IDS method
The group of criteria that analyze the loading history in the Ilyushin deviatoric space are gathered here. A transformation of stress tensor deviator components sij into the Ilyushin subspace follows these rules:
The problem afterwards is alike to common MCCM problem – the minimum circumscribed entity (hypersphere, hyperellipsoid) should be found. Nevertheless, this time it is not two- but five-dimensional. There are 3 methods of this type currently implemented in PragTic:
* Crossland method - searches for a hypersphere
* Gonçalves, Araújo & Mamiya (GAM) method – this method is today implemented in PragTic in a limited version usable only for iso-frequency in- and out-of-phase sinusoidal multiaxial loading;
* Sines method - searches for a hypersphere
The GAM method is defined with a construction of minimum circumscribed hyperellipsoid, which presents a further level of optmization. This is the reason why the reduced and simplified solution is used there. I expect to implement the full version before the end of 2007.
The methods do not involve any specific orientation of the final damage parameter as is the case of critical plane concepts. The circumscribed entity mentioned gives only one variable, the second one appearing in the criterion is usually determined in relation either to hydrostatic stress (which is also scalar) or to major principal stress.
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© PragTic, 2007
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