NairnFEA Icon

Imperfect Interface Elements

Introduction

Imperfect interfaces elements in NairnFEA allow modeling of imperfect interfaces in composite materials. These elements may be unique to NairnFEA. They are implement as described in Nairn (2007) following the theory described by Hashin (1992).

Mechanics Theory

At a perfect interface, all stresses and displacements are continuous. In contrast, at a crack or at an imperfect interface, the stresses will still be continuous, but the displacements may be discontinuous. Even an opened crack meets this definition - the surface traction on an opened crack will be zero (which is continuous) while the displacements will be discontinuous and describe the crack opening displacements. To define an imperfect interface, let [un] and [ut] be the normal and tangential displacement discontinuities. To be a linear-elastic, imperfect interface, the displacement discontinuities are proportional to the tractions in the same direction:

[un] = Tn / Dn
[ut] = Tt / Dt

where Tn and Tt are the normal and tangential components of the traction vector on the interfacial surface and Dn and Dt are interface parameters that define stiffnesses of the interface for development on normal or tangential displacement discontinuities. Interface parameters of Dn = Dt = ∞ leads to zero displacement discontinuity or a perfect interface; Dn = Dt = 0 leads to zero traction or a debonded interface. All other finite values define an imperfect interface.

Notes

  1. Imperfect interface elements are created by defining two separate, but identical paths within a object and then using the Area Command with those two paths. The two paths must have been previously used to mesh exactly one area each with solid elements. Imperfect interface elements will connect those two areas with an imperfect interface.
  2. The interface properties for the material assigned to the interface elements are set by defining an "Interface" material (see Material Command).
  3. For an imperfect interface in contact the normal traction will be compressive and thus a linear-elastic imperfect interface material will allow negative displacement discontinuity in the normal direction or overlap on the surfaces. A method to avoid such non-physical surface overlap is to set Dn = ∞ where ever the interfaces are in contact. Dt may be anything since sign of tangential displacement discontinuities can be positive or negative. If regions where the interfaces are in contact are not known in advance, they can be adjusted iteratively following inspection of interfacial normal stresses after each calculation.
  4. The interface elements in NairnFEAMPM were independently developed. Their derivation is an implementation of the variational principles for materials with imperfect interfaces derived by Hashin (1992). The details of the NairnFEAMPM implementation are given in Nairn (2007).
  5. Interface elements are not solid elements and thus can not define all elements of a stress tensor. When a calculation outputs elements stresses, the interface elements will output only normal and tangential components of the interfacial traction ( Tn and Tt). Tn will be output as σxx (or σrr for axisymmetric analyses) and Tn will be output as σxy (or σrz for axisymmetric analyses). All other output stresses will be zero. You can plot interfacial tractions in mesh plots, but they can only be plotted if the output file includes the element stresses.
  6. Interface elements will have energy related to tractions and displacements (see Hashin (1992)). This total energy will be proper result including interfacial energy.
  7. Perfect Interface: If both Dn and Dt are very large, the displacement discontinuities will be zero. In other words, the analysis will act like there is no interface. The finite element solution will be identical to the same mesh in which the interface is removed and the nodes on the two sides of the interface are combined.
  8. Sliding Interface or Mode II Crack: If Dn is very large but Dt is not, the interface will have [un]=0, which means the surfaces will not interpenetrate each other, but it will have non-zero tangential displacements. In other words, the interface may slide. This type of interface is often a good model for mode II cracks in which the interfaces contact each other and thus develop compressive stresses. Setting Dn large will give the correct compressive stresses while setting Dt=0 will allow frictionless sliding or mode II displacements. (Warning: Interface Elements are linear (as is necessary in linear finite element analysis). Thus, if your intention is to prevent contact between two crack surfaces, Interface Elements will only work if the resulting solution is compressive along the entire interface. If the crack tries to open, these element keep [un]=0 by introducing non-zero tensile stresses. Such a result may not be realistic for mode II cracks if it happens over a significant part of the crack surface.)
  9. Imperfect interfaces can also be modeling in NairnMPM and they have the additional option of allowing different stiffnesses in tension and compression for normal displacement discontinuities.