Proposal of m-Index for Rating Fracture and Damage Models by Their Ability to Represent a Set of Distinctive Experiments

Zdeněk P. Bažant*, Hoang Thai Nguyen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A recent comparative study revealed that the commonly offered experimental validations of peridynamics and phase-field fracture models have been insufficient because they involved only nondistinctive experiments, i.e., experiments that can be closely fitted by different models that at the same time give very different predictions in important practical applications. The comparisons showed that the peridynamic and phase-field models are incapable of simulating a set of 11 distinctive experiments-experiments that are critical for assessing the accuracy of different models and are representative of fracture behavior of engineering structures. Practical applications would be helped by common adoption of a model index that would compare the predictive capability of various fracture models quantitatively. Proposed here for further discussion is an example of a possible numerical index, the m-Index, which attempts to characterize how well the optimal calibration of model parameters can match the experimental evidence, such as the fracture patterns, measured response curves, size effect, and crack-parallel stress effect. Included are only the distinctive experiments. As an example, the m-Index is here calculated for a set of seven fracture models whose performance was previously compared with 11 distinctive experiments. This previous comparison of seven models is here extended to an eighth model, proposed as a fresh improvement of peridynamics. The choice of distinctive experiments is one of the subjects calling for further discussion. Despite inevitable imperfections, a widely adopted index for appraising new material models would mitigate waste of researchers' effort and grant funds, as well as the space in scientific journals and conference programs.

Original languageEnglish (US)
Article number04023047
JournalJournal of Engineering Mechanics
Issue number8
StatePublished - Aug 1 2023


  • Crack band (CB) models
  • Distinctive experiment
  • Fracture model
  • m-Index
  • Peridynamics (PD)
  • Phase-field (PF) models

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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