Three-dimensional cohesive zone model for fracture of cementitious materials based on the thermodynamics of irreversible processes

Francisco Evangelista, Jeffery R. Roesler, Sérgio P. Proença

Research output: Contribution to journalArticlepeer-review


This paper presents the formulation and implementation of a new 3-D cohesive zone element (CZM) with mode I traction-displacement laws for cementitious materials. The separation model is based on a damage mechanics framework which accounts for the thermodynamics of irreversible processes. Unlike many existing cohesive models, this proposed irreversible cohesive constitutive model prevents previous cohesive states from occurring on the fracture surface upon external or local unloading through a scalar damage parameter. In the proposed formulation, the interpenetration upon compressive loading is also avoided without any special contact algorithm. The CZM formulation and implementation are first verified using a 3-D uniaxial tension problem under tension and compression loading, unloading, and reloading. The proposed approach converged with higher values of the penalty stiffness without generating instabilities or oscillations in the traction profile. The damage-based evolution cohesive law was characterized by physically-defined fracture parameters derived from standard fracture tests for concrete materials (KIC, CTODC, Gf, and GF) and tensile strength (f 0 t). The proposed model was validated by predicting the fracture behavior of SEN(B) specimen for a wide range of concrete materials including plain concrete mixtures containing virgin aggregates and recycled concrete aggregates (RCA), and concrete with RCA and fibers or nano-silica particles. The proposed model was further validated by predicting the load-deflection of 1.8 m × 1.8m by 0.15 m concrete slabs experimentally tested on a soil foundation. The 3-D damage-based cohesive zone model simulations with bilinear softening, defined by small-scale fracture tests, were able to predict the concrete slab response and load capacity.

Original languageEnglish (US)
Pages (from-to)261-280
Number of pages20
JournalEngineering Fracture Mechanics
Issue number1
StatePublished - 2012


  • Cohesive zone
  • Concrete
  • Fracture
  • Quasi-brittle materials
  • Thermodynamic formulation
  • Three-dimensional crack propagation

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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