A rigorous universal model for the dynamic strength of materials across loading rates

Ye Feng, Jiadi Fan, Ellad B. Tadmor

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The dynamic strength for a broad range of materials with different microstructures exhibits surprisingly similar behavior. Two distinct regimes are observed with a sharp transition between them. At low loading rates, the strength has a weak linear dependence on the log loading rate until a critical rate above which a dramatic increase is observed. We explain this behavior by considering material failure as a bond-breaking process driven by external loading and thermal fluctuation within a Langevin dynamics framework. The analysis leads to nondimensional measures for which the dynamic response collapses onto a universal curve, independent of material properties, describing both loading rate regimes and the transition between them. A simple approximate model is derived that provides an excellent fit to experimental data for a broad range of materials, including concrete, ceramics, and metals.

Original languageEnglish (US)
Article number104715
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Feb 2022

Bibliographical note

Funding Information:
YF was supported by the International Exchange Program for Graduate Students, Tongji University (No. 201902016 ). EBT was partly supported by the National Science Foundation through awards DMR-1607670 and CMMI-1462807 .

Publisher Copyright:
© 2021 Elsevier Ltd


  • Damped dynamics
  • Dynamic fracture
  • Dynamic increase factor
  • Dynamic material strength
  • Fiber bundle model
  • Fokker–Planck equation
  • Langevin equation
  • Nonequilibrium statistical physics
  • Reaction rate theory


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