Traction-separation laws are critical when modeling interface behavior in contact or cohesive zones using Abaqus.
Traction-separation law assumes that, under external loading, the traction force of the material linearly increases with displacement. When the initial failure criterion is met, damage begins to occur and progressively extends, followed by a decrease in tensile force that ultimately reduces to zero.
In this article, we’ll cover everything engineers and analysts need to know about damage models in traction-separation laws, including QUADS, MAXS, QUADE, MAXE, MAXPS, and MAXPE criteria.
We’ll also explain what kind of input data each model requires and when to use them.
🧠 What Are Traction-Separation Laws?
In cohesive zone modeling, traction-separation laws define the relationship between tractions (forces per unit area) and relative displacements (separations) across a cohesive interface.
A traction-separation law governs how two surfaces separate when the cohesive ingredient joins them.
Traction-Separation Laws Applications
- Delamination in Composite Materials
- Adhesive Joint Failure
- Crack Propagation in Brittle/Ductile Materials
- Fiber-Matrix Interface Damage in Composites
- Bone Fracture and Biomechanics
- Electronic Packaging Reliability
- Geomechanics and Hydraulic Fracturing
- 3D-Printed Material Failure
- Concrete and Masonry Fracture
The general approach in Abaqus
Elastic Behavior: Defines stiffness before any damage
- Damage Initiation: When the first sign of failure appears
- Damage Evolution: How the surface degrades after damage initiation
Need Help With Your Damage Simulation?
Our experts can help you set up accurate Damage simulations in Abaqus and interpret the results.
🔥 Damage Initiation Criteria in Abaqus
1. MAXS – Maximum Nominal Stress Criterion
The nominal maximum stress is the maximum stress when the fatigue test begins.
- Damage initiates when maximum stress in any direction reaches a critical value.
- Simple and conservative.
Required input:
MAXS = [σ_max_tangential1, σ_max_tangential2, σ_max_normal]
Example:
MAXS = (50, 50, 60)means damage starts if stress in any direction exceeds these limits.
2. QUADS – Quadratic Nominal Stress Criterion
Damage is assumed to initiate when a quadratic interaction function involving the nominal stress ratios (as defined in the expression below) reaches a value of one. This criterion can be represented as
- Uses a quadratic interaction between tangential and normal nominal stresses.
Damage initiation condition:
ABAQUS/CAE Usage: Property module: material editor: Mechanical>Damage for Traction-Separation Laws>Quads Damage
Required input:
QUADS = [σ_max_tangential1, σ_max_tangential2, σ_max_normal]
Use when you want more realistic mixed-mode behavior compared to MAXS.
3. MAXE – Maximum Nominal Strain Criterion
- Initiation occurs when maximum strain exceeds a critical limit.
- The Maxe criterion is based on the maximum value of the three ratios, whereas the Quade criterion is based on a quadratic combination of all three ratios.
Enter damage parameters in the Data table:
| Damage initiation mode | Description (nominal strain at damage initiation) |
|---|---|
| Nominal Strain — Normal-only Mode | Nominal strain at damage initiation in a normal-only mode. Pure mode I (opening) separation where only the normal nominal strain component triggers onset of damage. |
| Nominal Strain — Shear-only Mode (First Direction) | Nominal strain at damage initiation in a shear-only mode that involves separation only along the first shear direction (mode II, in-plane shear). Damage is governed exclusively by tangential nominal strain component in the local 1‑direction. |
| Nominal Strain — Shear-only Mode (Second Direction) | Nominal strain at damage initiation in a shear-only mode that involves separation only along the second shear direction (mode III, transverse / out-of-plane shear). Initiation occurs solely due to nominal strain component in the second tangential direction. |
Required input:
MAXE = [ε_max_tangential1, ε_max_tangential2, ε_max_normal]
4. QUADE – Quadratic Nominal Strain Criterion
- Uses a quadratic combination of strains to detect damage onset.
Damage is assumed to initiate when a quadratic interaction function involving the nominal strain ratios (as defined in the expression below) reaches a value of one. This criterion can be represented as:
Required input:
QUADE = [ε_max_tangential1, ε_max_tangential2, ε_max_normal]
5. MAXPS – Maximum Principal Stress Criterion
The Maxps and Maxpe damage initiation criteria are used to predict damage initiation in the XFEM enriched region.
- Based on maximum principal stress within the interface.
- Useful when failure direction is unknown.
Required input:
- Principal stress value at damage onset.
Note: This is less commonly used than nominal-based models.
To define Maxps or Maxpe damage in Abaqus:
From the menu bar in the Edit Material dialog box, select >Mechanical >Damage for Traction Separation Laws>Maxps Damage or Maxpe Damage.
6. MAXPE – Maximum Principal Strain Criterion
- Damage initiates when maximum principal strain exceeds a critical threshold.
Required input:
- Principal strain threshold.
🧮 How to Define Traction-Separation Damage in Abaqus
Here’s the typical input sequence for cohesive zone modeling:
- Elastic behavior:
*Elastic, type=TRACTION
Kn, Kt1, Kt2
- Damage initiation:
*Damage Initiation, criterion=MAXS (or QUADS, etc.)
σn, σt1, σt2
- Damage evolution:
*Damage Evolution, type=ENERGY (or DISPLACEMENT)
Gc, power=α
- Optional stiffness degradation:
*Damage Stabilization
🛠️ When to Use Each Damage Model
| Criterion | Type | Best For |
|---|---|---|
| MAXS | Nominal Stress | Simple brittle behavior |
| QUADS | Nominal Stress | Mixed-mode cohesive failure |
| MAXE | Nominal Strain | Strain-based interface models |
| QUADE | Nominal Strain | Soft adhesives or polymers |
| MAXPS | Principal Stress | Complex, unknown failure direction |
| MAXPE | Principal Strain | Strain localization and debonding |
✅ Internal & Outbound Resources
🔗 Related blog posts:
- How to Set Up Contact Interaction in Abaqus
- Abaqus Material Models Under Different Loading Conditions
- How to Analyze Crack Growth Using XFEM in Abaqus
🌐 Outbound links:
- SIMULIA Documentation – Damage for Traction-Separation
- Abaqus Cohesive Behavior Explained (ResearchGate)
❓ Frequently Asked Questions for Traction-Separation Laws
What is the difference between MAXS and QUADS criteria in Abaqus?
MAXS checks if any stress exceeds a critical value, while QUADS combines all three stress components quadratically for mixed-mode damage detection.
How do I choose between stress and strain-based damage?
Use strain-based criteria (MAXE/QUADE) when interface behavior is strain-sensitive, like in soft adhesives. Use stress-based (MAXS/QUADS) when failure correlates with peak stresses.
Can I use cohesive zone models in 3D?
Yes! Abaqus supports cohesive behavior in 3D using cohesive elements or cohesive contact interactions.
How do I define fracture energy?
Use *Damage Evolution with the energy option. Specify mode I, mode II, or mixed-mode fracture energies (Gc) based on your material tests or literature data.
What if I don’t know which model fits best?
You can start with MAXS + linear softening as a baseline. Or contact our team at Mathech.com for expert consultation on damage modeling.
Conclusion
Accurate damage modeling with traction-separation laws is vital for analyzing delamination, joint failure, and composite behavior. Abaqus offers several built-in criteria for damage initiation and evolution, each with its specific input requirements and ideal use cases.
Choosing the right damage model can be complex—but our experts at Mathech.com are here to support you with consulting services for every step of your Abaqus simulation.
