and W.K. Liu
International Journal for Numerical Methods in Engineering, Vol 56, pp. 1261-1289, 2003.

Survey of Multi-scale Meshfree Particle Methods
L. Zhang, W. K. Liu, S. F. Li, D. Qian and S. Hao
Meshfree Methods for Partial Differential Equations, eds, Michael Griebel and Marc A. Schweitzer, Lecture Notes in Computational Science and Engineering, pp. 441-458, Spring, 2002.

Mechanics of carbon nanotubes
Dong Qian, Gregory J. Wagner, Wing Kam Liu, Min-Feng Yu and Rodney S. Ruoff
Applied Mechanics Reviews, 55(6), 495-553, 2002.

Moving Particle Finite Element Method
Su Hao, J., Qian, D., and Wing Kam Liu
International Journal for Numerical Methods in Engineering, Vol. 53-8, pp. 1937-1958, 2002.

Meshfree and Particle Methods and Their Applications
Shaofan Li and Wing Kam Liu
Applied Mechanics Review, vol. 55, pages 1-34, 2002.

A Parallelized Meshfree Method with Boundary Enrichment for large-Scale CFD
Lucy T. Zhang, Gregory J. Wagner and Wing Kam Liu
Journal of Computational Physics, vol. 176, 483-506, 2002.

Meshfree Galerkin Simulations of Dynamic Shear Band Propagation and Failure Mode Transition
Shaofan Li, Wing Kam Liu, Ares Rosakis, Ted Belytshko and Wei Hao
International Journal of Solids and Structures, Vol. 39,1213-1240, 2002.

Mechanics of C60 in nanotubes
Dong Qian, Wing Kam Liu and Rodney S. Ruoff
Journal of Physical Chemistry B, 105:10753-10758, 2001.

Locked twist in multi-walled carbon nanotube ribbons
Yu, M.F., Dyer, M.J., Chen, J., Qian, D., Liu, W.K, and Ruoff, R.S. 
Physical Review B, Rapid Communications, 64:241403R, 2001.

Dynamic Shear Band Propagation and Micro-Structure of Adiabatic Shear Band
Shaofan Li, Wing Kam Liu, Dong Qian, R. Guduru and A. J. Rosakis
Computer Methods in Applied Mechanics and Engineering, 191(1-2): 73-92 2001.

Effective models for prediction of springback in flanging
N. Song, D. Qian, J. Cao, W.K. Liu, V. Viswanathan and S. Li
ASME Journal of Engineering Materials and Technology, Vol.123, pp.456-461, October,2001.

The extended finite element method for rigid particles in Stokes flow
G.J.Wagner, N. Moes, W.K.Liu and T.Belytschko
International Journal for Numerical Methods in Enginnering, 51:293, 2001.

Hierarchical enrichment for bridging scales and meshfree boundary conditions
G.J. Wagner and W.K. Liu
Int. J. Num. Meth. Eng., Vol. 50, pp. 507-524, 2000.

Convergence Analysis of a Hierarchical Enrichment of Dirichlet Boundary Conditions in a Meshfree Method
Weimin Han, Gregory J. Wagner and Wing Kam Liu
International Journal for Numerical Methods in Engineering, 2000.

Localization-induced Band and Cohesive Model
Su Hao, Wing Kam Liu and Dong Qian
ASME Journal of Applied Mechanics, V.67, p 803-812, 2000.

A Meshfree Contact-detection Algorithm
Shaofan Li, D. Qian, Wing Kam Liu and Ted Belytschko
Computer Methods in Applied Mechanics and Engineering, V.190, 24-25, p3271-3292,2000.

Simulations of Fluids and Solids by Multi-Scale Meshfree Methods
W. K. Liu and S. Li and W. Hao
EPMESC VII Computational Methods in Engineering and Science, edited by Bento, Oliviera, and Pereira, Vol. 1, 43-52, 1999. Presented as keynote lecture at International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science, 2-5 August 1999, Macao.

Reproducing Kernel Hierarchical Partition of Unity Part I: Theoretical Formulation
S. Li and W. K. Liu
International Journal for Numerical Methods in Engineering, Vol. 45, pp. 251-288, 1999.

Reproducing Kernel Hierarchical Partition of Unity Part II: Globally Conforming ImCn Hierarchies
S. Li and W. K. Liu
International Journal for Numerical Methods in Engineering, Vol. 45, pp. 289-317, 1999.

Meshfree Method with Enhanced Boundary Condition Treatments for Metal Forming Simulation
J. S. Chen, H. Wang and W. K. Liu
Presented at 1999 NSF Design & Manufacturing Grantees Conference, Queen Mary, Long Beach, CA, January 5-8, 1999.

Explicit Reproducing Kernel Particle Methods for Large Deformation Problems
S. Jun, W. K. Liu and T. Belytschko
International Journal for Numerical Methods in Engineering, Vol. 41, pp. 137-166, 1998.

Meshless Methods for Shear-deformable Beams and Plates
B. Donning and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, Vol. 152, pp.47-72, 1998.

Multiple Scale Reproducing Kernel Particle Methods for Large Deformation Problems
W. K. Liu and S. Jun
International Journal for Numerical Methods in Engineering, Vol. 41, pp. 1339-1362, 1998.

Synchronized Reproducing Kernel Interpolant via Multiple Wavelet Expansion
S. Li and W. K. Liu
Computational Mechanics, Vol. 21, pp. 28-47, 1998.

Implementation of Boundary Conditions for Meshless Methods
F. C. Günther and W, K. Liu
Computer Methods in Applied Mechanics and Engineering, Vol. 163, Nos. 1-4, pp.205-230, 1998.

Enrichment of the Finite Element Method with the Reproducing Kernel Particle Method
W. K. Liu, R. A. Uras and Y. Chen
Journal of Applied Mechanics, ASME, Vol. 64, pp. 861-870, 1997.

Multiresolution Reproducing Kernel Particle Methods in Acoustics
R. A. Uras, C. T. Chang, Y. Chen and W. K. Liu
Journal of Computational Acoustics, Vol. 5, No.1, pp. 71-94, 1997.

Multiresolution Reproducing Kernel Particle Method for Computational Fluid Dynamics [2] [3] [4]
W. K. Liu, S. Jun, D. T. Sihling, Y. Chen and W. Hao
International Journal of Numerical Method in Fluids, Vol. 24, pp.1391-1415, 1997.

Multiresolution Reproducing Kernel Particle Methods
W. K. Liu, W. Hao, Y. Chen, S. Jun and J. Gosz
Computational Mechanics, Vol. 20, No. 4, pp.295-309, 1997.

Moving Least Square Reproducing Kernel Method Part I: Methodology and Convergence
W. K. Liu, S. Li and T. Belytschko
Computer Methods in Applied Mechanics and Engineering, Vol. 143, pp. 113-154, 1997.

Advances in Multiple Scale Kernel Particle Methods
W. K. Liu, Y. Chen, C. T. Chang and T. Belytschko
A special feature article for the 10th anniversary volume of "Computational Mechanics, Vol. 18, No. 2, pp. 73-111, June, 1996.

Generalized Multiple Scale Reproducing Kernel Particle Methods
W. K. Liu, Y. Chen, R. A. Uras and C. T. Chang
Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 91-158, 1996.

Moving Least Square Reproducing Kernel Method Part II: Fourier Analysis
S. Li and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 159-194, 1996.

Reproducing Kernel Particle Methods for Large Deformation Analysis of Nonlinear Structures
J. S. Chen, C. Pan, C. T. Wu and W. K. Liu
Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 195-228, 1996.

Smoothing and Accelerated Computations in the Element Free Galerkin Method
T. Belytschko, Y. Krongauz, M. Fleming, D. Organ and W. K. Liu
Journal of Computational and Applied Mathematics, Vol. 74, pp. 111-126, 1996.

Overview and Applications of the Reproducing Kernel Particle Methods
W. K. Liu, Y. Chen, S. Jun, J. S. Chen, T. Belytschko, C. Pan, R. A. Uras and C. T. Chang
Archives of Computational Methods in Engineering: State of the art reviews, Vol. 3, pp. 3-80, 1996.

Admissible Approximations for Essential Boundary Conditions in the Reproducing Kernel Particle Method
J. Gosz and W. K. Liu
Computational Mechanics, Vol. 19, pp. 120-135, 1996.

Reproducing Kernel Particle Methods
W. K. Liu, Jun, S., and Zhang, Y. F.
International Journal for Numerical Methods in Fluids, vol. 20, pp. 1081-1106, 1995.

 
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