Microplane model M7 for plain concrete. II: Calibration and verification

Ferhun C. Caner, Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


The microplane material model for concrete, formulated mathematically in the companion paper, is calibrated by material test data from all the typical laboratory tests taken from the literature. Then, the model is verified by finite-element simulations of data for some characteristic tests with highly nonuniform strain fields. The scaling properties of model M7 are determined. With the volumetric stress effect taken from the previous load step, the M7 numerical algorithm is explicit, delivering in each load step the stress tensor from the strain tensor with no iterative loop. This makes the model robust and suitable for large-scale finite-element computations. There are five free, easily adjustable material parameters, which make it possible to match the given compressive strength, the corresponding strain, the given hydrostatic compression curve, and certain triaxial aspects. In addition, there are many fixed, hard-to-adjust parameters, which can be taken to be the same for all concretes. The optimum values of material parameters are determined by fitting a particularly broad range of test results, including the important tests of compression-tension load cycles, mixed-mode fracture, tension-shear failure of double-edge-notched specimens, and vertex effect when axial compression is followed by torsion. Because of the lack of information on the material characteristic length or fracture energy, which can be obtained only by size effect tests on the same concrete, and on the precise boundary conditions and precise gauge locations, the finiteelement fitting of the present test data can hardly be expected to give better results than single-point simulations of specimens with approximately homogeneous strain states within the gauge length. Nevertheless, tensile test data with severe localization are delocalized on the basis of assumed material length. Model M7 is shown to fit a considerably broader range of test data than the preceding models M1- M6.

Original languageEnglish (US)
Pages (from-to)1724-1735
Number of pages12
JournalJournal of Engineering Mechanics
Issue number12
StatePublished - 2013


  • Concrete
  • Constitutive modeling
  • Cracking damage
  • Data fitting
  • Experimental verification
  • Finite-element analysis
  • Inelastic behavior
  • Model calibration

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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