Mixed Mode Traction Law
The Traction Law
This traction law implements a new coupled model for mixed-mode failure.[1] In brief, Triangular Traction Law, Exponential Traction Law, Cubic Traction Law and Trilinear Traction Law are all decoupled cohesive zone models. While technically valid, the concept that damage in normal direction has no affect on tangential properties (and vice versa) is likely unrealistic. The Coupled Traction Law is a published method to introduce coupling based on effective displacements.[2] Unfortunately, the coupling methods are only valid for interrelated normal and tangential traction laws. Other effective displacement models[3][4] place even more restriction on the traction laws.
This Mixed Mode Traction law model[1] allows completely independent normal and tangential traction laws and all calculations remain valid during mixed mode loading. The normal and tangential laws can be selecting from Triangular Traction Law, Exponential Traction Law, Cubic Traction Law and Trilinear Traction Law. The properties assigned to the laws are totally independent. It can even use different law types for normal and tangential traction.
Failure
The mixed-modeling of this law is done in terms of a single damage parater, D, that is 0 with no damage and reaches 1 at failure. Failure occurs when D reaches one and both normal and tangential tractions simultaneously reach zero at failure.
This law does not specify a failure criterion (as needed for other laws). Instead, the way the cohesive zone fails as a function of mixed-mode ratio is an output of the law. The shape of the GI vs. GII failure envelope at failure depends on the relative normal and tangential cohesive laws. Calculations show that this proper-mixed mode modeling predicts that all such failure envelopes are convex.[1] Note that prior coupling methods (implemented in Coupled Traction Law) predict all failure envelopes are linear. In other words, this new model is the only coupled method capable of modeling materials with non-linear failure envelopes.
Traction Law Properties
This law requires selecting the type of traction law to use for normal and tangential directions and then entering all properties for those laws:
| Property | Description | Units | Default |
|---|---|---|---|
| modelI | Decide which traction law to use for mode I or normal opening. The options are selected by traction law numerical ID and can be 12 (for Triangular Traction Law), 14 (for Cubic Traction Law), 20 (for Trilinear Traction Law), or 34 (for Exponential Traction Law) | Dimensionless | 12 |
| (mode I properties) | Enter all properties for the selected mode I law using mode I variable in that law. | (varies) | none |
| modelII | Same as mode I but used to select law for mode II or tangential opening. | Dimensionless | 12 |
| (mode II properties) | Enter all properties for the selected mode II law using mode II variables in that law. | (varies) | none |
| NewtonsMethod | The published update method[1] appears to work well for most laws, but it is possible that numerical methods might be needed for laws with no initial elastic regime or with a short, very stiff elastic regime. Enter 0 to used default methods or 1 to use numerical solution. | Dimensionless | none |
Note that if one law is Cubic Traction Law and the other is not, the solution will required numerical methods. As a results NewtonsMethod will automatically be changed to 1. If both laws are Cubic Traction Laws, they can be handles by a special-case approach and this do not require numerical methods despite lack of an initial elastic regime.
Traction History Variables
The material tracks to following history variables
- The damage variable D (it is <0 until initiation if both directions are cubic)
- A damage parameter characterized mode I damage, δn
- A damage parameter characterized mode II damage, δt
- Cumulative work energy
- Normal crack opening displacement (un)
- Tangential crack opening displacement (ut)
These history variables can be archived for later plotting. The cmdisp archiving option can archive total mode I and mode II cumulative dissipated energies. See Ref. [1] for mode details on D, δn, and δt.
References
- ↑ 1.0 1.1 1.2 1.3 1.4 J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" kin preparation (2020).
- ↑ J. L. H ögberg, "Mixed mode cohesive law," International Journal of Fracture, 141, 549–559 (2006).
- ↑ P. P. Camanho and C. G. Dàvila, "Mixed-mode decohesion finite elements for the simulation of delamination in composite materials," Technical Report, NASA/TM-2002-211737 (2002).
- ↑ G. T. Camacho and M. Ortiz, "Computational modelling of impact damage in brittle materials," Int. J. Solids Struct., 33, 2899–2938 (1996).