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Liu, Wing Kam

Co-Author Distance

Author ID:: liu.wing-kam
Published as:: Liu, Wing Kam;Liu, W. K.;Liu, Wing K.;Liu, Wingkam;Liu, Wing-Kam;Liu, Wing Kam Snm;Wing Kam Liu;Liu, W.more...less
Homepage:: http://www.mccormick.northwestern.edu/research-faculty/directory/profiles/liu-ka...
External Links:: MGP ·ORCID ·Wikidata ·Google Scholar ·ResearchGate ·dblp

Documents Indexed:

261 Publications since 1978, including3 Books and1 Additional arXiv Preprint

5 Contributions as Editor

Software Indexed:

3 Packages

Co-Authors:

282 Co-Authors with 263 Joint Publications

5,121 Co-Co-Authors

all top 5

Co-Authors

3	single-authored
54	Belytschko, Ted Bohdan
26	Li, Shaofan
26	Wagner, Gregory J.
18	Tang, Shaoqiang
16	Tang, Shan
15	Karpov, Eduard G.
13	Park, Harold S.
12	Qian, Dong
10	Chen, Wei
10	Gao, Jiaying
10	Hao, Su
10	Hughes, Thomas J. R.
10	Kafka, Orion L.
10	Lian, Yanping
10	Zhang, Lucy T.
9	Cao, Jian
9	Yu, Cheng
9	Zhang, Lei
8	Guo, Xu
8	Li, Hengyang
8	Lu, Ye
8	Mojumder, Satyajit
8	Park, Chanwook
7	Chen, Jiun-Shyan
7	Greene, M. Steven
7	Kopacz, Adrian Marcin
7	Liu, Zeliang
7	Lu, Hongsheng
7	McVeigh, Cahal
7	Moran, Brian
7	Olson, Gregory B.
7	Saha, Sourav
7	To, Albert C.
7	Zhang, Yifei
6	Bessa, Miguel A.
6	Guo, Jiachen
6	Kim, Do Wan
6	Lin, Stephen
6	Ong, Jame Shau-Jen
6	Smith, Jacob W.
6	Wang, Xiaodong
6	Yan, Wentao
5	Chen, Yijung
5	Fleming, Mark
5	Jun, Sukky
5	Kadowaki, Hiroshi
5	Liu, Yaling
5	Vernerey, Franck J.
5	Yang, Hang
5	Ying, Yuping
4	Apley, Daniel W.
4	Chang, Chin Tang
4	Farrell, David E.
4	Gonella, Stefano
4	Han, Weimin
4	Hao, Wei
4	Hu, Yu-Kan
4	Lam, Dennis
4	Li, Ying
4	Simkins, Daniel Craig jun.
4	Tian, Rong
3	Besterfield, Glen H.
3	Chang, Herman
3	Elkhodary, Khalil I.
3	Gan, Zhengtao
3	Guo, Yong
3	Knapik, Stefan
3	Li, Yangfan
3	Lindgren, Lars-Erik
3	Medyanik, Sergey N.
3	Patankar, Neelesh A.
3	Rosakis, Ares J.
3	Shakoor, Modesar
3	Siad, Larbi
3	Tajdari, Mahsa
3	Uras, Rasim Aziz
3	Zhang, Gang
2	Bostanabad, Ramin
2	Camanho, Pedro P.
2	Chan, Stephanie
2	Chang, Yoon-Suk
2	Cheng, Lin
2	Choi, Jae-Boong
2	Chung, Jaehyun
2	Cusatis, Gianluca
2	Günther, Frank C.
2	Guo, Tianfu
2	Hou, Thomas Yizhao
2	Huang, Owen
2	Huerta, Antonio
2	Jones, Kevontrez Kyvon
2	Kennedy, James M.
2	Kim, Youngjin
2	Klein, Patrick A.
2	Lua, Yuan Jie
2	Lyu, Yuhui
2	Moore, John A.
2	Qiu, Hai
2	Ramyar, Elham
2	Smolinski, Patrick
...and 182 more Co-Authors

all top 5

Serials

98	Computer Methods in Applied Mechanics and Engineering
56	Computational Mechanics
41	International Journal for Numerical Methods in Engineering
10	Journal of Computational Physics
10	Journal of the Mechanics and Physics of Solids
6	International Journal of Solids and Structures
5	Computers and Structures
5	Journal of Applied Mechanics
4	International Journal for Numerical Methods in Fluids
1	Computers and Fluids
1	Computer Physics Communications
1	Journal of Computational and Applied Mathematics
1	Journal of Statistical Planning and Inference
1	Mechanics Research Communications
1	SIAM Journal on Numerical Analysis
1	Finite Elements in Analysis and Design
1	Numerical Methods for Partial Differential Equations
1	Communications in Numerical Methods in Engineering
1	Advances in Computational Mathematics
1	CMES. Computer Modeling in Engineering & Sciences
1	Acta Mechanica Sinica

all top 5

Fields

214	Mechanics of deformable solids (74-XX)
64	Numerical analysis (65-XX)
47	Fluid mechanics (76-XX)
17	Partial differential equations (35-XX)
15	Computer science (68-XX)
8	Biology and other natural sciences (92-XX)
5	General and overarching topics; collections (00-XX)
5	Ordinary differential equations (34-XX)
5	Statistical mechanics, structure of matter (82-XX)
3	Classical thermodynamics, heat transfer (80-XX)
2	Statistics (62-XX)
1	Linear and multilinear algebra; matrix theory (15-XX)
1	Real functions (26-XX)
1	Dynamical systems and ergodic theory (37-XX)
1	Difference and functional equations (39-XX)
1	Approximations and expansions (41-XX)
1	Calculus of variations and optimal control; optimization (49-XX)
1	Probability theory and stochastic processes (60-XX)
1	Mechanics of particles and systems (70-XX)
1	Optics, electromagnetic theory (78-XX)
1	Quantum theory (81-XX)
1	Systems theory; control (93-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

249 Publications have been cited 10,359 times in5,304 Documents	Cited by ▼	Year ▼
Reproducing kernel particle methods. Zbl 0881.76072 Liu, Wing Kam;Jun, Sukky;Zhang, Yi Fei	1,098	1995
Nonlinear finite elements for continua and structures. Zbl 0959.74001 Belytschko, Ted;Liu, Wing Kam;Moran, Brian	614	2000
Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Zbl 0482.76039 Hughes, Thomas J. R.;Liu, Wing Kam;Zimmermann, Thomas K.	544	1981
Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Zbl 0918.73330 Chen, Jiun-Shyan;Pan, Chunhui;Wu, Cheng-Tang;Liu, Wing Kam	331	1996
Reproducing kernel particle methods for structural dynamics. Zbl 0840.73078 Liu, Wing Kam;Jun, Sukky;Li, Shaofan;Adee, Jonathan;Belytschko, Ted	330	1995
Moving least-square reproducing kernel methods. I: Methodology and convergence. Zbl 0883.65088 Liu, Wing Kam;Li, Shaofan;Belytschko, Ted	230	1997
Immersed finite element method. Zbl 1067.76576 Zhang, Lucy;Gerstenberger, Axel;Wang, Xiaodong;Liu, Wing Kam	223	2004
Meshfree particle methods. Zbl 1073.65002 Li, Shaofan;Liu, Wing Kam	210	2004
Coupling of atomistic and continuum simulations using a bridging scale decomposition. Zbl 1169.74635 Wagner, Gregory J.;Liu, Wing Kam	193	2003
Nonlinear finite elements for continua and structures. 2nd updated and extended ed. Zbl 1279.74002 Belytschko, Ted;Liu, Wing Kam;Moran, Brian;Elkhodary, Khalil	182	2013
Hourglass control in linear and nonlinear problems. Zbl 0522.73063 Belytschko, Ted;Ong, Jame Shau-Jen;Liu, Wing Kam;Kennedy, James M.	168	1984
Stress projection for membrane and shear locking in shell finite elements. Zbl 0581.73091 Belytschko, Ted;Stolarski, Henryk;Liu, Wing Kam;Carpenter, Nicholas;Ong, Jame Shau-Jen	161	1985
A unified stability analysis of meshless particle methods. Zbl 0972.74078 Belytschko, Ted;Guo, Yong;Liu, Wing Kam;Xiao, Shao Ping	161	2000
Finite element analysis of incompressible viscous flows by the penalty function formulation. Zbl 0412.76023 Hughes, Thomas J. R.;Liu, Wing Kam;Brooks, Alec	144	1979
Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Zbl 1436.74070 Liu, Zeliang;Bessa, M. A.;Liu, Wing Kam	139	2016
Nonlinear finite element analysis of shells. I. Three-dimensional shells. Zbl 0461.73061 Hughes, Thomas J. R.;Liu, Wing Kam	126	1981
Random field finite elements. Zbl 0597.73075 Liu, Wing Kam;Belytschko, Ted;Mani, A.	121	1986
Implicit-explicit finite elements in transient analysis: Stability theory. Zbl 0392.73076 Hughes, T. J. R.;Liu, W. K.	120	1978
Viscous flow with large free surface motion. Zbl 0655.76032 Huerta, Antonio;Liu, Wing Kam	109	1988
A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Zbl 1439.74014 Bessa, M. A.;Bostanabad, R.;Liu, Z.;Hu, A.;Apley, Daniel W.;Brinson, C.;Chen, W.;Liu, Wing Kam	108	2017
Immersed finite element method and its applications to biological systems. Zbl 1178.76232 Liu, Wing Kam;Liu, Yaling;Farrell, David;Zhang, Lucy;Wang, X. Sheldon;Fukui, Yoshio;Patankar, Neelesh;Zhang, Yongjie;Bajaj, Chandrajit;Lee, Junghoon;Hong, Juhee;Chen, Xinyu;Hsu, Huayi	103	2006
Wavelet and multiple scale reproducing kernel methods. Zbl 0885.76078 Liu, Wing Kam;Chen, Yijung	101	1995
Reproducing kernel element method. I: Theoretical formulation. Zbl 1060.74670 Liu, Wing Kam;Han, Weimin;Lu, Hongsheng;Li, Shaofan;Cao, Jian	97	2004
Smoothing and accelerated computations in the element free Galerkin method. Zbl 0862.73058 Belytschko, Ted;Krongauz, Yury;Fleming, Mark;Organ, Daniel;Liu, Wing Kam Snm	94	1996
Reproducing kernel hierarchical partition of unity. I: Formulation and theory. II: Applications. Zbl 0945.74079 Li, Shaofan;Liu, Wing Kam	93	1999
An introduction to computational nanomechanics and materials. Zbl 1079.74506 Liu, W. K.;Karpov, E. G.;Zhang, S.;Park, H. S.	93	2004
Extended immersed boundary method using FEM and RKPM. Zbl 1060.74676 Wang, Xiaodong;Liu, Wing Kam	91	2004
Generalized multiple scale reproducing kernel particle methods. Zbl 0896.76069 Liu, Wing Kam;Chen, Yijung;Uras, R. Aziz;Chang, Chin Tang	89	1996
Implicit-explicit finite elements in transient analysis: Implementation and numerical examples. Zbl 0392.73077 Hughes, T. J. R.;Liu, W. K.	87	1978
A meshfree unification: reproducing kernel peridynamics. Zbl 1398.74452 Bessa, M. A.;Foster, J. T.;Belytschko, T.;Liu, Wing Kam	82	2014
Finite-element methods for nonlinear elastodynamics which conserve energy. Zbl 0392.73075 Hughes, T. J. R.;Caughey, T. K.;Liu, W. K.	80	1978
Moving least-square reproducing kernel method. II: Fourier analysis. Zbl 0883.65089 Li, Shaofan;Liu, Wing Kam	72	1996
Finite element stabilization matrices - A unification approach. Zbl 0553.73065 Liu, Wingkam;Ong, Jame Shau-Jen;Uras, Rasim Aziz	69	1985
Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua. Zbl 0626.73076 Liu, Wing Kam;Chang, Herman;Chen, Jiun-Shyan;Belytschko, Ted	68	1988
Numerical simulations of large deformation of thin shell structures using meshfree methods. Zbl 0978.74087 Li, S.;Hao, W.;Liu, W. K.	68	2000
Nonlinear finite element analysis of shells. II. Two-dimensional shells. Zbl 0474.73093 Hughes, Thomas J. R.;Liu, Wing Kam	60	1981
Enrichment of the finite element method with the reproducing kernel particle method. Zbl 0920.73366 Liu, Wing Kam;Uras, R. A.;Chen, Y.	60	1997
Probabilistic finite elements for nonlinear structural dynamics. Zbl 0576.73066 Liu, Wing Kam;Belytschko, Ted;Mani, A.	59	1986
Meshless methods for shear-deformable beams and plates. Zbl 0959.74079 Donning, Brian M.;Liu, Wing Kam	59	1998
Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Zbl 1439.74063 Liu, Zeliang;Fleming, Mark;Liu, Wing Kam	58	2018
The extended finite element method for rigid particles in Stokes flow. Zbl 0998.76054 Wagner, G. J.;Moës, N.;Liu, W. K.;Belytschko, T.	58	2001
Multi-scale micromorphic theory for hierarchical materials. Zbl 1159.74314 Vernerey, Franck;Liu, Wing Kam;Moran, Brian	55	2007
Reproducing kernel element method. II: Globally conforming \(I^m/C^n\) hierarchies. Zbl 1093.74062 Li, Shaofan;Lu, Hongsheng;Han, Weimin;Liu, Wing Kam;Simkins, Daniel C.	53	2004
A multiscale projection method for the analysis of carbon nanotubes. Zbl 1079.74595 Qian, Dong;Wagner, Gregory J.;Liu, Wing Kam	52	2004
Synchronized reproducing kernel interpolant via multiple wavelet expansion. Zbl 0912.76057 Li, S.;Liu, W. K.	51	1998
A multiple-quadrature eight-mode hexahedral finite element for large deformation elastoplastic analysis. Zbl 0935.74068 Liu, Wing Kam;Guo, Yong;Tang, Sing;Belytschko, Ted	49	1998
Advances in multiple scale kernel particle methods. Zbl 0868.73091 Liu, W. K.;Chen, Y.;Chang, C. T.;Belytschko, T.	49	1996
Rheology of red blood cell aggregation by computer simulation. Zbl 1102.92010 Liu, Yaling;Liu, Wing Kam	49	2006
Resultant-stress degenerated-shell element. Zbl 0587.73113 Liu, Wing K.;Law, E. S.;Lam, D.;Belytschko, T.	48	1986
Implementation of boundary conditions for meshless methods. Zbl 0963.76068 Günther, Frank C.;Liu, Wing Kam	48	1998
Mathematical foundations of the immersed finite element method. Zbl 1178.74170 Liu, Wing Kam;Kim, Do Wan;Tang, Shaoqiang	47	2007
An arbitrary Lagrangian-Eulerian finite element method for path-dependent materials. Zbl 0585.73117 Liu, Wing Kam;Belytschko, Ted;Chang, Herman	46	1986
Application of essential boundary conditions in mesh-free methods: A corrected collocation method. Zbl 0965.76069 Wagner, Gregory J.;Liu, Wing Kam	44	2000
A Green’s function approach to deriving non-reflecting boundary conditions in molecular dynamics simulations. Zbl 1080.74050 Karpov, E. G.;Wagner, G. J.;Liu, Wing Kam	44	2005
Hierarchical enrichment for bridging scales and mesh-free boundary conditions. Zbl 1006.76073 Wagner, Gregory J.;Liu, Wing Kam	43	2001
Explicit reproducing kernel particle methods for large deformation problems. Zbl 0909.73088 Jun, Sukky;Liu, Wing Kam;Belytschko, Ted	43	1998
Multiresolution reproducing kernel particle method for computational fluid dynamics. Zbl 0880.76057 Liu, Wing Kam;Jun, Sukky;Sihling, Dirk Thomas;Chen, Yijung;Hao, Wei	42	1997
Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. Zbl 1090.74698 Li, Shaofan;Liu, Wing Kam;Rosakis, Ares J.;Belytschko, Ted;Hao, Wei	42	2002
Multiple-scale reproducing kernel particle methods for large deformation problems. Zbl 0916.73060 Liu, Wing Kam;Jun, Sukky	41	1998
Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering. Zbl 1506.68110 Saha, Sourav;Gan, Zhengtao;Cheng, Lin;Gao, Jiaying;Kafka, Orion L.;Xie, Xiaoyu;Li, Hengyang;Tajdari, Mahsa;Kim, H. Alicia;Liu, Wing Kam	37	2021
Mesh-free simulations of shear banding in large deformation. Zbl 0995.74082 Li, Shaofan;Hao, Wei;Liu, Wing Kam	36	2000
Three-dimensional bridging scale analysis of dynamic fracture. Zbl 1213.74267 Park, Harold S.;Karpov, Eduard G.;Klein, Patrick A.;Liu, Wing Kam	36	2005
Molecular dynamics boundary conditions for regular crystal lattices. Zbl 1079.74526 Wagner, Gregory J.;Karpov, Eduard G.;Liu, Wing Kam	35	2004
Reproducing kernel element method. III: Generalized enrichment and applications. Zbl 1060.74671 Lu, Hongsheng;Li, Shaofan;Simkins, Daniel C. jun.;Liu, Wing Kam;Cao, Jian	35	2004
Reproducing kernel element method. IV: Globally compatible \(C^n\) (\(n\geqslant 1\)) triangular hierarchy. Zbl 1093.74064 Simkins, Daniel C. jun.;Li, Shaofan;Lu, Hongsheng;Liu, Wing Kam	35	2004
A mathematical framework of the bridging scale method. Zbl 1117.74056 Tang, Shaoqiang;Hou, Thomas Y.;Liu, Wing Kam	35	2006
A stabilization matrix for the bilinear Mindlin plate element. Zbl 0474.73091 Belytschko, T.;Tsay, C. S.;Liu, W. K.	34	1981
Bridging multi-scale method for localization problems. Zbl 1060.74504 Kadowaki, Hiroshi;Liu, Wing Kam	34	2004
Admissible approximations for essential boundary conditions in the reproducing kernel particle method. Zbl 0889.73078 Gosz, J.;Liu, W. K.	34	1996
Multiresolution analysis for material design. Zbl 1118.74040 McVeigh, Cahal;Vernerey, Franck;Liu, Wing Kam;Brinson, L. Cate	34	2006
Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity. Zbl 1493.74017 Liu, Zeliang;Kafka, Orion L.;Yu, Cheng;Liu, Wing Kam	34	2018
An introduction and tutorial on multiple-scale analysis in solids. Zbl 1079.74508 Park, Harold S.;Liu, Wing Kam	33	2004
Linking microstructure and properties through a predictive multiresolution continuum. Zbl 1159.74311 McVeigh, Cahal;Liu, Wing Kam	33	2008
From virtual clustering analysis to self-consistent clustering analysis: a mathematical study. Zbl 1471.74079 Tang, Shaoqiang;Zhang, Lei;Liu, Wing Kam	32	2018
An improved reproducing kernel particle method for nearly incompressible finite elasticity. Zbl 0973.74088 Chen, Jiun-Shyan;Yoon, Sangpil;Wang, Hui-Ping;Liu, Wing Kam	32	2000
Bridging scale methods for nanomechanics and materials. Zbl 1116.74048 Liu, Wing Kam;Park, Harold S.;Qian, Dong;Karpov, Eduard G.;Kadowaki, Hiroshi;Wagner, Gregory J.	32	2006
Stability of multi-time step partitioned integrators for first-order finite element systems. Zbl 0599.65060 Belytschko, Ted;Smolinski, Patrick;Liu, Wing Kam	31	1985
Numerical simulations of strain localization in inelastic solids using mesh-free methods. Zbl 1052.74618 Li, Shaofan;Liu, Wing Kam	31	2000
A phonon heat bath approach for the atomistic and multiscale simulation of solids. Zbl 1194.74526 Karpov, E. G.;Park, H. S.;Liu, Wing Kam	30	2007
Clustering discretization methods for generation of material performance databases in machine learning and design optimization. Zbl 1470.74073 Li, Hengyang;Kafka, Orion L.;Gao, Jiaying;Yu, Cheng;Nie, Yinghao;Zhang, Lei;Tajdari, Mahsa;Tang, Shan;Guo, Xu;Li, Gang;Tang, Shaoqiang;Cheng, Gengdong;Liu, Wing Kam	30	2019
Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization. Zbl 1398.74053 Goury, Olivier;Amsallem, David;Bordas, Stéphane Pierre Alain;Liu, Wing Kam;Kerfriden, Pierre	30	2016
Efficient linear and nonlinear heat conduction with a quadrilateral element. Zbl 0542.65067 Liu, Wing Kam;Belytschko, Ted	29	1984
Mixed-time implicit-explicit finite elements for transient analysis. Zbl 0488.73071 Liu, W. K.;Belytschko, T.	29	1982
Multiple quadrature underintegrated finite elements. Zbl 0811.73063 Liu, Wing Kam;Hu, Yu-Kan;Belytschko, Ted	29	1994
Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics. Zbl 1135.92302 Liu, Yaling;Zhang, Lucy;Wang, Xiaodong;Liu, Wing Kam	29	2004
On computational issues of immersed finite element methods. Zbl 1158.74049 Wang, X. Sheldon;Zhang, L. T.;Liu, Wing Kam	28	2009
Maximum principle and convergence analysis for the meshfree point collocation method. Zbl 1155.65090 Kim, Do Wan;Liu, Wing Kam	27	2006
A parallelized meshfree method with boundary enrichment for large-scale CFD. Zbl 1060.76096 Zhang, Lucy T.;Wagner, Gregory J.;Liu, Wing K.	27	2002
The immersed/fictitious element method for fluid-structure interaction: Volumetric consistency, compressibility and thin members. Zbl 1159.74437 Wang, Hongwu;Chessa, Jack;Liu, Wing K.;Belytschko, Ted	27	2008
A micromorphic model for the multiple scale failure of heterogeneous materials. Zbl 1171.74312 Vernerey, Franck J.;Liu, Wing Kam;Moran, Brian;Olson, Gregory	27	2008
Self-consistent clustering analysis for multiscale modeling at finite strains. Zbl 1441.74309 Yu, Cheng;Kafka, Orion L.;Liu, Wing Kam	25	2019
A Petrov-Galerkin finite element method for the fractional advection-diffusion equation. Zbl 1439.65090 Lian, Yanping;Ying, Yuping;Tang, Shaoqiang;Lin, Stephen;Wagner, Gregory J.;Liu, Wing Kam	24	2016
A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110 Tang, Shaoqiang;Hou, Thomas Y.;Liu, Wing Kam	24	2006
Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing. Zbl 1471.74081 Yan, Wentao;Lin, Stephen;Kafka, Orion L.;Lian, Yanping;Yu, Cheng;Liu, Zeliang;Yan, Jinhui;Wolff, Sarah;Wu, Hao;Ndip-Agbor, Ebot;Mozaffar, Mojtaba;Ehmann, Kornel;Cao, Jian;Wagner, Gregory J.;Liu, Wing Kam	23	2018
Computer implementation aspects for fluid structure interaction problems. Zbl 0478.73061 Liu, Wing Kam;Ma, David C.	23	1982
A stabilized 3-D co-rotational formulation for geometrically nonlinear analysis of multi-layered composite shells. Zbl 0980.74066 Masud, A.;Tham, C. L.;Liu, W. K.	23	2000
Hierarchical deep-learning neural networks: finite elements and beyond. Zbl 07360501 Zhang, Lei;Cheng, Lin;Li, Hengyang;Gao, Jiaying;Yu, Cheng;Domel, Reno;Yang, Yang;Tang, Shaoqiang;Liu, Wing Kam	23	2021
Derivation of heterogeneous material laws via data-driven principal component expansions. Zbl 1467.74013 Yang, Hang;Guo, Xu;Tang, Shan;Liu, Wing Kam	23	2019
Phase field modeling of fracture in nonlinearly elastic solids via energy decomposition. Zbl 1440.74038 Tang, Shan;Zhang, Gang;Guo, Tian Fu;Guo, Xu;Liu, Wing Kam	22	2019
Implementation and application of a 9-node Lagrange shell element with spurious mode control. Zbl 0581.73089 Belytschko, Ted;Liu, Wing-Kam;Ong, Jame Shau-Jen;Lam, Dennis	22	1985
Extended tensor decomposition model reduction methods: training, prediction, and design under uncertainty. Zbl 1539.74553 Lu, Ye;Mojumder, Satyajit;Guo, Jiachen;Li, Yangfan;Liu, Wing Kam	2	2024
Solving diffusive equations by proper generalized decomposition with preconditioner. Zbl 1550.76201 Tang, Shaoqiang;Guan, Xinyi;Liu, Wing Kam	2	2024
Convolution hierarchical deep-learning neural network (C-HiDeNN) with graphics processing unit (GPU) acceleration. Zbl 1549.74561 Park, Chanwook;Lu, Ye;Saha, Sourav;Xue, Tianju;Guo, Jiachen;Mojumder, Satyajit;Apley, Daniel W.;Wagner, Gregory J.;Liu, Wing Kam	7	2023
JAX-FEM: a differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science. Zbl 1526.74068 Xue, Tianju;Liao, Shuheng;Gan, Zhengtao;Park, Chanwook;Xie, Xiaoyu;Liu, Wing Kam;Cao, Jian	6	2023
Convolution hierarchical deep-learning neural networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond. Zbl 1527.74082 Lu, Ye;Li, Hengyang;Zhang, Lei;Park, Chanwook;Mojumder, Satyajit;Knapik, Stefan;Sang, Zhongsheng;Tang, Shaoqiang;Apley, Daniel W.;Wagner, Gregory J.;Liu, Wing Kam	5	2023
Convolution hierarchical deep-learning neural network tensor decomposition (C-HiDeNN-TD) for high-resolution topology optimization. Zbl 1524.74386 Li, Hengyang;Knapik, Stefan;Li, Yangfan;Park, Chanwook;Guo, Jiachen;Mojumder, Satyajit;Lu, Ye;Chen, Wei;Apley, Daniel W.;Liu, Wing Kam	4	2023
Deep learning discrete calculus (DLDC): a family of discrete numerical methods by universal approximation for STEM education to frontier research. Zbl 1546.74087 Saha, Sourav;Park, Chanwook;Knapik, Stefan;Guo, Jiachen;Huang, Owen;Liu, Wing Kam	2	2023
Isogeometric convolution hierarchical deep-learning neural network: isogeometric analysis with versatile adaptivity. Zbl 1539.74492 Zhang, Lei;Park, Chanwook;Lu, Ye;Li, Hengyang;Mojumder, Satyajit;Saha, Sourav;Guo, Jiachen;Li, Yangfan;Abbott, Trevor;Wagner, Gregory J.;Tang, Shaoqiang;Liu, Wing Kam	2	2023
HiDeNN-FEM: a seamless machine learning approach to nonlinear finite element analysis. Zbl 1523.74175 Liu, Yingjian;Park, Chanwook;Lu, Ye;Mojumder, Satyajit;Liu, Wing Kam;Qian, Dong	1	2023
HiDeNN-TD: reduced-order hierarchical deep learning neural networks. Zbl 1507.65285 Zhang, Lei;Lu, Ye;Tang, Shaoqiang;Liu, Wing Kam	18	2022
Mechanistically informed data-driven modeling of cyclic plasticity via artificial neural networks. Zbl 1507.74082 Liu, Daoping;Yang, Hang;Elkhodary, K. I.;Tang, Shan;Liu, Wing Kam;Guo, Xu	8	2022
Concurrent \(n\)-scale modeling for non-orthogonal woven composite. Zbl 1501.74069 Gao, Jiaying;Mojumder, Satyajit;Zhang, Weizhao;Li, Hengyang;Suarez, Derick;He, Chunwang;Cao, Jian;Liu, Wing Kam	3	2022
Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering. Zbl 1506.68110 Saha, Sourav;Gan, Zhengtao;Cheng, Lin;Gao, Jiaying;Kafka, Orion L.;Xie, Xiaoyu;Li, Hengyang;Tajdari, Mahsa;Kim, H. Alicia;Liu, Wing Kam	37	2021
Hierarchical deep-learning neural networks: finite elements and beyond. Zbl 07360501 Zhang, Lei;Cheng, Lin;Li, Hengyang;Gao, Jiaying;Yu, Cheng;Domel, Reno;Yang, Yang;Tang, Shaoqiang;Liu, Wing Kam	23	2021
Multiresolution clustering analysis for efficient modeling of hierarchical material systems. Zbl 1468.74092 Yu, Cheng;Kafka, Orion L.;Liu, Wing Kam	9	2021
MAP123-EPF: a mechanistic-based data-driven approach for numerical elastoplastic modeling at finite strain. Zbl 1506.74069 Tang, Shan;Yang, Hang;Qiu, Hai;Fleming, Mark;Liu, Wing Kam;Guo, Xu	8	2021
Image-based modelling for adolescent idiopathic scoliosis: mechanistic machine learning analysis and prediction. Zbl 1506.92016 Tajdari, Mahsa;Pawar, Aishwarya;Li, Hengyang;Tajdari, Farzam;Maqsood, Ayesha;Cleary, Emmett;Saha, Sourav;Zhang, Yongjie Jessica;Sarwark, John F.;Liu, Wing Kam	4	2021
Efficient multiscale modeling for woven composites based on self-consistent clustering analysis. Zbl 1442.74057 Han, Xinxing;Gao, Jiaying;Fleming, Mark;Xu, Chenghai;Xie, Weihua;Meng, Songhe;Liu, Wing Kam	17	2020
MAP123-EP: a mechanistic-based data-driven approach for numerical elastoplastic analysis. Zbl 1442.74044 Tang, Shan;Li, Ying;Qiu, Hai;Yang, Hang;Saha, Sourav;Mojumder, Satyajit;Liu, Wing Kam;Guo, Xu	13	2020
Adaptive hyper reduction for additive manufacturing thermal fluid analysis. Zbl 1506.76143 Lu, Ye;Jones, Kevontrez Kyvon;Gan, Zhengtao;Liu, Wing Kam	7	2020
Analytical expression of RKPM shape functions. Zbl 1467.74094 Zhang, Lei;Tang, Shaoqiang;Liu, Wing Kam	4	2020
Clustering discretization methods for generation of material performance databases in machine learning and design optimization. Zbl 1470.74073 Li, Hengyang;Kafka, Orion L.;Gao, Jiaying;Yu, Cheng;Nie, Yinghao;Zhang, Lei;Tajdari, Mahsa;Tang, Shan;Guo, Xu;Li, Gang;Tang, Shaoqiang;Cheng, Gengdong;Liu, Wing Kam	30	2019
Self-consistent clustering analysis for multiscale modeling at finite strains. Zbl 1441.74309 Yu, Cheng;Kafka, Orion L.;Liu, Wing Kam	25	2019
Derivation of heterogeneous material laws via data-driven principal component expansions. Zbl 1467.74013 Yang, Hang;Guo, Xu;Tang, Shan;Liu, Wing Kam	23	2019
Phase field modeling of fracture in nonlinearly elastic solids via energy decomposition. Zbl 1440.74038 Tang, Shan;Zhang, Gang;Guo, Tian Fu;Guo, Xu;Liu, Wing Kam	22	2019
MAP123: a data-driven approach to use 1D data for 3D nonlinear elastic materials modeling. Zbl 1442.65417 Tang, Shan;Zhang, Gang;Yang, Hang;Li, Ying;Liu, Wing Kam;Guo, Xu	19	2019
Data science for finite strain mechanical science of ductile materials. Zbl 1467.74017 Shakoor, Modesar;Kafka, Orion L.;Yu, Cheng;Liu, Wing Kam	16	2019
Fast calculation of interaction tensors in clustering-based homogenization. Zbl 1467.74100 Zhang, Lei;Tang, Shaoqiang;Yu, Cheng;Zhu, Xi;Liu, Wing Kam	13	2019
Powder-scale multi-physics modeling of multi-layer multi-track selective laser melting with sharp interface capturing method. Zbl 1468.74014 Wang, Zekun;Yan, Wentao;Liu, Wing Kam;Liu, Moubin	10	2019
Fracture in tension-compression-asymmetry solids via phase field modeling. Zbl 1442.74025 Zhang, Gang;Guo, Tian Fu;Guo, Xu;Tang, Shan;Fleming, Mark;Liu, Wing Kam	8	2019
A Computational Mechanics special issue on: Data-driven modeling and simulation – theory, methods, and applications. Zbl 1476.00073	6	2019
An inverse modeling approach for predicting filled rubber performance. Zbl 1442.65141 Gao, Jiaying;Shakoor, Modesar;Jinnai, Hiroshi;Kadowaki, Hiroshi;Seta, Eisuke;Liu, Wing Kam	5	2019
A data-driven multiscale theory for modeling damage and fracture of composite materials. Zbl 1428.74229 Shakoor, Modesar;Gao, Jiaying;Liu, Zeliang;Liu, Wing Kam	2	2019
A sequential homogenization of multi-coated micromechanical model for functionally graded interphase composites. Zbl 1465.74141 Cheng, Yi;Cheng, Hui;Zhang, Kaifu;Jones, Kevontrez Kyvon;Gao, Jiaying;Hu, Junshan;Li, Hailin;Liu, Wing Kam	1	2019
Large eddy simulation of turbulent flow over and through a rough permeable bed. Zbl 1410.76098 Lian, Y. P.;Dallmann, J.;Sonin, B.;Roche, K. R.;Liu, W. K.;Packman, A. I.;Wagner, G. J.	1	2019
Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Zbl 1439.74063 Liu, Zeliang;Fleming, Mark;Liu, Wing Kam	58	2018
Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity. Zbl 1493.74017 Liu, Zeliang;Kafka, Orion L.;Yu, Cheng;Liu, Wing Kam	34	2018
From virtual clustering analysis to self-consistent clustering analysis: a mathematical study. Zbl 1471.74079 Tang, Shaoqiang;Zhang, Lei;Liu, Wing Kam	32	2018
Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing. Zbl 1471.74081 Yan, Wentao;Lin, Stephen;Kafka, Orion L.;Lian, Yanping;Yu, Cheng;Liu, Zeliang;Yan, Jinhui;Wolff, Sarah;Wu, Hao;Ndip-Agbor, Ebot;Mozaffar, Mojtaba;Ehmann, Kornel;Cao, Jian;Wagner, Gregory J.;Liu, Wing Kam	23	2018
Uncertainty quantification in multiscale simulation of woven fiber composites. Zbl 1440.74102 Bostanabad, Ramin;Liang, Biao;Gao, Jiaying;Liu, Wing Kam;Cao, Jian;Zeng, Danielle;Su, Xuming;Xu, Hongyi;Li, Yang;Chen, Wei	21	2018
Enriched reproducing kernel particle method for fractional advection-diffusion equation. Zbl 1404.65070 Ying, Yuping;Lian, Yanping;Tang, Shaoqiang;Liu, Wing Kam	16	2018
A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing. Zbl 1470.74072 Lian, Yanping;Lin, Stephen;Yan, Wentao;Liu, Wing Kam;Wagner, Gregory J.	10	2018
An integrated process-structure-property modeling framework for additive manufacturing. Zbl 1440.74147 Yan, Wentao;Lian, Yanping;Yu, Cheng;Kafka, Orion L.;Liu, Zeliang;Liu, Wing Kam;Wagner, Gregory J.	7	2018
Special issue on additive manufacturing: progress in modeling and simulation with experimental validations in additive manufacturing. Zbl 1405.00023	1	2018
A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Zbl 1439.74014 Bessa, M. A.;Bostanabad, R.;Liu, Z.;Hu, A.;Apley, Daniel W.;Brinson, C.;Chen, W.;Liu, Wing Kam	108	2017
High-order central difference scheme for Caputo fractional derivative. Zbl 1439.65101 Ying, Yuping;Lian, Yanping;Tang, Shaoqiang;Liu, Wing Kam	17	2017
An enriched finite element method to fractional advection-diffusion equation. Zbl 1429.65171 Luan, Shengzhi;Lian, Yanping;Ying, Yuping;Tang, Shaoqiang;Wagner, Gregory J.;Liu, Wing Kam	11	2017
A meshfree method for the fractional advection-diffusion equation. Zbl 1404.65208 Lian, Yanping;Wagner, Gregory J.;Liu, Wing Kam	8	2017
An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications. Zbl 1439.74442 Lin, Stephen;Smith, Jacob;Liu, Wing Kam;Wagner, Gregory J.	2	2017
Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Zbl 1436.74070 Liu, Zeliang;Bessa, M. A.;Liu, Wing Kam	139	2016
Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization. Zbl 1398.74053 Goury, Olivier;Amsallem, David;Bordas, Stéphane Pierre Alain;Liu, Wing Kam;Kerfriden, Pierre	30	2016
A Petrov-Galerkin finite element method for the fractional advection-diffusion equation. Zbl 1439.65090 Lian, Yanping;Ying, Yuping;Tang, Shaoqiang;Lin, Stephen;Wagner, Gregory J.;Liu, Wing Kam	24	2016
Linking process, structure, property, and performance for metal-based additive manufacturing: computational approaches with experimental support. Zbl 1382.74140 Smith, Jacob;Xiong, Wei;Yan, Wentao;Lin, Stephen;Cheng, Puikei;Kafka, Orion L.;Wagner, Gregory J.;Cao, Jian;Liu, Wing Kam	18	2016
Thermodynamically consistent microstructure prediction of additively manufactured materials. Zbl 1382.74126 Smith, Jacob;Xiong, Wei;Cao, Jian;Liu, Wing Kam	10	2016
Differential operator multiplication method for fractional differential equations. Zbl 1400.34013 Tang, Shaoqiang;Ying, Yuping;Lian, Yanping;Lin, Stephen;Yang, Yibo;Wagner, Gregory J.;Liu, Wing Kam	10	2016
Mechanics of hybrid polymer composites: analytical and computational study. Zbl 1382.74035 Tavares, Rodrigo P.;Melro, António R.;Bessa, Miguel A.;Turon, Albert;Liu, Wing K.;Camanho, Pedro P.	3	2016
Preface: Special issue of Computational Mechanics on “Connecting multiscale mechanics to complex material design”. Zbl 1333.00053	1	2016
A statistical descriptor based volume-integral micromechanics model of heterogeneous material with arbitrary inclusion shape. Zbl 1329.74026 Liu, Zeliang;Moore, John A.;Aldousari, Saad M.;Hedia, Hassan S.;Asiri, Saeed A.;Liu, Wing Kam	14	2015
Predicting band structure of 3D mechanical metamaterials with complex geometry via XFEM. Zbl 1334.74100 Zhao, Jifeng;Li, Ying;Liu, Wing Kam	9	2015
Multiscale modeling of electron beam and substrate interaction: a new heat source model. Zbl 1329.74077 Yan, Wentao;Smith, Jacob;Ge, Wenjun;Lin, Feng;Liu, Wing Kam	8	2015
A semi-numerical algorithm for instability of compressible multilayered structures. Zbl 1329.74289 Tang, Shan;Yang, Yang;Peng, Xiang He;Liu, Wing Kam;Huang, Xiao Xu;Elkhodary, Khalil	2	2015
Advancements in multiresolution analysis. Zbl 1352.74411 Moore, John A.;Li, Ying;O’Connor, Devin T.;Stroberg, Wylie;Liu, Wing Kam	1	2015
Particle method modeling of nonlocal multiresolution continua. Zbl 1342.76097 Dai, Zili;Bessa, Miguel A.;Li, Shaofan;Liu, Wing Kam	1	2015
A meshfree unification: reproducing kernel peridynamics. Zbl 1398.74452 Bessa, M. A.;Foster, J. T.;Belytschko, T.;Liu, Wing Kam	82	2014
Nonlinear finite elements for continua and structures. 2nd updated and extended ed. Zbl 1279.74002 Belytschko, Ted;Liu, Wing Kam;Moran, Brian;Elkhodary, Khalil	182	2013
Concurrent multiresolution finite element: formulation and algorithmic aspects. Zbl 1398.74410 Tang, Shan;Kopacz, Adrian M.;Chan O’Keeffe, Stephanie;Olson, Gregory B.;Liu, Wing Kam	7	2013
Archetype-blending continuum theory. Zbl 1297.74087 Elkhodary, Khalil I.;Steven Greene, M.;Tang, Shan;Belytschko, Ted;Liu, Wing K.	5	2013
A generalized uncertainty propagation criterion from benchmark studies of microstructured material systems. Zbl 1297.74011 Greene, M. Steven;Xu, Hongyi;Tang, Shan;Chen, Wei;Liu, Wing Kam	3	2013
Two-scale mechanism-based theory of nonlinear viscoelasticity. Zbl 1244.74098 Tang, Shan;Greene, M. Steven;Liu, Wing Kam	15	2012
A renormalization approach to model interaction in microstructured solids: application to porous elastomer. Zbl 1253.74071 Tang, Shan;Greene, M. Steven;Liu, Wing Kam	5	2012
The immersed molecular finite element method. Zbl 1253.76060 Kopacz, Adrian M.;Patankar, Neelesh A.;Liu, Wing K.	2	2012
Characterization of heterogeneous solids via wave methods in computational microelasticity. Zbl 1270.74036 Gonella, Stefano;Greene, M. Steven;Liu, Wing Kam	9	2011
Conforming local meshfree method. Zbl 1235.74375 Tian, Rong;To, Albert C.;Liu, Wing Kam	9	2011
A domain-reduction approach to bridging-scale simulation of one-dimensional nanostructures. Zbl 1398.74049 Qian, Dong;Phadke, Manas;Karpov, Eduard;Liu, Wing Kam	3	2011
Denoising methods for thermomechanical decomposition for quasi-equilibrium molecular dynamics simulations. Zbl 1228.74118 To, Albert C.;Fu, Yao;Liu, Wing Kam	2	2011
A level set approach for optimal design of smart energy harvesters. Zbl 1231.74358 Chen, Shikui;Gonella, Stefano;Chen, Wei;Liu, Wing Kam	19	2010
Multiscale methods for mechanical science of complex materials: bridging from quantum to stochastic multiresolution continuum. Zbl 1197.74007 Liu, Wing Kam;Qian, Dong;Gonella, Stefano;Li, Shaofan;Chen, Wei;Chirputkar, Shardool	16	2010
Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory. Zbl 1225.74008 Greene, M. Steven;Liu, Yu;Chen, Wei;Liu, Wing Kam	14	2010
A multiresolution continuum simulation of the ductile fracture process. Zbl 1200.74127 Tian, Rong;Chan, Stephanie;Tang, Shan;Kopacz, Adrian M.;Wang, Jian-Sheng;Jou, Herng-Jeng;Siad, Larbi;Lindgren, Lars-Erik;Olson, Gregory B.;Liu, Wing Kam	14	2010
Multiresolution continuum modeling of micro-void assisted dynamic adiabatic shear band propagation. Zbl 1193.74124 Mcveigh, Cahal;Liu, Wing Kam	13	2010
On computational issues of immersed finite element methods. Zbl 1158.74049 Wang, X. Sheldon;Zhang, L. T.;Liu, Wing Kam	28	2009
Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting. Zbl 1177.74155 Gonella, Stefano;To, Albert C.;Liu, Wing Kam	19	2009
Complexity science of multiscale materials via stochastic computations. Zbl 1176.74058 Liu, Wing Kam;Siad, Larbi;Tian, Rong;Lee, Sanghoon;Lee, Dockjin;Yin, Xiaolei;Chen, Wei;Chan, Stephanie;Olson, Gregory B.;Lindgen, Lars-Erik;Horstemeyer, Mark F.;Chang, Yoon-Suk;Choi, Jae-Boong;Kim, Young Jin	15	2009
Multiresolution modeling of ductile reinforced brittle composites. Zbl 1170.74321 McVeigh, Cahal;Liu, Wing Kam	13	2009
Multi-length scale micromorphic process zone model. Zbl 1166.74031 Vernerey, Franck;Liu, Wing Kam;Moran, Brian;Olson, Gregory	8	2009
Explicit numerical study of softening in porous ductile solids. Zbl 1258.74069 Siad, Larbi;Liu, Wing Kam;Benabbes, Anouar	1	2009
Multi-scale solid oxide fuel cell materials modeling. Zbl 1197.74027 Kim, Ji Hoon;Liu, Wing Kam;Lee, Christopher	1	2009
Linking microstructure and properties through a predictive multiresolution continuum. Zbl 1159.74311 McVeigh, Cahal;Liu, Wing Kam	33	2008
The immersed/fictitious element method for fluid-structure interaction: Volumetric consistency, compressibility and thin members. Zbl 1159.74437 Wang, Hongwu;Chessa, Jack;Liu, Wing K.;Belytschko, Ted	27	2008
A micromorphic model for the multiple scale failure of heterogeneous materials. Zbl 1171.74312 Vernerey, Franck J.;Liu, Wing Kam;Moran, Brian;Olson, Gregory	27	2008
Predictive multiscale theory for design of heterogeneous materials. Zbl 1304.74016 Liu, Wing Kam;McVeigh, Cahal	21	2008
Statistical volume element method for predicting microstructure-constitutive property relations. Zbl 1194.74291 Yin, Xiaolei;Chen, Wei;To, Albert;McVeigh, Cahal;Liu, Wing Kam	19	2008
Immersed finite element method for rigid body motions in the incompressible Navier-Stokes flow. Zbl 1158.76352 Lee, Tae-Rin;Chang, Yoon-Suk;Choi, Jae-Boong;Kim, Do Wan;Liu, Wing Kam;Kim, Young-Jin	17	2008
Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heat. Zbl 1195.74297 Qian, Dong;Eason, Thomas;Li, Shaofan;Liu, Wing Kam	9	2008
Concurrent quantum/continuum coupling analysis of nanostructures. Zbl 1159.74304 Qian, Dong;Liu, Wing Kam;Zheng, Qingjin	8	2008
Materials integrity in microsystems: a framework for a petascale predictive-science-based multiscale modeling and simulation system. Zbl 1421.74084 To, Albert C.;Liu, Wing Kam;Olson, Gregory B.;Belytschko, Ted;Chen, Wei;Shephard, Mark S.;Chung, Yip-Wah;Ghanem, Roger;Voorhees, Peter W.;Seidman, David N.;Wolverton, Chris;Chen, J. S.;Moran, Brian;Freeman, Arthur J.;Tian, Rong;Luo, Xiaojuan;Lautenschlager, Eric;Challoner, A. Dorian	6	2008
A finite temperature continuum theory based on interatomic potential in crystalline solids. Zbl 1239.74005 To, Albert C.;Liu, Wing Kam;Kopacz, Adrian	6	2008
Manipulation of nanoparticles and biomolecules by electric field and surface tension. Zbl 1158.76457 Liu, Yaling;Oh, Kieseok;Bai, John G.;Chang, Cheng-Ling;Yeo, Woonhoog;Chung, Jae-Hyun;Lee, Kyong-Hoon;Liu, Wing Kam	4	2008
Multiple time scale method for atomistic simulations. Zbl 1257.74178 Medyanik, Sergey N.;Liu, Wing Kam	2	2008
Simulation and prediction of endothelial cell adhesion modulated by molecular engineering. Zbl 1158.76455 Kopacz, Adrian Marcin;Liu, Wing Kam;Liu, Shu Q.	2	2008
...and 149 more Documents

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Cited by 7,805 Authors

182	Liu, Wing Kam
116	Belytschko, Ted Bohdan
90	Tezduyar, Tayfun E.
76	Takizawa, Kenji
74	Liu, Gui-Rong
70	Chen, Jiun-Shyan
68	Bazilevs, Yuri
56	Li, Shaofan
51	Rabczuk, Timon
50	Liew, Kim Meow
46	Hughes, Thomas J. R.
46	Wang, Dongdong
38	Tang, Shaoqiang
35	Wriggers, Peter
32	Bonet, Javier
32	Oñate Ibáñez de Navarra, Eugenio
30	Dehghan Takht Fooladi, Mehdi
30	Hsu, Ming-Chen
30	Li, Xiaolin
28	Fish, Jacob
27	Areias, Pedro M. A.
27	Combescure, Alain
26	Wagner, Gregory J.
24	Li, Guangyao
24	Zhang, Lu-Wen
23	Gil, Antonio J.
23	Tang, Shan
23	Wang, Lihua
23	Yan, Jinhui
22	Belinha, Jorge
22	Zhang, Zhiqian
22	Zhuang, Xiaoying
21	Wick, Thomas
20	Bordas, Stéphane Pierre Alain
20	Natal Jorge, Renato Manuel
20	Wen, Pihua
20	Wu, Cheng-Tang
20	Zhang, Lucy T.
19	Betsch, Peter
19	Gravouil, Anthony
19	Huerta, Antonio
19	Idelsohn, Sergio Rodolfo
19	Lian, Yanping
19	Wall, Wolfgang A.
19	Zhang, Aman
18	Han, Xu
18	Masud, Arif
18	Schillinger, Dominik
18	Steinmann, Paul
17	Duan, Qinglin
17	Kiendl, Josef
17	Ouyang, Jie
17	Zhang, Xiong
17	Zheng, Hong
16	Benson, David J.
16	Cheng, Yumin
16	Cueto, Elias
16	Gu, Yuantong
16	Guo, Xu
16	Lee, Chun Hean
16	Oden, John Tinsley
16	Qian, Dong
16	Reese, Stefanie
16	Sun, WaiChing
16	Wüchner, Roland
16	Zhang, Chuanzeng
16	Zhang, GuiYong
15	Bletzinger, Kai-Uwe
15	Cruchaga, Marcela A.
15	Hillman, Michael C.
15	Li, Xikui
15	Park, Harold S.
14	Cui, Xiangyang
14	Doblaré, Manuel
14	Du, Qiang
14	Fries, Thomas-Peter
14	Hu, Wei
14	Nguyen-Xuan, Hung
14	Noels, Ludovic
14	Simo, Juan Carlos
14	Tian, Xiaochuan
14	To, Albert C.
14	Vernerey, Franck J.
14	Waisman, Haim
14	Wei, Guowei
14	Zhang, Lei
13	Abbaszadeh, Mostafa
13	Bui, Tinh Quoc
13	Chen, Wei
13	Khoei, Amir R.
13	Krysl, Petr
13	Liu, Moubin
13	Liu, Yan
13	Park, Kwang-Chun
13	Reddy, Junuthula Narasimha
13	Zhou, Kun
12	Cao, Jian
12	Casquero, Hugo
12	Chi, Sheng-Wei
12	Griffith, Boyce E.
...and 7,705 more Authors

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Cited in 221 Serials

1,446	Computer Methods in Applied Mechanics and Engineering
670	International Journal for Numerical Methods in Engineering
609	Computational Mechanics
338	Engineering Analysis with Boundary Elements
327	Journal of Computational Physics
113	Computers and Fluids
97	Applied Mathematical Modelling
94	International Journal of Computational Methods
76	International Journal for Numerical Methods in Fluids
73	European Journal of Mechanics. A. Solids
72	Computers & Mathematics with Applications
58	Applied Mathematics and Computation
57	Acta Mechanica
52	Journal of Computational and Applied Mathematics
50	Communications in Numerical Methods in Engineering
47	Journal of the Mechanics and Physics of Solids
38	Archives of Computational Methods in Engineering
37	Mathematical Problems in Engineering
33	Computer Physics Communications
33	Engineering Computations
32	Journal of Scientific Computing
31	Acta Mechanica Sinica
30	International Journal of Solids and Structures
30	Applied Numerical Mathematics
30	International Journal of Structural Stability and Dynamics
28	International Journal of Engineering Science
25	International Journal for Computational Methods in Engineering Science and Mechanics
23	M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
22	Journal of Fluid Mechanics
20	Mathematics and Computers in Simulation
20	Meccanica
20	International Journal of Computational Fluid Dynamics
18	International Journal for Numerical Methods in Biomedical Engineering
17	International Journal of Plasticity
17	Applied Mathematics and Mechanics. (English Edition)
16	Numerical Methods for Partial Differential Equations
15	Archive of Applied Mechanics
15	Advances in Applied Mathematics and Mechanics
14	Computational and Applied Mathematics
14	International Journal of Fracture
13	Wave Motion
13	ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
12	Mathematics and Mechanics of Solids
11	Numerische Mathematik
11	International Journal of Numerical Methods for Heat & Fluid Flow
11	Communications in Nonlinear Science and Numerical Simulation
11	Communications in Computational Physics
10	International Journal of Computer Mathematics
10	Multibody System Dynamics
9	SIAM Journal on Numerical Analysis
9	Nonlinear Dynamics
9	European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8	International Journal for Numerical and Analytical Methods in Geomechanics
8	Journal of Applied Mathematics
7	Journal of Engineering Mathematics
6	International Journal of Heat and Mass Transfer
6	Mathematical Methods in the Applied Sciences
6	Mechanics Research Communications
6	Applied Mathematics Letters
6	Numerical Algorithms
6	SIAM Journal on Scientific Computing
6	Advances in Computational Mathematics
6	European Journal of Mechanics. B. Fluids
6	Computational Geosciences
6	Sādhanā
6	GAMM-Mitteilungen
5	Bulletin of Mathematical Biology
5	Computer Aided Geometric Design
5	Continuum Mechanics and Thermodynamics
5	Multiscale Modeling & Simulation
5	AMM. Applied Mathematics and Mechanics. (English Edition)
4	Mathematical and Computer Modelling
4	Advances in Engineering Software
4	Structural and Multidisciplinary Optimization
4	International Journal of Numerical Analysis and Modeling
4	Journal of Theoretical Biology
4	Computational Methods for Differential Equations
4	Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3	Mathematics of Computation
3	Numerical Functional Analysis and Optimization
3	Japan Journal of Industrial and Applied Mathematics
3	Physics of Fluids
3	Discrete and Continuous Dynamical Systems. Series B
3	Computational & Mathematical Methods in Medicine
3	Mathematical Modelling of Natural Phenomena
3	SIAM Journal on Imaging Sciences
3	Science China. Technological Sciences
3	Journal of Computational Physics: X
2	International Journal of Modern Physics B
2	Archives of Mechanics
2	Archive for Rational Mechanics and Analysis
2	Communications on Pure and Applied Mathematics
2	Journal of Mathematical Analysis and Applications
2	Journal of Mathematical Biology
2	Physics Letters. A
2	ZAMP. Zeitschrift für angewandte Mathematik und Physik
2	Chaos, Solitons and Fractals
2	BIT
2	Computing
2	Journal of Computational Mathematics
...and 121 more Serials

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Cited in 39 Fields

3,620	Mechanics of deformable solids (74-XX)
2,223	Numerical analysis (65-XX)
1,406	Fluid mechanics (76-XX)
398	Partial differential equations (35-XX)
205	Biology and other natural sciences (92-XX)
139	Classical thermodynamics, heat transfer (80-XX)
109	Computer science (68-XX)
108	Statistical mechanics, structure of matter (82-XX)
81	Mechanics of particles and systems (70-XX)
48	Probability theory and stochastic processes (60-XX)
48	Optics, electromagnetic theory (78-XX)
41	Calculus of variations and optimal control; optimization (49-XX)
41	Statistics (62-XX)
31	Geophysics (86-XX)
29	Ordinary differential equations (34-XX)
24	Operations research, mathematical programming (90-XX)
22	Integral equations (45-XX)
21	Real functions (26-XX)
18	Dynamical systems and ergodic theory (37-XX)
17	Approximations and expansions (41-XX)
15	Systems theory; control (93-XX)
12	Quantum theory (81-XX)
10	Functional analysis (46-XX)
7	Harmonic analysis on Euclidean spaces (42-XX)
6	Linear and multilinear algebra; matrix theory (15-XX)
6	Differential geometry (53-XX)
6	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5	Information and communication theory, circuits (94-XX)
4	Global analysis, analysis on manifolds (58-XX)
3	Measure and integration (28-XX)
3	Functions of a complex variable (30-XX)
3	Potential theory (31-XX)
3	Operator theory (47-XX)
2	General and overarching topics; collections (00-XX)
2	History and biography (01-XX)
2	Combinatorics (05-XX)
1	Difference and functional equations (39-XX)
1	Integral transforms, operational calculus (44-XX)
1	Relativity and gravitational theory (83-XX)

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