This paper aims at the development and implementation of an algorithm for the treatment of damage and fracture in smooth particle hydrodynamic (SPH) method, where free surface, crack opening, including its propagation and branching is modelled by weakening the interparticle interactions combined with the visibility criterion. The model is consistent with classical continuum damage mechanics approach, but does not use an effective stress concept. It is a difficult task to model fracture leading to fragmentation in materials subjected to high-strain rates using continuum mechanics. Meshless methods such as SPH are well suited to be applied to fracture mechanics problems, since they are not prone to the problems associated with mesh tangling. The SPH momentum equation can be rearranged and expressed in terms of a particle-particle interaction area. Damage acts to reduce this area, which is ultimately set to zero, indicating material fracture. The first implementation of the model makes use of Cochran-Banner damage parameter evolution and incorporates a multiple bond break criterion for each neighbourhood of particles. This model implementation was verified in simulation of the one-dimensional and three-dimensional flyer plate impact tests, where the results were compared to experimental data. The test showed that the model can recreate the phenomena associated with uniaxial spall to a high degree of accuracy. The model was then applied to orthotropic material formulation, combined with the failure modes typical for composites, and used for simulation of the hard projectile impact on composite target.
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering. 1999;45:601–20.
2.
Belytschko T, Guo Y, Kam Liu W, Ping Xiao S. A unified stability analysis of meshless particle methods. International Journal for Numerical Methods in Engineering. 2000;48:1359–400.
3.
Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering. 1996;39:923–38.
4.
Chang FK, Chang KY. Post-Failure Analysis of Bolted Composite Joints in Tension or Shear-Out Mode Failure. Journal of Composite Materials. 1987;21(9):809–33.
5.
Chang FK, Chang KY. A Progressive Damage Model for Laminated Composites Containing Stress Concentrations. Journal of Composite Materials. 1987;21(9):834–55.
6.
Cochran S, Banner D. Spall studies in uranium. Journal of Applied Physics. 1977;48(7):2729–37.
7.
Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society. 1977;181(3):375–89.
8.
Gravouil A, Moës 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(11):2569–86.
9.
Kachanov L. Time of the rupture process under creep conditions. Izy Akad Nank SSR Otd Tech Nauk. 1958;26–31.
10.
Krysl P, Belytschko T. The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks. International Journal for Numerical Methods in Engineering. 1999;44:767–800.
11.
Lemaitre J. A Continuous Damage Mechanics Model for Ductile Fracture. Journal of Engineering Materials and Technology. 1985;107(1):83–9.
12.
Libersky L, Petschek A. Smooth particle hydrodynamics with strength of materials. 1991;248–57.
13.
Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA. High Strain Lagrangian Hydrodynamics. Journal of Computational Physics. 1993;109(1):67–75.
14.
Lucy LB. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal. 1977;82:1013.
15.
Malvern L. Introduction to the Mechanics of a Continuous Medium. 1969;
16.
Mirkovic J. Modelling of Nonlinear Behaviour of Metallic Structure Components. 2004;
17.
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Methods Eng. 1999;(1):131–50.
18.
Moës N, Gravouil A, Belytschko T. Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model. International Journal for Numerical Methods in Engineering. 2002;53(11):2549–68.
19.
Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis. Int J Numer Methods Eng. 1999;(9):2–7.
20.
Pandolfi A, Krysl P, Ortiz M. Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture. International Journal of Fracture. 1999;95(1–4):279–97.
21.
Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering. 2004;61(13):2316–43.
22.
Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering. 2007;196(29–30):2777–99.
23.
Rabczuk T, Belytschko T, Xiao SP. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering. 2004;193(12–14):1035–63.
24.
Reveles J. Development of a Total Lagrangian SPH code for the simulation of solids under impact loading. 2007;
25.
Stolarska M, Chopp DL, Moës N, Belytschko T. Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering. 2001;51(8):943–60.
26.
Steinberg D. Equation of State and Strength Properties of Selected Materials. UCRL-MA-106439. 1996;
27.
Swegle JW, Attaway SW, Heinstein MW, Mello FJ, Hicks DL. An analysis of smoothed particle hydrodynamics. Office of Scientific and Technical Information (OSTI); 1994.
SWEGLE JW. Conservation of Momentum and Tensile Instability in Particle Methods. Office of Scientific and Technical Information (OSTI); 2000.
30.
Ventura G, Xu JX, Belytschko T. A vector level set method and new discontinuity approximations for crack growth by EFG. International Journal for Numerical Methods in Engineering. 2002;54(6):923–44.
31.
Vignjevic R, Reveles J, Campbell J. SPH in a total lagrangian formalism. CMES -Computer Modeling in Engineering and Sciences. 2006;
32.
Vignjevic R, Campbell J, Jaric J, Powell S. Derivation of SPH equations in a moving referential coordinate system. Computer Methods in Applied Mechanics and Engineering. 2009;198(30–32):2403–11.
33.
Vignjevic R, DeVuyst T, Campbell J. The nonlocal, local and mixed forms of the SPH method. Computer Methods in Applied Mechanics and Engineering. 2021;387:114164.
34.
Vignjevic R, Campbell J, Libersky L. A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Computer Methods in Applied Mechanics and Engineering. 2000;184(1):67–85.
35.
Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids. 1994;42(9):1397–434.
36.
Zhou F, Molinari JF. Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. International Journal for Numerical Methods in Engineering. 2003;59(1):1–24.
The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.
