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Volumn 44, Issue , 2010, Pages 73-168

Peridynamic Theory of Solid Mechanics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77956895495     PISSN: 00652156     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2156(10)44002-8     Document Type: Book
Times cited : (820)

References (84)
  • 1
    • 77953621457 scopus 로고    scopus 로고
    • A unified interpretation of stress in molecular systems
    • Admal N.C., Tadmor E.B. A unified interpretation of stress in molecular systems. Journal of Elasticity 2010, 100:63-143.
    • (2010) Journal of Elasticity , vol.100 , pp. 63-143
    • Admal, N.C.1    Tadmor, E.B.2
  • 4
    • 77956895279 scopus 로고    scopus 로고
    • Multiscale analysis of heterogeneous media in the peridynamic formulation. Technical Report IMA Preprint Series 2241, Institute for Mathematics and Its Applications, Minneapolis, Minnesota, USA.
    • Alali B., & Lipton, R. (2009). Multiscale analysis of heterogeneous media in the peridynamic formulation. Technical Report IMA Preprint Series 2241, Institute for Mathematics and Its Applications, Minneapolis, Minnesota, USA.
    • (2009)
    • Alali, B.1    Lipton, R.2
  • 5
    • 33744782338 scopus 로고    scopus 로고
    • Derivation of higher order gradient continuum models from atomistic models for crystalline solids
    • Arndt M., Griebel M. Derivation of higher order gradient continuum models from atomistic models for crystalline solids. Multiscale Modeling and Simulation 2005, 4:531-562.
    • (2005) Multiscale Modeling and Simulation , vol.4 , pp. 531-562
    • Arndt, M.1    Griebel, M.2
  • 7
    • 77956893781 scopus 로고    scopus 로고
    • The design of a hybrid material for multifunctional performance using advanced analysis techniques and testing. In Proceedings of 40th ISTC, Memphis, Tennessee, USA. Society for the Advancement of Material and Process Engineering.
    • Askari, E., Nelson, K., Weckner, O., Xu, J., & Silling, S.A. (2008). The design of a hybrid material for multifunctional performance using advanced analysis techniques and testing. In Proceedings of 40th ISTC, Memphis, Tennessee, USA. Society for the Advancement of Material and Process Engineering.
    • (2008)
    • Askari, E.1    Nelson, K.2    Weckner, O.3    Xu, J.4    Silling, S.A.5
  • 8
    • 34250771050 scopus 로고    scopus 로고
    • Peridynamic analysis of damage and failure in composites. In 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, number AIAA 2006-88. American Institute of Aeronautics and Astronautics.
    • Askari, E., Xu, J., & Silling, S. (2006). Peridynamic analysis of damage and failure in composites. In 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, number AIAA 2006-88. American Institute of Aeronautics and Astronautics.
    • (2006)
    • Askari, E.1    Xu, J.2    Silling, S.3
  • 9
    • 0024029187 scopus 로고
    • Nonlocal continuum damage, localization instability and convergence
    • Bazant Z.P., Pijaudier-Cabot G. Nonlocal continuum damage, localization instability and convergence. Journal of Applied Mechanics 1988, 55:287-290.
    • (1988) Journal of Applied Mechanics , vol.55 , pp. 287-290
    • Bazant, Z.P.1    Pijaudier-Cabot, G.2
  • 10
    • 34547444016 scopus 로고    scopus 로고
    • Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach
    • Bobaru F. Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach. Modelling and Simulation in Materials Science and Engineering 2007, 15:397-417.
    • (2007) Modelling and Simulation in Materials Science and Engineering , vol.15 , pp. 397-417
    • Bobaru, F.1
  • 16
    • 34250963757 scopus 로고
    • The thermodynamics of elastic materials with heat conduction and viscosity
    • Coleman B.D., Noll W. The thermodynamics of elastic materials with heat conduction and viscosity. Archive for Rational Mechanics and Analysis 1963, 13:167-178.
    • (1963) Archive for Rational Mechanics and Analysis , vol.13 , pp. 167-178
    • Coleman, B.D.1    Noll, W.2
  • 17
    • 33745173426 scopus 로고    scopus 로고
    • Kinetics of phase transformations in the peridynamic formulation of continuum mechanics
    • Dayal K., Bhattacharya K. Kinetics of phase transformations in the peridynamic formulation of continuum mechanics. Journal of the Mechanics and Physics of Solids 2006, 54:1811-1842.
    • (2006) Journal of the Mechanics and Physics of Solids , vol.54 , pp. 1811-1842
    • Dayal, K.1    Bhattacharya, K.2
  • 21
    • 34547165473 scopus 로고    scopus 로고
    • Analysis and numerical approximation of an integro-differential equation modeling non-local effects in linear elasticity
    • Emmrich E., Weckner O. Analysis and numerical approximation of an integro-differential equation modeling non-local effects in linear elasticity. Mathematics and Mechanics of Solids 2007, 12:363-384.
    • (2007) Mathematics and Mechanics of Solids , vol.12 , pp. 363-384
    • Emmrich, E.1    Weckner, O.2
  • 22
    • 39149115715 scopus 로고    scopus 로고
    • On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
    • Emmrich E., Weckner O. On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity. Communications in Mathematical Sciences 2007, 5:851-864.
    • (2007) Communications in Mathematical Sciences , vol.5 , pp. 851-864
    • Emmrich, E.1    Weckner, O.2
  • 24
    • 0020821706 scopus 로고
    • On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves
    • Eringen A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 1983, 54:4703-4710.
    • (1983) Journal of Applied Physics , vol.54 , pp. 4703-4710
    • Eringen, A.C.1
  • 27
    • 77956891831 scopus 로고    scopus 로고
    • Dynamic crack initiation toughness: experiments and peridynamic modeling. Ph.D. dissertation, Purdue University, reprinted in SAND2009-7217, Sandia National Laboratories, Albuquerque, New Mexico.
    • Foster, J.T. (2009). Dynamic crack initiation toughness: experiments and peridynamic modeling. Ph.D. dissertation, Purdue University, reprinted in SAND2009-7217, Sandia National Laboratories, Albuquerque, New Mexico.
    • (2009)
    • Foster, J.T.1
  • 30
    • 77956898933 scopus 로고    scopus 로고
    • New insights into classical particle mechanics
    • Fried E. New insights into classical particle mechanics. Discrete and Continuous Dynamical Systems 2010, 28:1469-1504.
    • (2010) Discrete and Continuous Dynamical Systems , vol.28 , pp. 1469-1504
    • Fried, E.1
  • 35
    • 77956919358 scopus 로고    scopus 로고
    • Peridynamic modeling of plain and reinforced concrete structures. In 18th International Conference on Structural Mechanics in Reactor Technology (SMiRT 18), Beijing, China, number SMIRT18-B01-2,
    • Gerstle, W.H., Sau, N., & Silling, S.A. (2005). Peridynamic modeling of plain and reinforced concrete structures. In 18th International Conference on Structural Mechanics in Reactor Technology (SMiRT 18), Beijing, China, number SMIRT18-B01-2, pp. 54-68.
    • (2005) , pp. 54-68
    • Gerstle, W.H.1    Sau, N.2    Silling, S.A.3
  • 36
    • 77956942703 scopus 로고    scopus 로고
    • A nonlocal vector calculus with application to nonlocal boundary value problems. Technical Report SAND2009-4666J, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550.
    • Gunzburger, M., & Lehoucq, R.B. (2010). A nonlocal vector calculus with application to nonlocal boundary value problems. Technical Report SAND2009-4666J, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550.
    • (2010)
    • Gunzburger, M.1    Lehoucq, R.B.2
  • 38
    • 36749107929 scopus 로고
    • Formulas for determining local properties in molecular-dynamics simulations: Shock waves
    • Hardy R.J. Formulas for determining local properties in molecular-dynamics simulations: Shock waves. Journal of Chemical Physics 1982, 76:622-628.
    • (1982) Journal of Chemical Physics , vol.76 , pp. 622-628
    • Hardy, R.J.1
  • 40
    • 33646967528 scopus 로고
    • The statistical mechanical theory of transport processes. IV. the equations of hydrodynamics
    • Irving J., Kirkwood J. The statistical mechanical theory of transport processes. IV. the equations of hydrodynamics. Journal of Chemical Physics 1950, 18:817-829.
    • (1950) Journal of Chemical Physics , vol.18 , pp. 817-829
    • Irving, J.1    Kirkwood, J.2
  • 41
    • 0000437550 scopus 로고
    • Failure mode transition at high rates of shear loading
    • Oberursel: DGM Informationsgesellschaft Verlag, C.Y. Chiem, H.D. Kunze, L.W. Meyer (Eds.)
    • Kalthoff J.F., Winkler S. Failure mode transition at high rates of shear loading. Impact loading and dynamic behavior of materials 1988, (Vol. 1:185-195. Oberursel: DGM Informationsgesellschaft Verlag. C.Y. Chiem, H.D. Kunze, L.W. Meyer (Eds.).
    • (1988) Impact loading and dynamic behavior of materials , pp. 185-195
    • Kalthoff, J.F.1    Winkler, S.2
  • 42
    • 0018724201 scopus 로고
    • A micropolar continuum theory for the flow of granular materials
    • Kanatani K.-I. A micropolar continuum theory for the flow of granular materials. International Journal of Engineering Science 1979, 17:419-432.
    • (1979) International Journal of Engineering Science , vol.17 , pp. 419-432
    • Kanatani, K.-I.1
  • 43
    • 67349288419 scopus 로고    scopus 로고
    • Peridynamic theory for progressive damage prediction in center-cracked composite laminates
    • Kilic B., Agwai A., Madenci E. Peridynamic theory for progressive damage prediction in center-cracked composite laminates. Composite Structures 2009, 90:141-151.
    • (2009) Composite Structures , vol.90 , pp. 141-151
    • Kilic, B.1    Agwai, A.2    Madenci, E.3
  • 44
    • 67449092066 scopus 로고    scopus 로고
    • Prediction of crack paths in a quenched glass plate by using peridynamic theory
    • Kilic B., Madenci E. Prediction of crack paths in a quenched glass plate by using peridynamic theory. International Journal of Fracture 2009, 156:165-177.
    • (2009) International Journal of Fracture , vol.156 , pp. 165-177
    • Kilic, B.1    Madenci, E.2
  • 46
    • 49949143801 scopus 로고
    • Elasticity theory of materials with long range cohesive forces
    • Kröner E. Elasticity theory of materials with long range cohesive forces. International Journal of Solids and Structures 1967, 3:731-742.
    • (1967) International Journal of Solids and Structures , vol.3 , pp. 731-742
    • Kröner, E.1
  • 50
    • 77953615036 scopus 로고    scopus 로고
    • Translation of Walter Noll's derivation of the fundamental equations of continuum thermodynamics from statistical mechanics
    • Lehoucq R.B., von Lilienfeld-Toal O.A. Translation of Walter Noll's derivation of the fundamental equations of continuum thermodynamics from statistical mechanics. Journal of Elasticity 2010, 100:5-24.
    • (2010) Journal of Elasticity , vol.100 , pp. 5-24
    • Lehoucq, R.B.1    von Lilienfeld-Toal, O.A.2
  • 53
    • 34547352890 scopus 로고    scopus 로고
    • Length scales at which classical elasticity breaks down for various materials
    • Maranganti R., Sharma P. Length scales at which classical elasticity breaks down for various materials. Physical Review Letters 2007, 98:195504.
    • (2007) Physical Review Letters , vol.98 , pp. 195504
    • Maranganti, R.1    Sharma, P.2
  • 54
    • 0005831509 scopus 로고
    • Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik
    • Noll W. Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. Journal of Rational Mechanics and Analysis 1955, 4:627-646.
    • (1955) Journal of Rational Mechanics and Analysis , vol.4 , pp. 627-646
    • Noll, W.1
  • 55
    • 77953615914 scopus 로고    scopus 로고
    • Thoughts on the concept of stress
    • Noll W. Thoughts on the concept of stress. Journal of Elasticity 2010, 100:25-32.
    • (2010) Journal of Elasticity , vol.100 , pp. 25-32
    • Noll, W.1
  • 58
    • 84980287971 scopus 로고
    • A path independent integral and the approximate analysis of strain concentration by notches and cracks
    • Rice J.R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 1968, 35:379-386.
    • (1968) Journal of Applied Mechanics , vol.35 , pp. 379-386
    • Rice, J.R.1
  • 59
    • 77956901846 scopus 로고    scopus 로고
    • The statistical mechanical foundations of peridynamics: I. mass and momentum conservation laws. Technical Report 2009-0791J, Sandia National Laboratories, Albuquerque, NM 87185.
    • Sears, M.P., & Lehoucq, R.B. (2009). The statistical mechanical foundations of peridynamics: I. mass and momentum conservation laws. Technical Report 2009-0791J, Sandia National Laboratories, Albuquerque, NM 87185.
    • (2009)
    • Sears, M.P.1    Lehoucq, R.B.2
  • 61
    • 0346055020 scopus 로고    scopus 로고
    • Reformulation of elasticity theory for discontinuities and long-range forces
    • Silling S.A. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids 2000, 48:175-209.
    • (2000) Journal of the Mechanics and Physics of Solids , vol.48 , pp. 175-209
    • Silling, S.A.1
  • 62
    • 84941643983 scopus 로고    scopus 로고
    • Dynamic fracture modeling with a meshfree peridynamic code
    • Amsterdam: Elsevier, K.-J. Bathe (Ed.)
    • Silling S.A. Dynamic fracture modeling with a meshfree peridynamic code. Computational fluid and solid mechanics 2003, 2003:641-644. Amsterdam: Elsevier. K.-J. Bathe (Ed.).
    • (2003) Computational fluid and solid mechanics , vol.2003 , pp. 641-644
    • Silling, S.A.1
  • 63
    • 77956920483 scopus 로고    scopus 로고
    • a. A coarsening method for linear peridynamics. Technical Report SAND2010-1880J, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550.
    • Silling, S.A. (2010a). A coarsening method for linear peridynamics. Technical Report SAND2010-1880J, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550.
    • (2010)
    • Silling, S.A.1
  • 64
    • 76649123914 scopus 로고    scopus 로고
    • Linearized theory of peridynamic states
    • Silling S.A. Linearized theory of peridynamic states. Journal of Elasticity 2010, 99:85-111.
    • (2010) Journal of Elasticity , vol.99 , pp. 85-111
    • Silling, S.A.1
  • 65
    • 8344261542 scopus 로고    scopus 로고
    • Peridynamic modeling of impact damage. In PVP, Problems Involving Thermal-Hydraulics, Liquid Sloshing, and Extreme Loads on Structures, San Diego, California, number PVP2004-3049, ASME.
    • Silling, S.A., & Askari, E. (2004). Peridynamic modeling of impact damage. In PVP-Vol.489, Problems Involving Thermal-Hydraulics, Liquid Sloshing, and Extreme Loads on Structures, San Diego, California, number PVP2004-3049, pp. 197-205. ASME.
    • (2004) , vol.489 , pp. 197-205
    • Silling, S.A.1    Askari, E.2
  • 66
    • 17744377618 scopus 로고    scopus 로고
    • A meshfree method based on the peridynamic model of solid mechanics
    • Silling S.A., Askari E. A meshfree method based on the peridynamic model of solid mechanics. Computers and Structures 2005, 83:1526-1535.
    • (2005) Computers and Structures , vol.83 , pp. 1526-1535
    • Silling, S.A.1    Askari, E.2
  • 69
    • 50249121899 scopus 로고    scopus 로고
    • Convergence of peridynamics to classical elasticity theory
    • Silling S.A., Lehoucq R.B. Convergence of peridynamics to classical elasticity theory. Journal of Elasticity 2008, 93:13-37.
    • (2008) Journal of Elasticity , vol.93 , pp. 13-37
    • Silling, S.A.1    Lehoucq, R.B.2
  • 77
    • 34547534245 scopus 로고    scopus 로고
    • Damage and failure analysis based on peridynamics - theory and applications. In 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, USA, number AIAA 2007-2314. American Institute of Aeronautics and Astronautics.
    • Weckner, O., Askari, A., Xu, J., Razi, H., & Silling, S. (2007). Damage and failure analysis based on peridynamics - theory and applications. In 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, USA, number AIAA 2007-2314. American Institute of Aeronautics and Astronautics.
    • (2007)
    • Weckner, O.1    Askari, A.2    Xu, J.3    Razi, H.4    Silling, S.5
  • 79
    • 33947617755 scopus 로고    scopus 로고
    • Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar
    • Weckner O., Emmrich E. Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. Journal of Computational and Applied Mechanics 2005, 6:311-319.
    • (2005) Journal of Computational and Applied Mechanics , vol.6 , pp. 311-319
    • Weckner, O.1    Emmrich, E.2
  • 80
    • 77956907660 scopus 로고    scopus 로고
    • Determination of the constitutive model in peridynamics from experimental dispersion data. International Journal of Multiscale Computational Engineering.
    • Weckner, O., & Silling, S.A. (2010). Determination of the constitutive model in peridynamics from experimental dispersion data. International Journal of Multiscale Computational Engineering.
    • (2010)
    • Weckner, O.1    Silling, S.A.2
  • 83
    • 0000774810 scopus 로고
    • Transition between crack patterns in quenched glass plates
    • Yuse A., Sano M. Transition between crack patterns in quenched glass plates. Nature 1993, 362:329-331.
    • (1993) Nature , vol.362 , pp. 329-331
    • Yuse, A.1    Sano, M.2
  • 84
    • 77956920185 scopus 로고    scopus 로고
    • A continuum theory with long-range forces for solids. Ph.D. dissertation, Department of Mechanical Engineering, Massachusetts Institute of Technology.
    • Zimmermann, M. (2005). A continuum theory with long-range forces for solids. Ph.D. dissertation, Department of Mechanical Engineering, Massachusetts Institute of Technology.
    • (2005)
    • Zimmermann, M.1


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