Lattice Discrete Particle Modeling of Size Effect in Slab Scratch Tests

Lin Han, Madura Pathirage, Ange Therese Akono, Gianluca Cusatis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


For a long time, geomechanicians have used scratch tests to characterize the compressive behavior and hardness of rocks. In recent years, this test has regained popularity in the field of mechanics, especially after a series of publications that highlighted the potential capability of the scratch test to determine the fracture properties of quasi-brittle materials. However, the complex failure mechanisms observed experimentally in scratch tests led to scientific debates and, in particular, raised the question of the size effect. This article intends to provide a better understanding of the problem by using numerical tools and fracture mechanics considerations. To narrow the investigation area, this study focuses on slab scratch tests of quasi-brittle materials and adopts two different numerical methods: (i) the lattice discrete particle model (LDPM) that includes constitutive laws for cohesive fracturing, frictional shearing, and nonlinear compressive behavior, and (ii) the meshless method based on Shepard function and partition of unity (MSPU) implementing linear elastic fracture mechanics (LEFM). The numerical results are further analyzed through Baant's size effect law (SEL) with an appropriate mixed-mode fracture criterion. Fracture properties are then calculated and compared to the results of typical notched three-point bending tests. The results show that mixed-mode fracture considerations are of paramount importance in analyzing the fracture process and size effect of scratch tests.

Original languageEnglish (US)
Article number1089724
JournalJournal of Applied Mechanics, Transactions ASME
Issue number2
StatePublished - Feb 1 2021


  • Scratch test
  • constitutive modeling of materials
  • failure criteria
  • fracture energy
  • lattice discrete particle model
  • linear elastic fracture mechanics
  • mechanical properties of materials
  • mixed-mode fracture
  • nonlinear fracture mechanics
  • size effect

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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