The CZM can be easily comprehended with the picture shown above. In the CZM, fracture is regarded as a gradual phenomenon. When material elements are pulled apart, separation will take place across a cohesive zone, and the pulling effect will be resisted by cohesive tractions. Here, the cohesive zone elements do not represent any physical materials but the cohesive forces. It is said that the traction T is dependent on the separation distance Δ, and this is the so-called Traction-separation laws.
Φ indicates the area under the traction separation curve, which corresponds to the energy needed for separation.
3. Location of the discontinuity --Level Set Method (LSM) A level set of a real-valued function is the set of all points at which the function attains a specified value. Here, for a crack, two functions Φ and Ψ are used to describe it.
Φ=0 defines the crack face; Φ=0 and Ψ=0 defines the crack front. Φ is the signed distance of the node from the crack face Ψ is the signed distance of the node from an almost-orthogonal surface passing through the crack front
4. Criteria for crack initiation and propagation
Essential Steps for Abaqus XFEM modelling of cracks
1. Define damage criteria in the material model a) Damage initialization *MATERIAL ... *DAMAGE INITIATION, CRITERION=MAXPS, TOL=0.05 b) Damage evolution *DAMAGE EVOLUTION, , MIXED MODE BEHAVIOR=POWER LAW, POWER=1.0 2870.0, 2870.0, 2870.0 c) Damage stabilization *DAMAGE STABILIZATION 1.e-5
2. Define an enrichment region (the associated material model should include damage)
3. Define an initial crack, if present Create a separate part representing the crack surface or line and assemble it along with the part representing the structure to be analyzed
4. If needed, set analysis controls to aid convergence *STEP *STATIC, inc=10000 0.01, 1.0, 1.0e-09, 0.01 … *CONTROLS, ANALYSIS=DISCONTINUOUS *CONTROLS, PARAMETER=TIME INCREMENTATION , , , , , , , 20
5. Two more output request in addition to usual output in static analysis a) PHILSM --φ value of the level set method b) STATUSXFEM -- Status of XFEM element with a value between 0.0 and 1.0 (A value of 1.0 indicates that the element is completely cracked, with no traction across the crack faces.)