Estimation of Energy of Fracture Initiation in Brittle Materials with Cracks

  • Ruslan L. Lapin
  • Nikita D. Muschak
  • Vadim A. Tsaplin
  • Vitaly V. KuzkinEmail author
  • Anton M. Krivtsov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 100)


We study deformation and fracture of a brittle material under mixed quasi-static loading. Numerical simulations of deformation of a cubic sample containing a single crack are carried out using the particle dynamics method. Effect of ratio of compressive and shear loads on energy of fracture initiation is investigated for two crack shapes and various crack orientations. The energy of fracture initiation in a material containing multiple cracks is estimated using the non-interaction approximation. It is shown that in the case of mixed loading (compression and shear) the energy is significantly lower than in the case of pure compression. Presented results may serve for minimization of energy consumption during disintegration of solid minerals.


Brittle fracture Fracture initiation Cracks Particle dynamics method Desintegration of rocks Energy consumption 


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This work was supported by the Russian Science Foundation (Grant No. 17-79-30056). The authors are deeply grateful L.A Vaisberg for formulation of the problem and useful discussions. The work was initiated in the course of joint investigation of technological processes of vibration disintegration of materials, the main developer of which is REC “Mekhanobr-Tekhnika”. Numerical modeling was performed using the Polytechnic supercomputer center at Peter the Great St. Petersburg Polytechnic University.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruslan L. Lapin
    • 1
  • Nikita D. Muschak
    • 1
  • Vadim A. Tsaplin
    • 1
    • 2
  • Vitaly V. Kuzkin
    • 1
    • 2
    Email author
  • Anton M. Krivtsov
    • 1
    • 2
  1. 1.Peter the Great St. Petersburg Polytechnic University, Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsSt. PetersburgRussia
  2. 2.Laboratoty “Discrete models in mechanics”Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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