nD material for unit to unit connections in aggregates - eesd-epfl/OpenSees GitHub Wiki
To model the response of the interface between two units, an nD material model named CohesionFriction3D was implemented into OpenSEES (McKenna et al. 2000) and defined in the library CohesionFriction3D.dll.
In the direction normal to the interface (x-direction of the interface), a uniaxial material model is assigned by a user. The shear displacement is computed as resultant from the displacements in the y- and z-direction of the interface, which are the in-plane directions of the interface. The shear force that can be transmitted by the interface is limited by the friction force, which is computed from the instantaneous axial force that acts across the interface, a friction coefficient and an exponentially degrading cohesion law. It was built upon the work by Lourenco (1996) and Vanin et al. (2020) and extended the latter from a 2D to a 3D problem.
In the first step of the material iterative cycle, the axial force acting on the interface is computed based on the uniaxial material model assigned to the axial direction. In the second step, the calculated axial force is used to compute a yield function for the shear stress in the local y-z plane. For this purpose, an iterative return-mapping algorithm was implemented. The degradation of the cohesion is modelled through the input of the fracture energy value, and the frictional force is evaluated from the axial force and the friction coefficient. The input parameters for this interface model are therefore: a uniaxial material model, the cohesion force of the interface (ci), Mode II fracture energy of the interface (Gf,II) and a friction coefficient of the interface (μi).
The input structure is:
nDMaterial CohesionFriction3d $matTag $G $mu $c $GfII -axialMaterial axialmatTag
Where:
| matTag | Material tag |
|---|---|
| G | Shear stiffness of the interface |
| mu | Friction coefficient at the interface |
| c | Cohesion of the interface |
| GfII | Shear fracture energy of the interface |
| axialmatTag | Axial material tag |
The CohesionFriction3D ND material model is often paired with TensionDamage1D non crushing material to simulate the axial interaction and obtain the force for the computation of the yield function.
References
Lourenco, P. B. (1996). Computing Strategies for masonry structures (Doctoral dissertation, PhD. Thesis: Delft Univ. of Technology).
McKenna, F., Fenves, G. L., Scott, M. H., & Jeremic, B. (2000). Open system for earthquake engineering simulation (OpenSees). Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.
Vanin, F., Penna, A., & Beyer, K. (2020). Equivalent-frame modeling of two shaking table tests of masonry buildings accounting for their out-of-plane response. Frontiers in Built Environment, 6, 42.