Using cohesive elements to model delamination in a lap shear experiment

I have conducted single lap shear tests on aluminium laminates, bonded with a polypropylene film adhesive, and am now trying to model the experiments. I am using cohesive elements, with a bi-linear traction separation law to model the adhesive layer. I can obtain reasonable agreement for the peak force, using the nominal shear stress obtained by experiment as the stress at which the cohesive element begins to soften. However, the initial slope of the computation force-displacement curve is approximately double that of the experiment. I am using a penalty stiffness of the order of 1e12 N/m^3 which is already low in comparison to most K values quoted in the literature. I have tried stiffness values 2-3 orders of magnitude lower, which does not change the F-d slope at all. If I drop K even lower, the computation becomes unstable. This is all fairly consistent with what I have seen in the literature about cohesive elements.

My question is whether anyone is familiar with published research on modelling of "pure shear" with cohesive elements? I know that a lap shear specimen is not "pure shear" but it is definitely more Mode I than Mode II. All of the literature I have come across so far focusses on test geometries where the slope of the global force displacement curve is governed by something other than the cohesive element (e.g. in a double cantilever beam experiment the bending stiffness of the cantilevers drives the initial force-displacement response) - in most of the published experiments the displacements are at least on the millimeter scale and in most cases final displacements  are in 10s of mm. In my experiments peak load occurs at at a displacement of  0.15mm(after correcting for test frame compliance).