Spacetime dimensional analysis and self-similar solutions of linear elastodynamics and cohesive dynamic fracture

R. Abedi, R. B. Haber

Research output: Contribution to journalArticlepeer-review


We present a dimensional analysis and self-similar solutions for linear elastodynamics with extensions to dynamic fracture models based on cohesive traction-separation relations. We formulate the problem using differential forms in spacetime and show that the scaling rules expressed in terms of forms are simpler and more uniform than those obtained for tensor representations of the solution. In the extension to cohesive elastodynamic fracture, we identify and study the influence of certain intrinsic cohesive scales on dynamic fracture behavior and describe a fundamental set of nondimensional groups that uniquely identifies families of self-similar solutions. We present numerical studies of the influence of selected nondimensional parameters on dynamic fracture response to verify the dimensional analysis, including the identification of the fundamental set for cohesive fracture mechanics. We show that distinct values of a widely-used nondimensional quantity can produce self-similar solutions. Therefore, this quantity is not fundamental, and it cannot parameterize dynamic, cohesive-fracture response.

Original languageEnglish (US)
Pages (from-to)2076-2087
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number13
StatePublished - Jun 15 2011


  • Cohesive model
  • Dimensional analysis
  • Ductile-to-brittle transition
  • Elastodynamics
  • Fracture mechanics
  • Similitude
  • Traction-separation relation

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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