Abstract
A parallel computation methodology is proposed to study the dynamic fracture process of a flexible multibody system with initial cracks. The potential fracture domains of the flexible body system are described by using the particles of smoothed particle hydrodynamics (SPH), and the other domains of the system are modeled by using the finite elements of absolute nodal coordinate formulation (ANCF). In order to preserve the continuity of deformation field, extra virtual particles are uniformly embedded into the interface, where the finite elements of ANCF and the particles of SPH are connected, so as to transmit the interaction forces. The OpenACC derivatives are used to parallelize both the particle contact detection and the solution of the integral equations. A predictor-corrector scheme is used to solve the ordinary differential equations for the particles of SPH, while the generalized-alpha method is used to solve the huge set of differential algebraic equations for the multibody system. The OpenMP derivatives are also used to parallelize the evaluation of the elastic force vectors and their Jacobi matrices of the finite elements. Finally, three case studies are given to validate the proposed computation methodology.
Similar content being viewed by others
References
Belytschko, T., Chen, H., Xu, J., Zi, G.: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. Methods Eng. 58, 1873–1905 (2003)
Taylor, D., Cornetti, P., Pugno, N.: The fracture mechanics of finite crack extension. Eng. Fract. Mech. 72, 1021–1038 (2005)
Mergheim, J., Kuhl, E., Steinmann, P.: A finite element method for the computational modelling of cohesive cracks. Int. J. Numer. Methods Eng. 63, 276–289 (2005)
Armero, F., Linder, C.: Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int. J. Fract. 160, 119–141 (2009)
Li, M., Werner, E., You, J.: Fracture mechanical analysis of tungsten armor failure of a water-cooled divertor target. Fusion Eng. Des. 89, 2716–2725 (2014)
Song, J., Wang, H., Belytschko, T.: A comparative study on finite element methods for dynamic fracture. Comput. Mech. 42, 239–250 (2008)
Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, New York (2005)
Shabana, A.A.: Computational Dynamics, 3rd edn. Wiley, New York (2010)
Irwin, G.R.: Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957)
Wells, A.A.: Application of fracture mechanics at and beyond general yield. Br. Weld. J. 10, 563–570 (1963)
Sukumar, N., Belytschko, T.: Arbitrary branched and intersecting cracks with the extended finite element method. Int. J. Numer. Methods Eng. 48, 1741–1760 (2000)
Portela, A., Aliabadi, M.H., Rooke, D.P.: The dual boundary element method: effective implementation for crack problems. Int. J. Numer. Methods Eng. 33, 1269–1287 (1992)
Pan, E.: A general boundary element analysis of 2-D linear elastic fracture mechanics. Int. J. Fract. 88, 41–59 (1997)
Areias, P.M.A., Belytschko, T.: Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int. J. Numer. Methods. Eng. 63, 760–788 (2005)
Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1020 (1977)
Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)
Benz, W., Asphaug, E.: Simulations of brittle solids using smooth particle hydrodynamics. Comput. Phys. Commun. 87, 253–265 (1995)
Xu, F., Zhao, Y., Li, Y., Kikuchi, M.: Study of numerical and physical fracture with SPH method. Acta Mech. Solida Sin. 23, 49–56 (2010)
Maurel, B., Combescure, A.: An sph shell formulation for plasticity and fracture analysis in explicit dynamics. Int. J. Numer. Methods Eng. 76, 949–971 (2008)
Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003)
Liu, G.R.: Mesh Free Methods: Moving Beyond the Finite Element Method, p. 692. CRC Press, Boca Raton (2003)
Das, R., Cleary, P.: Effect of rock shapes on brittle fracture using smoothed particle hydrodynamics. Theor. Appl. Fract. Mech. 53, 47–60 (2010)
Chakraborty, S., Shaw, A.: A pseudo-spring based fracture model for SPH simulation of impact dynamics. Int. J. Impact Eng. 58, 84–95 (2013)
Liu, W.K., Chen, Y.: Wavelet and multiple scale reproducing kernel methods. Int. J. Numer. Methods Fluids 21, 901–931 (1995)
Chen, J.K., Beraun, J.E., Carney, T.C.: A corrective smoothed particle method for boundary value problems in heat conduction. Comput. Methods Appl. Mech. Eng. 46, 231–252 (1999)
Chen, J.K., Beraun, J.E., Jih, C.J.: Completeness of corrective smoothed particle method for linear elastodynamics. Comput. Mech. 24, 273–285 (1999)
Monaghan, J.J.: SPH without a tensile instability. J. Comput. Phys. 159, 290–311 (2000)
Gray, J.P., Monaghan, J.J., Swift, R.P.: SPH elastic dynamics. Comput. Methods Appl. Mech. Eng. 190, 6641–6662 (2001)
Hu, W., Tian, Q., Hu, H.Y.: Dynamic simulation of liquid-filled flexible multibody systems via absolute nodal coordinate formulation and SPH method. Nonlinear Dyn. 75, 653–671 (2014)
Pazouki, A., Serban, R., Negrut, D.: A high performance computing approach to the simulation of fluid-solid interaction problems with rigid and flexible components. Arch. Mech. Eng. 61, 227–251 (2014)
Rojek, J., Oñate, E., Labra, C., Kargl, H.: Discrete element simulation of rock cutting. Int. J. Rock Mech. Min. 48, 996–1010 (2011)
Johnson, G.R.: Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations. Nucl. Eng. Des. 150, 265–74 (1994)
Johnson, G.R., Stryk, R.A., Beissel, S.R.: SPH for high velocity impact computations. Comput. Methods Appl. Mech. Eng. 139, 347–373 (1996)
Fernández-Méndez, S., Bonet, J., Huerta, A.: Continuous blending of SPH with finite elements. Comput. Struct. 83, 1448–1458 (2005)
Zhang, Z., Qiang, H., Gao, W.: Coupling of smoothed particle hydrodynamics and finite element method for impact dynamics simulation. Eng. Struct. 33, 255–264 (2011)
Chuzel-Marmot, Y., Ortiz, R., Combescure, A.: Three dimensional SPH–FEM gluing for simulation of fast impacts on concrete slabs. Comput. Struct. 89, 2484–2494 (2011)
Rabczuk, T., Xiao, S.P., Sauer, M.: Coupling of meshfree methods with finite elements: basic concept and test results. Commun. Numer. Methods Eng. 22, 1031–65 (2006)
Vuyst, T.D., Vignjevic, R., Campbell, J.C.: Coupling between meshless and finite element methods. Int. J. Impact Eng. 31, 1054–1064 (2005)
Shabana, A.A.: An Absolute Nodal Coordinates Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies. Technical report no. MBS96-1-UIC, University of Illinois at Chicago (1996)
Liu, C., Tian, Q., Hu, H.Y.: Dynamics of large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26, 283–305 (2011)
Liu, C., Tian, Q., Hu, H.Y.: Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF. Comput. Methods Appl. Mech. Eng. 258, 81–95 (2013)
Tian, Q., Zhang, Y., Chen, L., Yang, J.: An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 4, 021009 (2009)
Olshevskiy, A., Dmitrochenko, O., Dai, M.D., Kim, C.W.: The simplest 3-, 6- and 8-noded fully-parameterized ANCF plate elements using only transverse slopes. Multibody Syst. Dyn. 34, 1–29 (2014)
Yoo, W.S., Dmitrochenko, O., Yu, D.: Review of finite elements using absolute nodal coordinates for large-deformation problems and matching physical experiments. In: ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA (2005), DETC2005-84720
Schiehlen, W.: Research trends in multibody system dynamics. Multibody Syst. Dyn. 18, 3–13 (2007)
Gerstmayr, J., Sugiyama, H., Mikkola, A.: Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. J. Comput. Nonlinear Dyn. 8, 369–384 (2013)
Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)
Libersky, L.D., Petschek, A.G.: Smooth particle hydrodynamics with strength of materials. Lect. Notes Phys. 395, 248–257 (1991)
Monaghan, J.J.: Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30, 543–574 (1992)
Monaghan, J.J.: On the problem of penetration in particle methods. J. Comput. Phys. 82, 1–15 (1989)
Swegle, J.W., Hicks, D.L., Attaway, S.W.: Smoothed particle hydrodynamics stability analysis. J. Comput. Phys. 116, 123–134 (1995)
Balsara, D.S.: Von neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms. J. Comput. Phys. 121, 357–372 (1995)
Colagrossi, A., Landrini, M.: Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191, 448–475 (2003)
Dilts, G.A.: Moving-least-squares-particle hydrodynamics-I. Consistency and stability. Int. J. Numer. Methods Eng. 44, 1115–1155 (1999)
Randles, P.W., Libersky, L.D.: Smoothed particle hydrodynamics: some recent improvements and applications. Comput. Methods Appl. Mech. Eng. 139, 375–408 (1996)
Gutfraind, R., Savage, S.B.: Smoothed particle hydrodynamics for the simulation of broken-ice fields: Mohr–Coulombtype rheology and frictional boundary conditions. J. Comput. Phys. 134, 203–215 (1997)
Wang, J., Chan, D.: Frictional contact algorithms in SPH for the simulation of soil–structure interaction. Int. J. Numer. Anal. Meth. Geomech. 38, 747–770 (2014)
Shabana, A.A., Yakoub, R.Y.: Three-dimensional absolute nodal coordinate formulation for beam elements: theory. J. Mech. Design. 123, 606–613 (2001)
Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. J. Mech. Design. 123, 614–621 (2001)
Liu, C., Tian, Q., Hu, H.Y., García-Vallejo, D.: Simple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems. Nonlinear Dyn. 69, 127–147 (2012)
Liu, C., Tian, Q., Hu, H.Y.: New spatial curved beam and cylindrical shell elements of gradient deficient absolute nodal coordinate formulation. Nonlinear Dyn. 70, 1903–1918 (2012)
Hussein, B., Negrut, D., Shabana, A.A.: Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dyn. 54, 283–296 (2008)
Shabana, A.A., Hussein, B.: A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: application to multibody systems. J. Sound Vib. 327, 557–563 (2009)
Hussein, B., Shabana, A.A.: Sparse matrix implicit numerical integration of the stiff differential/algebraic equation: implementation. Nonlinear Dyn. 65, 369–382 (2011)
Chung, J., Hulbert, G.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J. Appl. Mech. 60, 371–375 (1993)
Arnold, M., Brüls, O.: Convergence of the generalized-\(\alpha \) scheme for constrained mechanical systems. Multibody Syst. Dyn. 18, 185–202 (2007)
Tian, Q., Sun, Y.L., Liu, C., Hu, H.Y., Paulo, F.: Elastohydrodynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114, 106–120 (2013)
Tian, Q., Zhang, Y., Chen, L., Yang, J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60, 489–511 (2010)
Tian, Q., Liu, C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64, 25–67 (2011)
Liu, C., Tian, Q., Hu, H.Y.: Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mech. Mach. Theory 52, 106–129 (2012)
Tian, Q., Xiao, Q.F., Sun, Y.L., Hu, H.Y., Liu, H., Flores, P.: Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints. Multibody Syst. Dyn. 33, 259–284 (2015)
Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–406 (1994)
Hermanns, M.: Parallel Programming in Fortran 95 Using OpenMP. http://www.openmp.org/presentations/miguel/F95_OpenMPv1_v2.pdf (2002)
The OpenACC Standard. http://www.openacc-standard.org
Monaghan, J.J., Kos, A.: Solitary waves on a Cretan beach. J. Waterw. Port Coast. Ocean Eng. 125, 145–154 (1999)
Amini, Y., Emdad, H., Farid, M.: A new model to solve fluid–hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method. Eur. J. Mech. B Fluids. 30, 184–194 (2011)
James, M.G., Barry, J.G.: Mechanics of Materials, 7th edn. CL-Engineering, Stamford, CT (2008)
Acknowledgments
This work was supported in part by National Natural Science Foundations of China under Grants 11290151, 11221202 and 11472042. The work was also supported in part by Excellent Young Scholar Research Fund from Beijing Institute of Technology and supported in part by the Beijing Higher Education Young Elite Teacher Project under Grant YETP1201.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hu, W., Tian, Q. & Hu, H. Dynamic fracture simulation of flexible multibody systems via coupled finite elements of ANCF and particles of SPH. Nonlinear Dyn 84, 2447–2465 (2016). https://doi.org/10.1007/s11071-016-2657-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-016-2657-9