Areas of Research

Potential-Based Cohesive Zone Model

PPR model

  • In the cohesive zone model, the fundamental issue for simulation of failure mechanisms is the characterization of cohesive interactions along the fracture surface.
  • PPR Model: A generalized potential-based constitutive model (PPR: Park-Paulino-Roesler) for mixed-mode cohesive fracture is developed in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions (Park 2009; Park et al., 2009). It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle).
  • Cohesive Frictional-Contact Model: Based on the PPR model, a cohesive frictional-contact model is developed in conjunction with a stick-slip condition, which provides consistent cohesive frictional forces under an unloading/reloading condition (Baek and Park, 2018). The proposed model reproduces slip-weakening behaviors along a fault plane and captures experimental shear stress-slip relations according to the change in compressive stress on the fracture surface.
  • Consistency of the Cohesive Zone Model: The PPR model provides a consistent traction-separation relationship. However, the model in Abaqus can lead to non-physical responses because of a pathological positive tangent stiffness under softening condition. This is reflected in cohesive tractions that increase and decrease repeatedly while the cohesive separation monotonically increases (Park et al., 2016).


Dynamic Cohesive Fracture

  • Microbarnching Instability: In general, the crack velocity cannot go beyond the Rayleigh wave speed because of microcrack formations (Sharon and Fineberg, 1996). Such physical phenomenon is captured in this computational example.
  • Mixed-Mode Crack Propagation: Kalthoff and Winkler (1987) tested a specimen, and observed that relatively lower loading rate resulted in brittle failure with a crack propagation angle of about 70 degree. Such physical phenomenon is captured in this computational example.
  • Adaptive Mesh Refinement & Coarsening: In order to reduce computational cost, adaptive mesh refinement is employed around crack tip regions while adaptive mesh coarsening is utilized on the basis of an error estimation.
  • Compact Compression Speciemen Test: Rittel and Maigre (1996) developed a test configuration to investigate mixed-mode dynamic crack initiation. In this computation, the edge-swap and nodal perturbation operators are employed to improve crack geometry representation.


  • J.F. Kalthoff, and S. Winkler, 1987, Failure mode transition at high rates of shear loading, International Conference on Impact Loading and Dynamic Behavior of Materials 1, 185-195
  • K. Park, 2009, Potential-based Fracture Mechanics Using Cohesive Zone and Virtual Internal Bond Modeling, Ph.D. Thesis, University of Illinois at Urbana-Champaign
  • K. Park, G.H. Paulino, W. Celes, and R. Espinha, 2012, Adaptive mesh refinement and coarsening for cohesive dynamic fracture, International Journal for Numerical Methods in Engineering (in press)
  • G.H. Paulino, K. Park, W. Celes, and R. Espinha, 2010, Adaptive dynamic cohesive fracture simulation using edge-swap and nodal perturbation operators, International Journal for Numerical Methods in Engineering 84 (11), 1303-1343
  • D. Rittel, and H. Maigre, 1996, An investigation of dynamic crack initiation in PMMA, Mechanics of Materials 23 (3), 229-239
  • E. Sharon, and J. Fineberg, 1996, Microbranching instability and the dynamic fracture of brittle materials, Physical Review B (Condensed Matter) 54 (10), 7128-7139

Fracture of Quasi-brittle Materials

PPR model

  • Concrete Fracture and Size Effect: The bilinear softening model is determined by measured fracture properties without calibration (Park et al., 2009; Roesler et al., 2007a). The proposed model is validated to predict mode-I fracture and size effect for concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 5050 blend of RCA and virgin coarse aggregate.
  • Fiber Reinforced Concrete: The cohesive traction-separation relationship for fiber reinforced concrete (FRC) is proposed by considering aggregate bridging zone and fiber bridging zone (Park et al., 2010; Roesler et al., 2007b). The proposed model predicts the fracture behavior of either fiber reinforced concrete beams or a combination of plain and fiber reinforced concrete functionally layered in a single beam specimen.
  • FRP Debonding: Interfacial debonding between concrete and fiber reinforced polymer (FRP) is investigated by measuring fracture properties and predicting FRP debonding failure without a calibration procedure (Park et al., 2015; Ha et al., 2018). The experimental computational results shows that the nominal interfacial strength decreases with increases in the specimen size, i.e., the size effect of the interfacial fracture. Thus, fracture parameters, such as the fracture energy, should be measured and evaluated to predict the interfacial fracture between concrete and FRP.



ABAQUS UEL for the PPR potential-based cohesive model

The PPR potential-based cohesive zone model is implemented in a commercial software, i.e. ABAQUS, as a user-defined element (UEL) subroutine. The source code of the UEL subroutine is provided for a two-dimensional linear cohesive element for educational purposes.

Integration of singular enrichment functions

A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and convergence properties of the technique.

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