# Cohesive element formulation

A cohesive element fomulation 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.

In LS-DYNA V971, solid formulations ELFORM 19/20 and material models *MAT_138, *MAT_184, *MAT_185, *MAT_186 (*MAT_COHESIVE_MIXED_MODE, *MAT_COHESIVE_ELASTIC, *MAT_COHESIVE_TH, *MAT_COHESIVE_GENERAL)  correspond to cohesive elements, whereby *MAT_138 is not available until LS-DYNA V971 R3.

### Element connectivity of a cohesive element:

There are two element formulations in LS-DYNA, which can be used with cohesive material models: ELMORM 19/20. ELFORM 20 will transfer moments between the bonded parts, whereas ELFORM 19 will not. The order of the nodes in defining the element is important. If the cohesive element bonds Element A to Element B, nodes 1-2-3-4  of the cohesive element should be shared by  Element A or by Element B.  In the first case, the normal of face 1-2-3-4 should point towards Element B and nodes 5-6-7-8 should be shared by Element B. In the second case, the normal of face 1-2-3-4 should point towards Element A and nodes 5-6-7-8 should be shared by Element A.

### General remarks:

• The cohesive element formulations can have zero thickness and even invert without becoming unstable. Think of a cohesive element as consisting of three nonlinear springs (one in the normal direction and two in the two shear directions).
• When cohesive elements bond plies together, contact between the plies must be considered after cohesive elements fail and are deleted. This requires the use of an eroding type contact.