Educational Perspective of the PPR Potential Based Cohesive Model

The PPR UELs in 2D and 3D, based on the Engineering Fracture Mechanics journal papers below, are available for download on this page.

"Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective." K. Park and G.H. Paulino. Engineering Fracture Mechanics. Vol. 93, pp. 239-262, 2012.
Link to PDF

"A growing library of three-dimensional cohesive elements for use in ABAQUS." D. W. Spring and G.H. Paulino. Engineering Fracture Mechanics. Vol. 126, pp. 190-216, 2014.
Link to PDF

“Computational Homogenization of the Debonding of Particle Reinforced Composites: The Role of Interphases in Interfaces” D. W. Spring and G. H. Paulino. Computational Materials Science. Accepted

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Fortran UEL and Resources

The flowchart to the left shows the major steps of the PPR UEL, which is available below. The subroutine is entered and exited from the ABAQUS finite element routine at the green ellipses.

Downloads:

2D UEL (zip format)
3D BRICK UEL (zip format)
3D TET4 UEL (zip format)
3D TET10 UEL (3D) (zip format)



Additional PPR Resources:
  • Nomenclature (equivalence between variables in paper and in UEL)

sample flow chart

Flow chart of the PPR UEL

Example: Mixed mode bending analysis
ABAQUS analysis using the PPR UEL is shown below for the mixed-mode bending test. The domain is discretized by bilinear quadrilateral elements (Q4), and cohesive elements are inserted along the horizontal direction, which corresponds to the potential crack path, i.e. the intrinsic cohesive zone model. The analytical solution is available for 3 stages and is compared to the results obtained with the PPR model below.

Schematic of MBB beam
The ABAQUS input file representing the problem above is available for download below. The file contains the relevant information pertaining to the mesh (nodes and element connectivity), material properties for the bulk and cohesive elements, and loads and boundary conditions, etc.

Download input file (2D)
Download input file (3D)


The results shown in the figure to the right can be obtained using a simple Matlab script that parses the relevant information from the ABAQUS output file (*.dat) and plots the result.

Download MatLab parser/plotter
Example: Small deformation coated particle debonding
The following example is that of a single coated particle imbedded in an elastic matrix. The model considers a single octant of the particle, with symmetric boundary conditions, as illustrated in the Figure. The particle has a radius of 1 mm, the coating has a thickness of 0.2 mm, and the particle volume fraction is 40%. Linear, eight-node brick (B8) elements are used to discretize the domain. Approximately 150,000 elements discretize the bulk domain, while 3230 cohesive elements are inserted between the coating and the bulk matrix to account for the debonding behavior.




The ABAQUS input file representing the problem above is available for download below. The file contains the relevant information pertaining to the mesh (nodes and element connectivity), material properties for the bulk and cohesive elements, and loads and boundary conditions, etc.

Download input file (3D)


The results shown in the figure to the left can be obtained using a simple Matlab script that parses the relevant information from the ABAQUS output file (*.dat) and plots the result.

Download MatLab parser/plotter
Example: Activation of friction in a masonry wallette
This example considers the shear loading of a masonry wallette, and demonstrates the influence of the coupled cohesive-friction model when a significant frictional effect is activated. The masonry wallette consists of three bricks, linked with two mortar joints, however, the numerical model uses symmetric boundary conditions and only considers half the full model, as illustrated in the Figure. The domain is discretized using a uniform mesh of linear brick elements of dimension 5 x 5 x 5 mm. The resulting discretization contains 68,400 elements and 75,579 nodes. Moreover, 3,500 cohesive elements are used to capture the failure/friction response of the interface.




The ABAQUS input file representing the problem above is available for download below. The file contains the relevant information pertaining to the mesh (nodes and element connectivity), material properties for the bulk and cohesive elements, and loads and boundary conditions, etc.

Download UEL w/ friction
Download input file


The results shown in the figure to the left can be obtained using a simple Matlab script that parses the relevant information from the ABAQUS output file (*.dat) and plots the result. 

Download MatLab parser/plotter