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3D crack growth with remeshing using Z-set/Zebulon

Recent advance in adaptive remeshing techniques now gives the possibility to efficiently simulate complex 3D crack growth using conform meshing of the discontinuity. An exemple of such kind of mixed mode simulation with adpative remeshing can be seen on YouTube:

In the framework of the finite element software Z-set/Zebulon
(co-developped by Onera - The French Aerospace Lab, Center of materials
at Ecole des Mines ParisTech and NW Numerics) a module has been recently
developped. Called Z-cracks, it allows to discretize cracks in complex
structures using both remeshing techniques or X-FEM/level-sets
strategies, perform energy release rates or SIF computations, apply
Paris or more complex laws to propagate efficiently cracks under fatigue
loading to produce lifetime evaluations. A real time tutorial that shows how to perform crack insertion, SIF computation and propagation using the integrated Z-cracks user interface is also present as a YouTube animation:


likask's picture


That is very interesting. You show great analysis, it and looks nice. Could you give more details about boundary conditions, material parameters and geometry? I like to reproduce this. 

Recently I developed similar approach based only on r/p-adaptivity. I build hierarchical approximation basis.

As you could see, I need to solve front tracking problem. Could You direct me to paper about z-set/Zebulon. 

What you see is ALE approach where fully coupled problem in physical and material space is solved. The mesh quality is controlled by volume-length quality measure with barrier function. Algorithm is parallelised.







Thank you for your comment, your approach also seems very interesting.

Concerning the multiperforated sample, here can be found a geometry of the structure (from the Iniria geometry database, geometry is not scaled to build the FE mesh) :

Behavior is linear elastic (E=210 000MPa, nu=.3) under small deformations.

Boundary conditions are : prescibed null displacement in all directions on the bottom face (z=-50), vertical displacement U3=1 and sheer displacement U2=-2 on the top face (z=50). Fatigue loading is imposed with a simple [ 0 -> 1 -> 0 ] loading cycle. A Paris law is used with a m=3 exponent on the (Delta K) equivalent SIF. Initial crack is a 5. radius disc with a (50.0000 1.79113 -8.14958) center position and a vertical normal direction (0. 0. 1.).

Zset global solution process is :

(1) FE implicit solution

(2) SIF computations and branching direction search

(3) Fatigue propagation law integration

(4) Geometry update if necessary

back to (1).

I'm really interested in your results, I would appreciate you keep me informed.

Publications that detail both remeshing algorithm and SIF computations are still in reparation.

likask's picture

Thanks for details. I will run this test next weak and we will see what it gives. I let you know about failure or success.



Hi Vincent,

Is site to download z-crack code? McAfee's SiteAdvisor recommend to to stay away from this website. Where really is site to download z-crack? Thanks.



Hi Mike,

No is not related to Zcracks at all... The website (still-in-developpement of Zcracks) is :

Which gives informations about the way to the contact the disributors of the software in the US (Coventry, RI) and elsewhere (Paris, France). However Zcracks is a comercial software and can't be directly downloaded, but don't hesitate to contact us to discuss about the way it could fit your needs.

I hope it will help you, regards,



Hi Vincent,

Thanks for a prompt reply. I have a few questions.
- Can I have a demo version Zcrack (honestly, this is a very provocative title - it looks like the hacker terminology)?
- What type of elements can be used with Zcrack?
- Is it possible to use Zcrack in real complicated 3D geometry, or it more likely 3D plane stress/strain simulation?
- What type of simulation code allows to do: stationary crack, cyclic loading, the initiation, J-integral, CTOD?
- How different is this algorithm from one that Abaqus uses?



Hi Mike,

I'm not allowed to supply any demo version of Z-cracks, but as I said in my last post, if you're intersted you can contact:

Centre des Matériaux Pierre-Marie Fourt
B.P. 87, 91003 EVRY CEDEX
tel:  33 1 60 76 30 53


NW Numerics & Modeling, Inc   
641, Arnold Road, Coventry
RI 02816
tel:  1 401 615 76 00

Z-cracks doesn't aim to be a provocative title at all: is the macroscopic failure analysis module of the Z-set material and structure analysis suite (that was originaly developped to provide an easy way to model complex material consititutive laws in a wide range of commercial FE software: Ansys, Abaqus, etc.).

Tetrahedral elements must be used in 3D where adaptive remeshing is required (linked to any kind of continuum element). For 2D or shell, triangular or quadrangular elements can be used. In all cases linear or quadratic interpolation can be applied, but only in small deformation.

Z-cracks has been designed to deal with complex 3D cracked industrial structures, as shown in the movies: it has capacities to model complex cracked surfaces even with contact, to perform enegetic integrals on curved fronts and under mixed mode loading to extract stress intensity factors (or energy release rate in the most suitable direction), to apply simple, complex or user developped propagation laws in fatigue, all within a integrated user interface (shown on the second movie with real-time computations).

The range of application of the software is from initiated cracks to long cracks under fatigue loading (stationnary studies are always possible). Concerning crack initiation and damage to fracture transition, techniques are under developement at Onera and Ecole des Mines - ParisTech but not avaible for commercial usage.

I don't personnaly use Abaqus, but for what I know, using a very robust adaptive remeshing technique (instead of X-FEM), Z-cracks is far more advanced, fast and efficient to deal with complex 3D crack propagation simulations.

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