Discrete mechanical models of concrete fracture

John E. Bolander*, Jan Eliáš, Gianluca Cusatis, Kohei Nagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


Discrete models of solids have been motivated, in large part, by the discontinuous and heterogeneous nature of material structure and its breakdown under loading. The capabilities of discrete models have evolved over the past several decades, offering novel means for investigating material structure–property relationships. However, lack of understanding of both the utilities and disadvantages of discrete models limits their further development and applications. This paper reviews relevant features of discrete approaches applied to modeling the mechanical behavior of geomaterials, concrete materials in particular. The discrete models are classified according to their form and abilities to represent elastic and fracture behaviors in the presence of large-scale material heterogeneity. Discretization of the material domain plays a large role in this respect. Emphasis is placed on particle-based lattice models. The relative merits of various strategies for introducing reinforcing components, which are essential for many applications, are outlined. Recent advances are highlighted, including the use of discrete models for coupled, multi-field analysis. The merits of discrete approaches are summarized in the conclusions.

Original languageEnglish (US)
Article number108030
JournalEngineering Fracture Mechanics
StatePublished - Nov 2021


  • Discrete model
  • Elasticity
  • Fracture
  • Lattice model
  • Rigid-body–spring model

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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