Abstract
The dynamic fracture of a thin-walled structure that is mainly due to impact and explosive loading is studied. Use is made of a meshless SPH shell formulation based on Mindlin–Reissner’s theory. The formulation is an extension of the continuum-corrected and stabilized SPH method allowing a thin structure to be modelled using only one particle characterizing the mean position of the shell surface. Fracture is based on an effective criterion similar to that of the visibility method. Four numerical examples are studied among which tearing of pre-notched plates, fracture due to impact loading and dynamic fracture of cylindrical shells.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Antipov YA, Willis JR (2007) Propagation of a mode-ii crack in a viscoelastic medium with different bulk and shear relaxation. J Eng Math 59: 359–371
Lee DS (2000) Nonlinear dynamic buckling of orthotropic cylindrical shells subjected to rapidly applied loads. J Eng Math 38: 141–154
Johnson GR, Stryk RA (2003) Conversion of 3d distorted elements into meshless particles during dynamic deformation. Int J Impact Eng 28: 947–966
Rabczuk T, Eibl J (2006) Modelling dynamic failure of concrete with meshfree methods. Int J Impact Eng 32: 1878–1897
Lucy L (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82: 1013–1024
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181: 375–389
Randles PW, Libersky LD (1997) Recent improvements in SPH modeling of hypervelocity impact. Int J Impact Eng 20: 525–532
Khayyer A, Shao SD, Gotoh H (2008) Corrected incompressible SPH method for accurate water-surface tracking in breaking waves. Coast Eng 55(3): 236–250
Bonet J, Kulasegaram S (2000) Correction and stabilization of smooth particle hydrodynamics methods with application in metal forming simulations. Int J Numer Methods Eng 47(6): 1189–1214
Johnson GR, Beissel SR (1996) Normalized smoothing functions for SPH impact computations. Comput Methods Appl Mech Eng 39: 2127–2741
Vignjevic R, Campbell J, Libersky LD (2000) A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Comput Methods Appl Mech Eng 184: 67–85
Swegle JW, Hicks DL, Attaway SW (1995) Smoothed particle hydrodynamics stability analysis. J Comput Phys 116: 123–134
Randles PW, Libersky L (2000) Normalized SPH with stress points. Int J Numer Methods Eng 48: 1445–1461
Rodriguez-Paz M, Bonet J (2005) A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Comput Struct 83(17–18): 1396–1410
Chen J-S, Wu C-T, Yoon S, You YS (2001) A stabilized conforming nodal integration for galerkin mesh-free method. Int J Numer Methods Eng 50: 435n–466
Wang DD, Chen JS (2006) A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration. Comput Mech 39(1): 83–90
Rabczuk T, Belytschko T, Xiao SP (2004) Stable particle methods based on lagrangian kernels. Comput Methods Appl Mech Eng 193: 1035–1063
Beissel S, Belytschko T (1996) Nodal integration of the element-free galerkin method. Comput Methods Appl Mech Eng 139: 49–74
Noguchi H, Kawashima T, Miyamura T (2000) Element free analysis of shell and spatial structures. Int J Numer Methods Eng 47: 1215–1240
Rabczuk T, Areias PMA, Belytschko T (2007) A meshfree thin shell method for non-linear dynamic fracture. Int J Numer Methods Eng 72(5): 524–548
Rabczuk T, Areias P (2006) A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Comput Model Eng Sci 16(2): 115–130
Leitao VMA (2001) A meshless method for kirchhoff plate bending problems. Int J Numer Methods Eng 52: 1107–1130
Liew KM, Chen XL (2004) Mesh-free radial point interpolation method for the buckling analysis of mindlin plates. Int J Numer Methods Eng 60: 1877–1961
Krysl P, Belytschko T (1996) Analysis of thin shells by the element-free galerkin method. Int J Numer Methods Eng 33: 3057–3078
Krongauz Y, Belytschko T (1997) Consistent pseudo derivatives in meshless methods. Comput Methods Appl Mech Eng 146: 371–386
Maurel P, Combescure A (2008) An SPH shell formulation for plasticity and fracture analysis in explicit dynamics. Int J Numer Methods Eng 75: 949–971
Organ D, Fleming M, Terry T, Belytschko T (1996) Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Comput Mech 18: 225–235
Belytschko T, Guo Y, Liu WK, Xiao SP (2000) A unified stability analysis of meshfree particle methods. Int J Numer Methods Eng 48: 1359–1400
Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139: 3–47
Dilts GA (2000) Moving least square particle hydrodynamics I. Consistency and stability. Int J Numer Methods Eng 44: 1115–1155
Rabczuk T, Eibl J (2003) Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int J Numer Methods Eng 56: 1421–1444
Libersky L, Petscheck AG (1993) High strain lagrangian hydrodynamics. J Comput Phys 109: 67–75
Petscheck AG, Libersky L (1994) Cylindrical sph. J Comput Phys 109: 76
Monaghan JJ, Gingold R (1983) Shock simulation by the particle method sph. J Comput Phys 52: 374–389
Monaghan JJ (1994) Simulating free surface flows with sph. J Comput Phys 110: 399–406
Ilyushin AA (1956) Plasticite. Eyrolles, Paris
Zeng Q, Combescure A, Arnaudeau F (2001) An efficient plasticity algorithm for shell elements application to metal forming simulations. Comput Struct 7: 1525–1540
Belytschko T, Liu WK, Moran B (2001) Nonlinear finite elements for continua and structures. Wiley, New York
Lubliner J (2001) Plasticity theory. Wiley, New York
Onate E, Owens R (2007) Computational plasticity. Springer
Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free galerkin methods. Eng Fract Mech 51(2): 295–315
Belytschko T, Tabbara M (1996) Dynamic fracture using element-free galerkin methods. Int J Numer Methods Eng 39(6): 923–938
Belytschko T, Fleming M (1999) Smoothing, enrichment and contact in the element free galerkin method. Comput Struct 71: 173–195
Belytschko T, Lu YY, Gu L (1994) Element-free galerkin methods. Int J Numer Methods Eng 37: 229–256
Rabczuk T, Belytschko T (2005) Adaptivity for structured meshfree particle methods in 2d and 3d. Int J Numer Methods Eng 63(11): 1559–1582
Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13): 2316–2343
Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42: 1397–1434
Zimmermann T (1986) Failure and fracturing analysis of concrete structures. Nucl Eng Des 92(3): 389–410
Rabczuk T, Akkermann J, Eibl J (2005) A numerical model for reinforced concrete structures. Int J Solids Struct 42(5–6): 1327–1354
Rabczuk T, Belytschko T (2006) Application of particle methods to static fracture of reinforced concrete structures. Int J Fract 137(1–4): 19–49
Rabczuk T, Song J-H, Belytschko T (2009) Simulations of instability in dynamic fracture by the cracking particles method. Eng Fract Mech 76: 730–741
Rabczuk T, Zi G, Gerstenberger A, Wall WA (2008) A new crack tip element for the phantom node method with arbitrary cohesive cracks. Int J Numer Methods Eng 75: 577–599
Rabczuk T, Areias PMA (2006) A new approach for modelling slip lines in geological materials with cohesive models. Int J Numer Anal Methods Geomech 30(11): 1159–1172
Rabczuk T, Areias PMA, Belytschko T (2007) A meshfree thin shell method for non-linear dynamic fracture. Int J Numer Methods Eng 72(5): 524–548
Rabczuk T, Bordas S, Zi G (2007) A three-dimensional meshfree method for continuous multiple crack initiation, nucleation and propagation in statics and dynamics. Comput Mech 40(3): 473–495
Bordas S, Rabczuk T, Zi G (2008) Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by extrinsic discontinuous enrichment of meshfree methods without asymptotic enrichment. Eng Fract Mech 75: 943–960
Fleming M, Chu YA, Moran B, Belytschko T (1997) Enriched element-free galerkin methods for crack tip fields. Int J Numer Methods Eng 40: 1483–1504
Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79: 763–813
Muscat-Fenech CM, Atkins AG (1997) Out-of-plane stretching and tearing fracture in ductile sheet materials. Int J Fract 84: 297–306
Teng X, Rohr I, Wierzbicki T, Hiermaier S (2005) Numerical prediction of fracture in the taylor test. Int J Solids Struct 42(910): 2929–2948
Chao TW (2004) Gaseous detonation-driven fracture of tubes. PhD thesis, California Institute of Technology
Rabczuk T, Gracie R, Song JH, Belytschko T (2010) Immersed particle method for fluid-structure interaction. Int J Numer Methods Eng 81: 48–71
Li S, Hao W, Liu WK (2000) Numerical simulations of large deformation of thin shell structures using meshfree methods. Comput Mech 25: 102–116
Qian D, Eason T, Li S, Liu WK (2008) Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heat. Int J Numer Methods Eng 76: 1159–1184
Zhou M, Ravichandran G, Rosakis AJ (1996) Dynamically propagating shear bands in impact-loaded prenotched plates, 2. numerical simulations. J Mech Phys Solids 44(6): 1007–1032
Ravi-Chandar K (1998) Dynamic fracture of nominally brittle materials. Int J Fract 90: 83–102
Sharon E, Gross PSP, Fineberg J (1995) Local crack branching as a mechanism for instability in dynamic fracture. Phys Rev Lett 74: 5096–5099
Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29–30): 2777–2799
Rabczuk T, Bordas S, Zi G (2007) A three dimensional meshfree method for static and dynamic multiple crack nucleation/propagation with crack path continuity. Comput Mech 40(3): 473–495
Zi G, Rabczuk T, Wall W (2007) Extended meshfree methods without branch enrichment for cohesive cracks. Comput Mech 40(2): 367–382
Rabczuk T, Xiao SP, Sauer A (2006) Coupling of mesh-free methods with finite elements: basic concepts and test results. Commun Numer Methods Eng 22(10): 1031–1065
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, J. Meshless study of dynamic failure in shells. J Eng Math 71, 205–222 (2011). https://doi.org/10.1007/s10665-010-9442-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-010-9442-4