Dual-horizon peridynamics
Summary In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with diffe...
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| Published in | International journal for numerical methods in engineering Vol. 108; no. 12; pp. 1451 - 1476 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Bognor Regis
Blackwell Publishing Ltd
21.12.2016
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
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| Abstract | Summary
In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH‐PD. All three peridynamic formulations, namely, bond‐based, ordinary state‐based, and non‐ordinary state‐based peridynamics, can be implemented within the DH‐PD framework. Our DH‐PD formulation allows for h‐adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two‐dimensional and three‐dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force' issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the 'partial stress tensor' nor the 'slice' technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd. In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force' issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the 'partial stress tensor' nor the 'slice' technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Summary In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH‐PD. All three peridynamic formulations, namely, bond‐based, ordinary state‐based, and non‐ordinary state‐based peridynamics, can be implemented within the DH‐PD framework. Our DH‐PD formulation allows for h‐adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two‐dimensional and three‐dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd. In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH‐PD. All three peridynamic formulations, namely, bond‐based, ordinary state‐based, and non‐ordinary state‐based peridynamics, can be implemented within the DH‐PD framework. Our DH‐PD formulation allows for h ‐adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two‐dimensional and three‐dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd. |
| Author | Ren, Huilong Zhuang, Xiaoying Cai, Yongchang Rabczuk, Timon |
| Author_xml | – sequence: 1 givenname: Huilong surname: Ren fullname: Ren, Huilong organization: Chair of Computational Mechanics, Bauhaus University Weimar, 99423, Weimar, Germany – sequence: 2 givenname: Xiaoying surname: Zhuang fullname: Zhuang, Xiaoying organization: State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, 200092, Shanghai, China – sequence: 3 givenname: Yongchang surname: Cai fullname: Cai, Yongchang organization: State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, 200092, Shanghai, China – sequence: 4 givenname: Timon surname: Rabczuk fullname: Rabczuk, Timon email: timon.rabczuk@tdt.edu.vn, Correspondence to: Timon Rabczuk, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam and Xiaoying Zhuang, Tongji University, 1239 Siping Road, Shanghai, 200092 ;, timon.rabczuk@tdt.edu.vnzhuang@ikm.uni-hannover.de organization: Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam |
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| Notes | FP7 Marie Curie Actions ITN-INSIST and IIF-HYDROFRAC - No. 623667 Ministry of Science and Technology of China - No. SLDRCE14-B-28; No. SLDRCE14-B-31 NSFC - No. 51474157 istex:597FB08B1ECD4F000E39E394885212832A856A39 ArticleID:NME5257 National Basic Research Program of China - No. 973 Program: 2011CB013800 ark:/67375/WNG-LTL54ZNR-D Science and Technology Commission of Shanghai Municipality - No. 16QA1404000 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
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| PublicationDate | 21 December 2016 |
| PublicationDateYYYYMMDD | 2016-12-21 |
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| PublicationPlace | Bognor Regis |
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| PublicationTitle | International journal for numerical methods in engineering |
| PublicationTitleAlternate | Int. J. Numer. Meth. Engng |
| PublicationYear | 2016 |
| Publisher | Blackwell Publishing Ltd Wiley Subscription Services, Inc |
| Publisher_xml | – name: Blackwell Publishing Ltd – name: Wiley Subscription Services, Inc |
| References | Oterkus E, Madenci E, Weckner O, Silling S, Bogert P, Tessler A. Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot. Composite Structures 2012; 94: 839-850. Areias P, Dias-da-Costa D, Sargado JM, Rabczuk T. Element-wise algorithm for modeling ductile fracture with the Rousselier yield function. Computational Mechanics 2013; 52(6): 1429-1443. Silling SA, Askari E. A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures 2005; 83(17): 1526-1535. Wang P, Yang T, Yu Q, Liu H, Zhang P. Characterization on jointed rock masses based on PFC2D. Frontiers of Structural and Civil Engineering 2013; 7(1): 32-38. Areias P, Rabczuk T, Camanho PP. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics 2013; 52(4): 931-947. Zhuang X, Zhu H, Augarde C. An improved meshless Shepard and least square method possessing the delta property and requiring no singular weight function. Computational Mechanics 2014; 53: 343-357. Warren TL, Silling SA, Askari A, Weckner O, Epton MA, Xu J. A non-ordinary state-based peridynamic method to model solid material deformation and fracture. International Journal of Solids and Structures 2008; 46: 1186-1195. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 2010; 199(37): 2437-2455. Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - part ii: level set update. International Journal for Numerical Methods in Engineering 2002; 53: 2569-2586. Yu K, Xin XJ, Lease KB. A new adaptive integration method for the peridynamic theory. Modelling and Simulation in Materials Science and Engineering 2011; 19(4): 045003. Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61(13): 2316-2343. Dipasquale D, Zaccariotto M, Galvanetto U. Crack propagation with adaptive grid refinement in 2D peridynamics. International Journal of Fracture 2014; 190(1-2): 1-22. Nguyen-Thanh N, Muthu J, Zhuang X, Rabczuk T. An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics. Computational Mechanics; 53(2): 369-385. Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software 2015; 80: 82-92. Rabczuk T, Areias PMA, Belytschko T. A simplified mesh-free method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering 2007; 69(5): 993-1021. Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids 2000; 48(1): 175-209. Lai X, Ren B, Fan H, Li S, Wu CT, Regueiro RA, Liu L. Peridynamics simulations of geomaterial fragmentation by impulse loads. International Journal for Numerical and Analytical Methods in Geomechanics 2015. Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics 2014; 53(1): 45-57. Zhuang X, Cai Y, Augarde C. A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields. Theoretical and Applied Fracture Mechanics 2014; 69: 118-125. Ha YD, Bobaru F. Studies of dynamic crack propagation and crack branching with peridynamics. International Journal of Fracture 2010; 162: 229-244. Xu X-P, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42(9): 1397-1434. Nguyen-Thanh N, Valizadeh N, Nguyen MN, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering 2015; 284: 265-291. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4): 993-1013. Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering 2003; 58(12): 1873-1905. Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering 2013; 94(12), 1099-1122. Gerstle W, Sau N, Silling S. Peridynamic modeling of concrete structures. Nuclear Engineering and Design 2007; 237(12): 1250-1258. Song J-H, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67(6): 868-893. Batra RC, Ravinsankar MVS. Three-dimensional numerical simulation of the Kalthoff experiment. International Journal of fracture 2000; 105(2): 161-186. Graff KF. Wave Motion in Elastic Solids. Clarendon: Oxford, 1975. Silling SA, Lehoucq RB. Peridynamic theory of solid mechanics. Advances in Applied Mechanics 2010; 44: 73-168. Bobaru F, Ha YD. Adaptive refinement and multiscale modeling in 2D peridynamics. Journal for Multiscale Computational Engineering 2011; 9(635-659). Li S, Liu WK, Rosakis AJ, Belytschko T, Hao W. Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. International Journal of Solids and Structures 2002; 39(5): 1213-1240. OGrady J, Foster J. Peridynamic plates and flat shells: a non-ordinary, state-based model. International Journal of Solids and Structures 2014; 51: 4572-4579. Sharon E, Gross SP, Fineberg J. Local crack branching as a mechanism for instability in dynamic fracture. Physical Review Letters 1995; 74(25): 5096. Areias PMA, Rabczuk T, Camanho PP. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics 2014; 72: 50-63. Moyer ET, Miraglia MJ. Peridynamic solutions for Timoshenko beams. Engineering 2014; 6: Article ID:46262. Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J. Convergence, adaptive refinement, and scaling in 1D peridynamics. International Journal for Numerical Methods in Engineering 2009; 77(6): 852-877. Silling SA. Dynamic fracture modeling with a meshfree peridynamic code. Computational Fluid and Solid Mechanics 2003: 641-644. Rabczuk T, Zi G, Bordas S. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures 2010; 88: 1391-1411. Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A computational library for multiscale modelling of material failure. Computational Mechanics 2014; 53(5): 1047-1071. Ravi-Chandar K. Dynamic fracture of nominally brittle materials. International Journal of Fracture 1998; 90(1-2): 83-102. Silling SA, Epton M, Weckner O, Xu J, Askari E. Peridynamic states and constitutive modeling. Journal of Elasticity 2007; 88(2): 151-184. Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics 2014; 53(6): 1129-1148. Areias P, Msekh MA, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics 2016: 116-143. Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics 2013; 110: 113-137. Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling. Frontiers of Structural and Civil Engineering 2013; 7(4): 369-378. Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures 2015; 147: 138-146. Cheng KW, Fries TP. Higher-order XFEM for curved strong and weak discontinuities. International Journal for Numerical Methods in Engineering. 10.1002/nme.2768. 2015; 284 2002; 39 1995; 74 2001; 50 2004; 61 2002; 53 2000; 48 2015; 147 2014; 190 2008 2003; 58 1975 2014; 69 1995 2010; 162 2015; 80 2003 2005; 83 2013; 7 2011; 19 53 2011; 9 1994; 42 2012; 94 2010; 88 2009; 77 2010; 44 2007; 237 2006; 67 2000; 105 2013; 94 2013; 52 2010; 199 1998; 90 2008; 46 2016 2015 2013; 110 2014 2014; 51 2014; 72 2007; 88 2014; 6 2007; 69 2014; 53 Graff KF (e_1_2_9_49_1) 1975 e_1_2_9_31_1 e_1_2_9_52_1 e_1_2_9_50_1 e_1_2_9_10_1 e_1_2_9_12_1 e_1_2_9_33_1 e_1_2_9_14_1 e_1_2_9_39_1 Nguyen‐Thanh N (e_1_2_9_19_1); 53 e_1_2_9_16_1 e_1_2_9_18_1 e_1_2_9_41_1 e_1_2_9_20_1 e_1_2_9_22_1 e_1_2_9_45_1 Cai Y (e_1_2_9_21_1) 2013; 7 e_1_2_9_24_1 e_1_2_9_43_1 e_1_2_9_8_1 e_1_2_9_6_1 e_1_2_9_4_1 e_1_2_9_2_1 e_1_2_9_26_1 e_1_2_9_28_1 e_1_2_9_47_1 e_1_2_9_30_1 e_1_2_9_51_1 e_1_2_9_11_1 e_1_2_9_34_1 e_1_2_9_13_1 e_1_2_9_32_1 Askari E (e_1_2_9_37_1) 2008 e_1_2_9_15_1 e_1_2_9_38_1 e_1_2_9_17_1 e_1_2_9_36_1 e_1_2_9_42_1 e_1_2_9_40_1 e_1_2_9_46_1 e_1_2_9_44_1 e_1_2_9_7_1 e_1_2_9_5_1 Bobaru F (e_1_2_9_35_1) 2011; 9 e_1_2_9_3_1 Cheng KW (e_1_2_9_23_1) e_1_2_9_9_1 e_1_2_9_25_1 e_1_2_9_27_1 Silling SA (e_1_2_9_48_1) 2003 e_1_2_9_29_1 |
| References_xml | – reference: Bobaru F, Ha YD. Adaptive refinement and multiscale modeling in 2D peridynamics. Journal for Multiscale Computational Engineering 2011; 9(635-659). – reference: Silling SA, Lehoucq RB. Peridynamic theory of solid mechanics. Advances in Applied Mechanics 2010; 44: 73-168. – reference: Rabczuk T, Areias PMA, Belytschko T. A simplified mesh-free method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering 2007; 69(5): 993-1021. – reference: Nguyen-Thanh N, Muthu J, Zhuang X, Rabczuk T. An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics. Computational Mechanics; 53(2): 369-385. – reference: Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling. Frontiers of Structural and Civil Engineering 2013; 7(4): 369-378. – reference: OGrady J, Foster J. Peridynamic plates and flat shells: a non-ordinary, state-based model. International Journal of Solids and Structures 2014; 51: 4572-4579. – reference: Areias PMA, Rabczuk T, Camanho PP. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics 2014; 72: 50-63. – reference: Sharon E, Gross SP, Fineberg J. Local crack branching as a mechanism for instability in dynamic fracture. Physical Review Letters 1995; 74(25): 5096. – reference: Areias P, Dias-da-Costa D, Sargado JM, Rabczuk T. Element-wise algorithm for modeling ductile fracture with the Rousselier yield function. Computational Mechanics 2013; 52(6): 1429-1443. – reference: Cheng KW, Fries TP. Higher-order XFEM for curved strong and weak discontinuities. International Journal for Numerical Methods in Engineering. 10.1002/nme.2768. – reference: Moyer ET, Miraglia MJ. Peridynamic solutions for Timoshenko beams. Engineering 2014; 6: Article ID:46262. – reference: Dipasquale D, Zaccariotto M, Galvanetto U. Crack propagation with adaptive grid refinement in 2D peridynamics. International Journal of Fracture 2014; 190(1-2): 1-22. – reference: Yu K, Xin XJ, Lease KB. A new adaptive integration method for the peridynamic theory. Modelling and Simulation in Materials Science and Engineering 2011; 19(4): 045003. – reference: Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics 2014; 53(1): 45-57. – reference: Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering 2003; 58(12): 1873-1905. – reference: Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A computational library for multiscale modelling of material failure. Computational Mechanics 2014; 53(5): 1047-1071. – reference: Lai X, Ren B, Fan H, Li S, Wu CT, Regueiro RA, Liu L. Peridynamics simulations of geomaterial fragmentation by impulse loads. International Journal for Numerical and Analytical Methods in Geomechanics 2015. – reference: Graff KF. Wave Motion in Elastic Solids. Clarendon: Oxford, 1975. – reference: Areias P, Rabczuk T, Camanho PP. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics 2013; 52(4): 931-947. – reference: Zhuang X, Zhu H, Augarde C. An improved meshless Shepard and least square method possessing the delta property and requiring no singular weight function. Computational Mechanics 2014; 53: 343-357. – reference: Wang P, Yang T, Yu Q, Liu H, Zhang P. Characterization on jointed rock masses based on PFC2D. Frontiers of Structural and Civil Engineering 2013; 7(1): 32-38. – reference: Rabczuk T, Zi G, Bordas S. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures 2010; 88: 1391-1411. – reference: Silling SA, Epton M, Weckner O, Xu J, Askari E. Peridynamic states and constitutive modeling. Journal of Elasticity 2007; 88(2): 151-184. – reference: Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics 2013; 110: 113-137. – reference: Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software 2015; 80: 82-92. – reference: Oterkus E, Madenci E, Weckner O, Silling S, Bogert P, Tessler A. Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot. Composite Structures 2012; 94: 839-850. – reference: Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - part ii: level set update. International Journal for Numerical Methods in Engineering 2002; 53: 2569-2586. – reference: Song J-H, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67(6): 868-893. – reference: Xu X-P, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42(9): 1397-1434. – reference: Ha YD, Bobaru F. Studies of dynamic crack propagation and crack branching with peridynamics. International Journal of Fracture 2010; 162: 229-244. – reference: Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics 2014; 53(6): 1129-1148. – reference: Areias P, Msekh MA, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics 2016: 116-143. – reference: Silling SA, Askari E. A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures 2005; 83(17): 1526-1535. – reference: Silling SA. Dynamic fracture modeling with a meshfree peridynamic code. Computational Fluid and Solid Mechanics 2003: 641-644. – reference: Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering 2013; 94(12), 1099-1122. – reference: Nguyen-Thanh N, Valizadeh N, Nguyen MN, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering 2015; 284: 265-291. – reference: Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 2010; 199(37): 2437-2455. – reference: Ravi-Chandar K. Dynamic fracture of nominally brittle materials. International Journal of Fracture 1998; 90(1-2): 83-102. – reference: Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4): 993-1013. – reference: Li S, Liu WK, Rosakis AJ, Belytschko T, Hao W. Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. International Journal of Solids and Structures 2002; 39(5): 1213-1240. – reference: Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J. Convergence, adaptive refinement, and scaling in 1D peridynamics. International Journal for Numerical Methods in Engineering 2009; 77(6): 852-877. – reference: Batra RC, Ravinsankar MVS. Three-dimensional numerical simulation of the Kalthoff experiment. International Journal of fracture 2000; 105(2): 161-186. – reference: Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61(13): 2316-2343. – reference: Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures 2015; 147: 138-146. – reference: Gerstle W, Sau N, Silling S. Peridynamic modeling of concrete structures. Nuclear Engineering and Design 2007; 237(12): 1250-1258. – reference: Warren TL, Silling SA, Askari A, Weckner O, Epton MA, Xu J. A non-ordinary state-based peridynamic method to model solid material deformation and fracture. International Journal of Solids and Structures 2008; 46: 1186-1195. – reference: Zhuang X, Cai Y, Augarde C. A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields. Theoretical and Applied Fracture Mechanics 2014; 69: 118-125. – reference: Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids 2000; 48(1): 175-209. – volume: 190 start-page: 1 issue: 1‐2 year: 2014 end-page: 22 article-title: Crack propagation with adaptive grid refinement in 2D peridynamics publication-title: International Journal of Fracture – volume: 53 start-page: 2569 year: 2002 end-page: 2586 article-title: Non‐planar 3D crack growth by the extended finite element and level sets – part ii: level set update publication-title: International Journal for Numerical Methods in Engineering – volume: 237 start-page: 1250 issue: 12 year: 2007 end-page: 1258 article-title: Peridynamic modeling of concrete structures publication-title: Nuclear Engineering and Design – volume: 88 start-page: 1391 year: 2010 end-page: 1411 article-title: On three‐dimensional modelling of crack growth using partition of unity methods publication-title: Computers & Structures – volume: 46 start-page: 1186 year: 2008 end-page: 1195 article-title: A non‐ordinary state‐based peridynamic method to model solid material deformation and fracture publication-title: International Journal of Solids and Structures – volume: 7 start-page: 32 issue: 1 year: 2013 end-page: 38 publication-title: Characterization on jointed rock masses based on PFC2D. Frontiers of Structural and Civil Engineering – volume: 44 start-page: 73 year: 2010 end-page: 168 article-title: Peridynamic theory of solid mechanics publication-title: Advances in Applied Mechanics – volume: 80 start-page: 82 year: 2015 end-page: 92 article-title: Concurrent multiscale modelling of three dimensional crack and dislocation propagation publication-title: Advances in Engineering Software – volume: 42 start-page: 1397 issue: 9 year: 1994 end-page: 1434 article-title: Numerical simulations of fast crack growth in brittle solids publication-title: Journal of the Mechanics and Physics of Solids – volume: 50 start-page: 993 issue: 4 year: 2001 end-page: 1013 article-title: Arbitrary discontinuities in finite elements publication-title: International Journal for Numerical Methods in Engineering – year: 1975 – volume: 53 start-page: 1129 issue: 6 year: 2014 end-page: 1148 article-title: An adaptive multiscale method for quasi‐static crack growth publication-title: Computational Mechanics – volume: 53 start-page: 369 issue: 2 end-page: 385 article-title: An adaptive three‐dimensional RHT‐splines formulation in linear elasto‐statics and elasto‐dynamics publication-title: Computational Mechanics – volume: 105 start-page: 161 issue: 2 year: 2000 end-page: 186 article-title: Three‐dimensional numerical simulation of the Kalthoff experiment publication-title: International Journal of fracture – volume: 77 start-page: 852 issue: 6 year: 2009 end-page: 877 article-title: Convergence, adaptive refinement, and scaling in 1D peridynamics publication-title: International Journal for Numerical Methods in Engineering – year: 2014 – volume: 7 start-page: 369 issue: 4 year: 2013 end-page: 378 publication-title: A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling. Frontiers of Structural and Civil Engineering – year: 2008 – volume: 9 issue: 635‐659 year: 2011 article-title: Adaptive refinement and multiscale modeling in 2D peridynamics publication-title: Journal for Multiscale Computational Engineering – volume: 58 start-page: 1873 issue: 12 year: 2003 end-page: 1905 article-title: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment publication-title: International Journal for Numerical Methods in Engineering – volume: 53 start-page: 1047 issue: 5 year: 2014 end-page: 1071 article-title: A computational library for multiscale modelling of material failure publication-title: Computational Mechanics – volume: 94 start-page: 839 year: 2012 end-page: 850 article-title: Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot publication-title: Composite Structures – year: 2015 article-title: Peridynamics simulations of geomaterial fragmentation by impulse loads publication-title: International Journal for Numerical and Analytical Methods in Geomechanics – volume: 88 start-page: 151 issue: 2 year: 2007 end-page: 184 article-title: Peridynamic states and constitutive modeling publication-title: Journal of Elasticity – volume: 162 start-page: 229 year: 2010 end-page: 244 article-title: Studies of dynamic crack propagation and crack branching with peridynamics publication-title: International Journal of Fracture – volume: 69 start-page: 118 year: 2014 end-page: 125 article-title: A meshless sub‐region radial point interpolation method for accurate calculation of crack tip fields publication-title: Theoretical and Applied Fracture Mechanics – volume: 19 issue: 4 year: 2011 article-title: A new adaptive integration method for the peridynamic theory publication-title: Modelling and Simulation in Materials Science and Engineering – volume: 67 start-page: 868 issue: 6 year: 2006 end-page: 893 article-title: A method for dynamic crack and shear band propagation with phantom nodes publication-title: International Journal for Numerical Methods in Engineering – volume: 94 start-page: 1099 issue: 12 year: 2013 end-page: 1122 article-title: Finite strain fracture of plates and shells with configurational forces and edge rotation publication-title: International Journal for Numerical Methods in Engineering – volume: 74 start-page: 5096 issue: 25 year: 1995 article-title: Local crack branching as a mechanism for instability in dynamic fracture publication-title: Physical Review Letters – volume: 69 start-page: 993 issue: 5 year: 2007 end-page: 1021 article-title: A simplified mesh‐free method for shear bands with cohesive surfaces publication-title: International Journal for Numerical Methods in Engineering – volume: 147 start-page: 138 year: 2015 end-page: 146 article-title: T‐spline based XIGA for fracture analysis of orthotropic media publication-title: Computers & Structures – volume: 52 start-page: 1429 issue: 6 year: 2013 end-page: 1443 article-title: Element‐wise algorithm for modeling ductile fracture with the Rousselier yield function publication-title: Computational Mechanics – volume: 83 start-page: 1526 issue: 17 year: 2005 end-page: 1535 article-title: A meshfree method based on the peridynamic model of solid mechanics publication-title: Computers & Structures – volume: 61 start-page: 2316 issue: 13 year: 2004 end-page: 2343 article-title: Cracking particles: a simplified meshfree method for arbitrary evolving cracks publication-title: International Journal for Numerical Methods in Engineering – start-page: 641 year: 2003 end-page: 644 article-title: Dynamic fracture modeling with a meshfree peridynamic code publication-title: Computational Fluid and Solid Mechanics – volume: 6 start-page: Article ID:46262 year: 2014 article-title: Peridynamic solutions for Timoshenko beams publication-title: Engineering – volume: 51 start-page: 4572 year: 2014 end-page: 4579 article-title: 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In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the... In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’... Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the... In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force'... |
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| SubjectTerms | adaptive refinement Angular momentum Bonding Computational efficiency Cracks dual horizon ghost force Ghosts Horizon horizon variable Mathematical models Numerical analysis peridynamics spurious wave reflection |
| Title | Dual-horizon peridynamics |
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