Cohesive Zone Model (CZM)
Cohesive Zone Model (CZM): Theoretical Foundations
What is CZM?
Professor, CZM was also mentioned on the interlaminar delamination page, but can it be used for general fracture as well?
CZM (Cohesive Zone Model) is a versatile fracture model that describes interface failure using a traction-separation law. It is applicable not only to interlaminar delamination but also to adhesive joint debonding, ductile cracking in metals, and concrete cracking.
Traction-Separation Law
Bilinear type:
1. Linear Elasticity — Stress increases with stiffness $K$
2. Damage Initiation — Reaches strength $t^0$
3. Softening — Stress decreases while opening increases
4. Complete Separation — Fracture after consuming energy $G_c$
Advantages of CZM
Summary
The Competing Works of the Dugdale-Barenblatt Model
The cohesive zone model was independently published in 1960 by Dugdale (UK) and Barenblatt (USSR). Dugdale approximated the plastic zone in steel plates as a strip, while Barenblatt formulated a more general attraction relationship. Due to the Cold War, there was no information exchange for several years, and they only learned of each other's papers in the 1970s. Today's CZM was born from the competing works of these two individuals.
Computational Methods for Cohesive Zone Model (CZM)
CZM in FEM
Two implementations:
1. Cohesive Elements — Place thin cohesive elements at the interface (COH3D8, etc.)
2. Surface-based CZM — Set CZM on contact surfaces (no additional elements)
The following is a schematic cohesive-element setup. Symbolic values and set names are placeholders, not a runnable model; calibrate properties, constitutive thickness and units to the test and model. Surface-based cohesive contact is separately defined through *SURFACE INTERACTION and *COHESIVE BEHAVIOR.
*COHESIVE SECTION, ELSET=COH_SET, MATERIAL=COH_MAT, RESPONSE=TRACTION SEPARATION
*MATERIAL, NAME=COH_MAT
*ELASTIC, TYPE=TRACTION
K_n, K_s, K_t
*DAMAGE INITIATION, CRITERION=QUADS
t_n, t_s, t_t
*DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=1.5
G_Ic, G_IIc, G_IIIcAbaqus cohesive section · Abaqus contact cohesive behavior · Abaqus damage evolution
Mesh Requirements
3 to 5 elements within the process zone. $l_{cz} \approx EG_c/(t^0)^2$.
Summary
Relationship Between TSL Curve Shape and Fracture Toughness
The traction-separation law (TSL) in cohesive zone models has several shapes such as triangular, trapezoidal, and exponential. Different shapes change crack propagation behavior even for the same fracture energy Gc. Trapezoidal shapes often better represent experiments for high-strength adhesives, while exponential shapes fit rubber-based adhesives. The peak strength σmax and area Gc are the minimum required two parameters; using only one of them worsens FEM convergence.
Cohesive Zone Model (CZM) in Practice
CZM in Practice
Interlaminar delamination in composites, strength evaluation of adhesive joints, concrete cracking, fracture in welded joints.
Practical Checklist
Delamination Simulation of Aircraft Panels
For a composite-to-metal bonded interface, calibrate mode-I and mode-II fracture energies and interface strengths from tests, then validate predictions for the joint geometry and loading.
Cohesive Zone Model (CZM): Software & Solver Comparison
CZM Tools
Abaqus CZM Implementation and Contact Elements
Abaqus/Standard offers cohesive elements and surface-based cohesive contact. Element material definitions and contact interaction properties are distinct; consult the documentation for the chosen model and contact conditions.
Advanced Technologies
Advanced CZM
Application of CZM to Biomaterials
Since the 2010s, cohesive zone models have also been applied to fracture healing simulations. Converting cortical bone fracture toughness Kc=2.2 MPa√m to CZM parameters can reproduce debonding at bone-implant interfaces. In 2018, a group at KIT predicted bone fixation strength of hip implants using CZM and obtained results matching actual measurements 3 months post-surgery within 10% error.