Abaqus Cohesive Elements in Compression

Hello,

 I am currently using
abaqus to attempt to replicate tribology experiments I am conducting with pig
aorta. The model is 2D with a circular indenter, modelled as a rigid body,
pushing down and the dragging on a pig aorta imposed by contact between the
indenter and top surface of the tissue. The aorta is modelled a two layer
hyperleastic material joined by a cohesive zone with dimensions less than one
hundredth of the dimensions of the two layers. The cohesive zone is a traction
separation model, damage is modelled trough fracture energy and it is attached
to the two layers by tie constraints. The bottom surface of the lower layer is
fixed and the indenter has a load applied on the first step which is then
maintained in the subsequent step whilst a displacement is applied to drag the
indenter across the tissue. I am using a static solver. 

 The problem I have is
that if I run this model the cohesive elements do not resist the compression
but deform and the two layers of tissue appear to pass through one another, I
have found a way around this by imposing general contact with an individual
property assignment between the indenter and top surface. However this seems
unnecessary and costly when from what I have read in the manual the elements
should resist the compression. 

Thank you for any help you can
provide