Cohesive Initial Stiffness Sensitivity Illustration

Calculator

Cohesive initial stiffness K:

  T = K × δ  (before damage initiation)

Artificial compliance from cohesive layer:
  C_artificial = t_adhesive / K
  where t_adhesive = adhesive thickness

The artificial compliance should be small
relative to the structural compliance:

  C_artificial / C_structural << 1

Trade-off:
  K too low: excessive artificial compliance
  → joint/laminate too flexible

  K too high: numerical conditioning issues
  → explicit time step very small
  → implicit solver ill-conditioning

Rule of thumb:
  K ≈ E_adhesive / t_adhesive × (50 to 100)
  (penalty factor 50-100× the adhesive modulus)

Check: vary K by 2× and confirm results
are insensitive. If they change, K is too
low or the mesh is too coarse.

Values are illustrative —
calibrate for each application.

Assumptions

• Illustrative — not a design tool
• Penalty stiffness approach
• User must check sensitivity for their application

Limitations

This helper illustrates the trade-off. The actual optimum stiffness depends on the adhesive, the mesh, the solver and the application. Always check sensitivity by varying K and confirming results are insensitive. Do not use a universal stiffness value.