Fracturing rate effect and creep in microplane model for dynamics

Zdenek P. Bazant*, Ferhun C. Caner, Mark D. Adley, Stephen A. Akers

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


The formulation of microplane model M4 in Parts I and II is extended to rate dependence. Two types of rate effect in the nonlinear triaxial behavior of concrete are distinguished: (1) Rate dependence of fracturing (microcrack growth) associated with the activation energy of bond ruptures, and (2) creep (or viscoelasticity). Short-time linear creep (viscoelasticity) is approximated by a nonaging Maxwell spring-dashpot model calibrated so that its response at constant stress would be tangent to the compliance function of model B3 for a time delay characteristic of the problem at hand. An effective explicit algorithm for step-by-step finite-element analysis is formulated. The main reason that the rate dependence of fracturing must be taken into account is to simulate the sudden reversal of postpeak strain softening into hardening revealed by recent tests. The main reason that short-time creep (viscoelasticity) must be taken into account is to simulate the rate dependence of the initial and unloading stiffness. Good approximations of the rate effects observed in material testing are achieved. The model is suitable for finite-element analysis of impact, blast, earthquake, and shorttime loads up to several hours duration.

Original languageEnglish (US)
Pages (from-to)962-970
Number of pages9
JournalJournal of Engineering Mechanics
Issue number9
StatePublished - Sep 2000

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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