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## Silling, Stewart A.

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 Author ID: silling.stewart-a Published as: Silling, S. A.; Silling, Stewart A. External Links: MGP
 Documents Indexed: 27 Publications since 1987, including 1 Book
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#### Co-Authors

 13 single-authored 5 Weckner, Olaf 4 Askari, Ebrahim 4 Bobaru, Florin 3 Epton, Michael A. 3 Lehoucq, Richard B. 3 Xu, Jifeng 2 Foster, John T. jun. 2 Geubelle, Philippe H. 1 Abeyaratne, Rohan C. 1 Alves, Leonardo Frota 1 Askari, Abe 1 Breitenfeld, M. S. 1 Brunk, Gerd 1 Horgan, Cornelius Oliver 1 Parks, Michael L. 1 Plimpton, Steven J. 1 Warren, Thomas L. 1 Yang, Mijia
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#### Serials

 8 Journal of Elasticity 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of the Mechanics and Physics of Solids 3 International Journal for Numerical Methods in Engineering 2 Journal of Applied Mechanics 1 Computer Physics Communications 1 International Journal of Non-Linear Mechanics 1 International Journal of Solids and Structures 1 Journal of Computational Physics 1 Mathematics and Mechanics of Solids 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Fracture 1 Advances in Applied Mathematics (Boca Raton)
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#### Fields

 26 Mechanics of deformable solids (74-XX) 4 Numerical analysis (65-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 General and overarching topics; collections (00-XX) 1 Partial differential equations (35-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

24 Publications have been cited 1,279 times in 475 Documents Cited by Year
Reformulation of elasticity theory for discontinuities and long-range forces. Zbl 0970.74030
Silling, S. A.
2000
Peridynamic states and constitutive modeling. Zbl 1120.74003
Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E.
2007
Convergence of peridynamics to classical elasticity theory. Zbl 1159.74316
Silling, S. A.; Lehoucq, R. B.
2008
Convergence, adaptive refinement, and scaling in 1D peridynamics. Zbl 1156.74399
Bobaru, Florin; Yang, Mijia; Alves, Leonardo Frota; Silling, Stewart A.; Askari, Ebrahim; Xu, Jifeng
2009
Linearized theory of peridynamic states. Zbl 1188.74008
Silling, S. A.
2010
Deformation of a peridynamic bar. Zbl 1061.74031
Silling, S. A.; Zimmermann, M.; Abeyaratne, R.
2003
Peridynamic modeling of membranes and fibers. Zbl 1349.74231
Silling, S. A.; Bobaru, F.
2005
Crack nucleation in a peridynamic solid. Zbl 1425.74045
Silling, S. A.; Weckner, O.; Askari, E.; Bobaru, F.
2010
A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Zbl 1236.74012
Warren, Thomas L.; Silling, Stewart A.; Askari, Abe; Weckner, Olaf; Epton, Michael A.; Xu, Jifeng
2009
Implementing peridynamics within a molecular dynamics code. Zbl 1197.82014
Parks, Michael L.; Lehoucq, Richard B.; Plimpton, Steven J.; Silling, Stewart A.
2008
Force flux and the peridynamic stress tensor. Zbl 1171.74319
Lehoucq, R. B.; Silling, S. A.
2008
Non-ordinary state-based peridynamic analysis of stationary crack problems. Zbl 1296.74099
Breitenfeld, M. S.; Geubelle, P. H.; Weckner, O.; Silling, S. A.
2014
Viscoplasticity using peridynamics. Zbl 1183.74035
Foster, J. T.; Silling, S. A.; Chen, W. W.
2010
Handbook of peridynamic modeling. Zbl 1351.74001
Bobaru, Florin (ed.); Foster, John T. (ed.); Geubelle, Philippe H. (ed.); Silling, Stewart A. (ed.)
2016
Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid. Zbl 0634.73041
Silling, S. A.
1988
Numerical studies of loss of ellipticity near singularities in an elastic material. Zbl 0634.73040
Silling, S. A.
1988
Stability of peridynamic correspondence material models and their particle discretizations. Zbl 1439.74017
Silling, S. A.
2017
Phase changes induced by deformation in isothermal elastic crystals. Zbl 0679.73060
Silling, S. A.
1989
Finite difference modeling of phase changes and localization in elasticity. Zbl 0635.73119
Silling, S. A.
1988
Green’s functions in non-local three-dimensional linear elasticity. Zbl 1186.74018
Weckner, Olaf; Brunk, Gerd; Epton, Michael A.; Silling, Stewart A.; Askari, Ebrahim
2009
Dynamic growth of martensitic plates in an elastic material. Zbl 0762.73009
Silling, S. A.
1992
Incompressibility in dynamic relaxation. Zbl 0618.73098
Silling, S. A.
1987
Stability and accuracy of differencing methods for viscoplastic models in wavecodes. Zbl 0768.73092
Silling, S. A.
1993
Stress concentration factors in finite anti-plane shear: Numerical calculations and analytical estimates. Zbl 0611.73051
Horgan, C. O.; Silling, S. A.
1987
Stability of peridynamic correspondence material models and their particle discretizations. Zbl 1439.74017
Silling, S. A.
2017
Handbook of peridynamic modeling. Zbl 1351.74001
Bobaru, Florin; Foster, John T.; Geubelle, Philippe H.; Silling, Stewart A.
2016
Non-ordinary state-based peridynamic analysis of stationary crack problems. Zbl 1296.74099
Breitenfeld, M. S.; Geubelle, P. H.; Weckner, O.; Silling, S. A.
2014
Linearized theory of peridynamic states. Zbl 1188.74008
Silling, S. A.
2010
Crack nucleation in a peridynamic solid. Zbl 1425.74045
Silling, S. A.; Weckner, O.; Askari, E.; Bobaru, F.
2010
Viscoplasticity using peridynamics. Zbl 1183.74035
Foster, J. T.; Silling, S. A.; Chen, W. W.
2010
Convergence, adaptive refinement, and scaling in 1D peridynamics. Zbl 1156.74399
Bobaru, Florin; Yang, Mijia; Alves, Leonardo Frota; Silling, Stewart A.; Askari, Ebrahim; Xu, Jifeng
2009
A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Zbl 1236.74012
Warren, Thomas L.; Silling, Stewart A.; Askari, Abe; Weckner, Olaf; Epton, Michael A.; Xu, Jifeng
2009
Green’s functions in non-local three-dimensional linear elasticity. Zbl 1186.74018
Weckner, Olaf; Brunk, Gerd; Epton, Michael A.; Silling, Stewart A.; Askari, Ebrahim
2009
Convergence of peridynamics to classical elasticity theory. Zbl 1159.74316
Silling, S. A.; Lehoucq, R. B.
2008
Implementing peridynamics within a molecular dynamics code. Zbl 1197.82014
Parks, Michael L.; Lehoucq, Richard B.; Plimpton, Steven J.; Silling, Stewart A.
2008
Force flux and the peridynamic stress tensor. Zbl 1171.74319
Lehoucq, R. B.; Silling, S. A.
2008
Peridynamic states and constitutive modeling. Zbl 1120.74003
Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E.
2007
Peridynamic modeling of membranes and fibers. Zbl 1349.74231
Silling, S. A.; Bobaru, F.
2005
Deformation of a peridynamic bar. Zbl 1061.74031
Silling, S. A.; Zimmermann, M.; Abeyaratne, R.
2003
Reformulation of elasticity theory for discontinuities and long-range forces. Zbl 0970.74030
Silling, S. A.
2000
Stability and accuracy of differencing methods for viscoplastic models in wavecodes. Zbl 0768.73092
Silling, S. A.
1993
Dynamic growth of martensitic plates in an elastic material. Zbl 0762.73009
Silling, S. A.
1992
Phase changes induced by deformation in isothermal elastic crystals. Zbl 0679.73060
Silling, S. A.
1989
Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid. Zbl 0634.73041
Silling, S. A.
1988
Numerical studies of loss of ellipticity near singularities in an elastic material. Zbl 0634.73040
Silling, S. A.
1988
Finite difference modeling of phase changes and localization in elasticity. Zbl 0635.73119
Silling, S. A.
1988
Incompressibility in dynamic relaxation. Zbl 0618.73098
Silling, S. A.
1987
Stress concentration factors in finite anti-plane shear: Numerical calculations and analytical estimates. Zbl 0611.73051
Horgan, C. O.; Silling, S. A.
1987
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#### Cited by 667 Authors

 37 Du, Qiang 19 Gunzburger, Max D. 17 Tian, Xiaochuan 14 Silling, Stewart A. 13 Mengesha, Tadele 11 Foster, John T. jun. 11 Oterkus, Selda 10 Bobaru, Florin 10 Ju, Lili 10 Wang, Hong 9 Li, Shaofan 9 Lipton, Robert P. 9 Zingales, Massimiliano 8 Aksoylu, Burak 8 Oterkus, Erkan 8 Rossi, Julio Daniel 7 Failla, Giuseppe 7 Lehoucq, Richard B. 7 Madenci, Erdogan 7 Weckner, Olaf 6 Bellido, José Carlos 6 D’Elia, Marta 6 Di Paola, Mario 6 Mora-Corral, Carlos 6 Steigmann, David J. 6 Yu, Yue 6 Zhou, Xiaoping 5 Celiker, Fatih 5 Han, Fei 5 Jha, Prashant K. 5 Lubineau, Gilles 5 Scott, James M. 5 Seleson, Pablo 5 Tian, Hao 5 Trask, Nathaniel A. 5 Xu, Jifeng 5 You, Huaiqian 4 Fuschi, Paolo 4 Galvanetto, Ugo 4 Gu, Xin 4 Hu, Ping 4 Ni, Tao 4 Parks, Michael L. 4 Pisano, Aurora Angela 4 Qiao, Pizhong 4 Rabczuk, Timon 4 Radu, Petronela 4 Reddy, Junuthula Narasimha 4 Shen, Guozhe 4 Wang, Linjuan 4 Xia, Yang 4 Zaccariotto, Mirco 4 Zhang, Hongwu 4 Zhang, Xiaobing 4 Zheng, Guojun 4 Zheng, Yonggang 4 Zhu, Qi-Zhi 3 Abeyaratne, Rohan C. 3 Alali, Bacim 3 Andrés, Fuensanta 3 Askari, Ebrahim 3 Chen, Minghua 3 Chen, Youping 3 Cheng, Aijie 3 Coombs, William M. 3 Diehl, Patrick 3 Emmrich, Etienne 3 Fang, Guodong 3 Fosdick, Roger L. 3 Fu, Maoqing 3 Ha, Youn Doh 3 Hattori, Gabriel 3 Hong, Jung-Wuk 3 Jiang, Qing 3 Katiyar, Amit 3 Liang, Jun 3 Littlewood, David J. 3 Liu, Shuo 3 Liu, Wenyang 3 Liu, Zhengguang 3 Lu, Jianfang 3 Mamiya, Edgar Nobuo 3 Muñoz, Julio 3 Otárola, Enrique 3 Ouchi, Hisanao 3 Pence, Thomas J. 3 Pereira, Marcone Corrêa 3 Placidi, Luca 3 Ren, Huilong 3 Rosakis, Phoebus 3 Roy, Pranesh 3 San Antolín, Angel 3 Sharma, Mukul M. 3 Shojaei, Arman 3 Sofi, Alba 3 Tao, Yunzhe 3 Wang, Jianxiang 3 Weißenfels, Christian 3 Wriggers, Peter 3 Xu, Feifei ...and 567 more Authors
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#### Cited in 98 Serials

 93 Computer Methods in Applied Mechanics and Engineering 36 Journal of Elasticity 26 Computational Mechanics 22 Mathematics and Mechanics of Solids 18 Journal of Computational Physics 15 Journal of the Mechanics and Physics of Solids 15 Engineering Analysis with Boundary Elements 12 SIAM Journal on Numerical Analysis 10 Computers & Mathematics with Applications 10 International Journal for Numerical Methods in Engineering 10 European Journal of Mechanics. A. Solids 9 International Journal of Engineering Science 9 Journal of Scientific Computing 8 Archive for Rational Mechanics and Analysis 7 International Journal of Solids and Structures 7 Applied Mathematics and Computation 6 Continuum Mechanics and Thermodynamics 6 Multiscale Modeling & Simulation 6 International Journal of Fracture 5 Acta Mechanica 5 Journal of Mathematical Analysis and Applications 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Mathematics of Computation 5 SIAM Journal on Mathematical Analysis 5 Calculus of Variations and Partial Differential Equations 4 Meccanica 4 Communications on Applied Mathematics and Computation 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 Applied Mathematical Modelling 3 Journal of Nonlinear Science 3 SIAM Journal on Scientific Computing 3 Discrete and Continuous Dynamical Systems. Series B 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Computer Physics Communications 2 International Journal of Plasticity 2 Nonlinearity 2 Reports on Mathematical Physics 2 Journal of Differential Equations 2 Mechanics Research Communications 2 SIAM Journal on Matrix Analysis and Applications 2 NoDEA. Nonlinear Differential Equations and Applications 2 Advances in Computational Mathematics 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Communications in Contemporary Mathematics 2 Lobachevskii Journal of Mathematics 2 Foundations of Computational Mathematics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Applicable Analysis 1 Computers and Fluids 1 International Journal of Heat and Mass Transfer 1 Journal d’Analyse Mathématique 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Physica A 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Optimization 1 BIT 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 SIAM Journal on Control and Optimization 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Numerical Methods for Partial Differential Equations 1 Journal of Integral Equations and Applications 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Archive of Applied Mechanics 1 Journal of Mathematical Imaging and Vision 1 Potential Analysis 1 Topological Methods in Nonlinear Analysis 1 Computational and Applied Mathematics 1 Differential Equations and Dynamical Systems 1 Revista Matemática Complutense 1 Communications in Nonlinear Science and Numerical Simulation 1 Differential Equations 1 Nonlinear Analysis. Real World Applications 1 Archives of Computational Methods in Engineering 1 Computational Methods in Applied Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Numerical Mathematics 1 Communications on Pure and Applied Analysis 1 International Journal of Computational Methods 1 Boundary Value Problems 1 Complex Variables and Elliptic Equations 1 Acta Mechanica Sinica 1 Journal of Theoretical Biology 1 Forum of Mathematics, Sigma 1 East Asian Journal on Applied Mathematics
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#### Cited in 29 Fields

 340 Mechanics of deformable solids (74-XX) 137 Numerical analysis (65-XX) 103 Partial differential equations (35-XX) 65 Integral equations (45-XX) 36 Fluid mechanics (76-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 27 Statistical mechanics, structure of matter (82-XX) 20 Functional analysis (46-XX) 19 Real functions (26-XX) 18 Operator theory (47-XX) 18 Classical thermodynamics, heat transfer (80-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Mechanics of particles and systems (70-XX) 4 Ordinary differential equations (34-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Information and communication theory, circuits (94-XX)