Lattice Discrete Particle Modeling of Size Effect in Slab Scratch Tests

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

Research output: Contribution to journalArticlepeer-review


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 size effect. This manuscript intends to provide a better understanding of the problem by using numerical tools and fracture mechanics considerations. In order 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 Bažant'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)
JournalJournal of Applied Mechanics
StateE-pub ahead of print - Oct 30 2020


  • constitutive modeling of materials
  • failure criteria
  • mechanical properties of materials
  • mixed mode fracture

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