There are two basic ways (Loikkanen [undated]) to model cohesive/delamination in
LS-DYNA, 1) use solid elements to explicitly model the bonding material between
the plies, or 2) use the contact-tiebreak definition between the plies.
 
With *MAT_138, *MAT_184, *MAT_185, *MAT_186, and *MAT_240, 8-node
solids can model finite thickness of the bonding layer, or the solid elements can also
represent zero thickness layers (the bottom 4 nodes are co-incident with the top 4
nodes).
 
If the bonding layer is thin so that there is no need to consider the mass of the
bonding layer, one might consider/prefer to use *CONTACT_xxxx_TIEBREAK
with OPTION 7, 9, 10, or 11. These options have the traction separation laws built
into the contact definition. This reduces the input data significantly and makes the
modeling simpler.

 
cohesive element formulation
 
http://www.dynasupport.com/howtos/element/cohesive-element-formulation
 
A cohesive element formulation connects via nonlinear spring elements the relative
displacements between the upper and lower surface to a force per unit area. The
element is really two dimensional. Instead of strains, the deformation is in terms
of the relative displacements between the upper and lower surfaces interpolated to
the Gauss points. Unlike strains, the incoming deformations have units of length.
The output of the material model is the force per unit area (LS-DYNA manual:
traction) at the Gauss points, acting to oppose the displacement.
 
--------------------------------------
 
As the title states, guidelines for modeling delamination in composite materials:
 
Loikkanen, M.J., "Guidelines for Modeling Delamination in Composite Materials
Using LS-DYNA", Boeing Commercial Airplanes, Seattle, Washington, (undated
publication).

jk  
7/18/16
(response to question in LSPP User Group)