Anisotropic damage model for concrete and other quasi-brittle materials

Jani Vilppo, Reijo Kouhia (Corresponding Author), Juha Hartikainen, Kari Kolari, Alexis Fedoroff, Kim Calonius

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)


A thermodynamically consistent formulation to model anisotropic damage for quasi-brittle materials is proposed. The model is based on proper expressions for the specific Gibbs free energy and the complementary form of the dissipation potential. Damaging of the material is described by a symmetric positive definite second order damage tensor. Especially, the failure surface is formulated in such a way that it will mimic the behaviour of the well known Ottosen's four parameter failure surface. While testing the model against the experimental results found in literature, the results were in good agreement in uniaxial tensile and compressive loadings as well as in biaxial compression. Besides the correct failure stress states, the model predicts the correct failure modes of concrete: axial splitting along the direction of uniaxial compression and tensile damaging normal to the direction of tension.

Original languageEnglish
Article number111048
Number of pages13
JournalInternational Journal of Solids and Structures
Early online date28 Apr 2021
Publication statusPublished - 15 Aug 2021
MoE publication typeA1 Journal article-refereed


  • Anisotropic damage
  • Axial splitting
  • Concrete
  • Constitutive equations
  • Dissipation potential
  • Elastic-brittle material
  • Failure modes
  • Ottosen's 4-parameter criterion
  • The specific Gibbs free energy


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