Nonlinear Imperfect Interface

Description

This imperfect interface contact law implements an imperfect interface with tractions that depend on displacement discontinuities at the interface. The tractions must have continuous first derivative. The current implements allows only two traction laws. The material model, however, can easily be edited to create a custom imperfect interface model.

Nonlinear Interface Laws

The normal and tangential interface laws currently available are listed below. These can be selected for either direction using the normal_shape or tangential_shape properties.

Linear Interface

This implementation is essentially that same as a Linear Imperfect Interface, but it is implemented without assuming a linear interface law (one use to to verify it matches more detailed solution in the Linear Imperfect Interface). Because this non-linear implementation assumes continuous first derivative, however, this linear interface has to have the same stiffness in tension and compression (i.e., Dnt=Dnc). If you need to model a bilinear interface laws, use the Linear Imperfect Interface model instead.

Morse Potential

A Morse potential is sometimes used in molecular modeling to describe bonding potential between two atoms as a function of separation distance. It is used here as an example of a reversible traction law with a peak traction. For this law, the interfacial potential energy is:

      [math]\displaystyle{ \phi_i = D_e\left(1-e^{-\alpha [u]}\right) }[/math]

where [math]\displaystyle{ D_e }[/math] is dissociation energy and [math]\displaystyle{ \alpha }[/math] controls with width of the potential well. The interfacial traction as a function of discontinuity [math]\displaystyle{ [u] }[/math] is found by differentiating energy:

      [math]\displaystyle{ T = 2\alpha D_ee^{-\alpha [u]}\left(1-e^{-\alpha [u]}\right) }[/math]

When using this potential to model an imperfect interface, it is convenient to express it using interface parameters as

      [math]\displaystyle{ \alpha = \frac{D}{4T_{max}} \quad{\rm and}\quad D_e = \frac{8T_{max}^2}{D} }[/math]

where D is interfacial stiffness at [math]\displaystyle{ [u]=0 }[/math] (i.e, [math]\displaystyle{ T'(0)=D }[/math]) and [math]\displaystyle{ T_{max} }[/math] is the peak traction. A dimensionless plot for interfacial traction is shown in the figure. This law is very stiff in compression. It reaches a peak value when discontinuity is

      [math]\displaystyle{ [u] = \frac{4T_{max}\ln 2}{D} = \frac{\ln 2}{\alpha} }[/math]

If used for tangential traction, the calculations always find [math]\displaystyle{ [u_t]\ge0 }[/math] meaning the tensile section of the plot will be used in both directions for tangential tractions.

Like all imperfect interface laws, this traction is reversible and interfacial energy is always area under the curve from 0 to current discontinuity. To use this law in normal or tangential direction, set the shape property and then enter both stiffness and peak value for that direction. Note that the peak in the normal direction will only affect simulations if the discontinuity at the peak value is less than twice the cell size in the calculations. If it too large, the materials will numerically separate before reaching the peak. The simulation output will give peak location to be compared to grid resolution.

Properties

The properties for this law are:

Property	Description	Units	Default
normal_shape or tangential_shape	Pick which interface law to use for normal or tangential directions, respectively, by interger. Use 0 for linear law or 1 for Morse potential.	0
Dn and Dt	See Linear Imperfect interface properties. Note that this model cannot model bilinear interface and therefore one cannot set Dnt≠Dnc	pressure/length units	-1
Npeak or Tpeak	For a Morse potential, this properties pick the normal or tangential peak traction, respectively.	pressure units]]	none

Create Custom Imperfect Interface

Here

Examples

 Material "interfaceID","My Imperfect Interface","NoninearInterface"
   Dn 500
   Dt -1
   order 1
 Done