Difference between revisions of "Mixed Mode Traction Law"
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== The Traction Law == | == The Traction Law == | ||
This [[Traction Laws|traction law]] implements a new coupled model for mixed-mode failure.<ref name="mixedmode"/> | This [[Traction Laws|traction law]] implements a new coupled model for mixed-mode failure.<ref name="mixedmode"/> In brief, [Triangular Traction Law]], [[Exponential Traction Law]], [[Cubic Traction Law]] and [[Trilinear Traction Law]] are all decoupled cohesive modes. 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.<ref name="hogberg"/> Unfortunately, the coupling methods are only valid for interrelated [[Coupled Traction Law#Property Limitations|normal and tangential traction laws]]. Other ''effective'' displacement models<ref name="comanho"/><ref name="comacho"/> place even more restriction on the traction laws. | ||
The model<ref name="mixedmode"/> allows completely independent normal and tangential traction laws an 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 need for [[Triangular Traction Law#Failure|other law]]). Instead, the way the cohesive zone fails as a function of mixed-mode ratio is an output of the law. The shape of ''G<sub>I</sub>'' ''vs.'' ''G<sub>II</sub>'' failure envelope at failure depends on the relative normal and tangential cohesive laws. Calculations show that this proper-mixed mode model predicts that all such failure envelopes are convex.<ref name="mixedmode"/>. | |||
== References == | == References == | ||
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<references> | <references> | ||
<ref name="mixedmode">J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" <i>kin preparation</i> (2020).</ref> | <ref name="mixedmode">J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" <i>kin preparation</i> (2020).</ref> | ||
<ref name="hogberg">J. L. H ögberg, "Mixed mode cohesive law," <i>International Journal of Fracture</i>, <b>141</b>, 549–559 (2006).</ref> | |||
<ref name="comanho">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).</ref> | |||
<ref name="comacho">G. T. Camacho and M. Ortiz, "Computational modelling of impact damage in brittle materials," <i>Int. J. Solids Struct.</i>, <b>33</b>, 2899–2938 (1996).</ref> | |||
</references> | </references> | ||
Revision as of 23:17, 2 January 2021
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 modes. 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.
The model[1] allows completely independent normal and tangential traction laws an 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 need for other law). Instead, the way the cohesive zone fails as a function of mixed-mode ratio is an output of the law. The shape of GI vs. GII failure envelope at failure depends on the relative normal and tangential cohesive laws. Calculations show that this proper-mixed mode model predicts that all such failure envelopes are convex.[1].
References
- ↑ 1.0 1.1 1.2 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).