MSSR method
Criteria utilising the MSSR concept expect, that damage in the point examined is directly related to the plane, where Maximum Shear Stress/Strain Range (MSSR) is found during whole load history. This assumption is in a close relation to the “axiom” that the shear stress has a primary influence on the crack initiation, but it wholly misses any secondary effect of the normal stress.
Because the damage parameter is usually built as a composition of a shear stress part and a normal stress part, this omission brings a further complication to the algorithm for a search of the critical plane. There can be more planes, where the same maximum MSSR can be found under specific load conditions. Any of the search algorithms implemented:
is discrete in its nature. The user sets the density, with which the optimum maximum value is looked for, in the Calculation Methods dialogue. Nevertheless, there are more planes with the same maximum MSSR in our example, which have significantly different results of the damage parameter. The search process thus has to be robust enough to find the plane with the maximum MSSR and the maximum damage parameter as well, while the search time will be as low as possible. The second requirement excludes the possibility to lessen the angular step, with which the search is running.
The algorithm in PragTic searches for a plane, where the shear stress/strain range reaches at least 0.8 multiple of the highest MSSR up to now. Once found, an optimization technique tracking the highest gradient in MSSR is used in order to find the plane of MSSR, which is probably somewhere close and which was missed due to the discrete search. Once this plane is retrieved, a further similar scan is done in the neighborhood but now the whole damage parameter is maximized, while the level of shear stress/strain range is hold. The final plane position, MSSR value and the damage parameter value are then saved in memory and further search for other possible plane orientations continues. In order to avoid the optimization technique to repeatedly mislead to the same maximum point, it is stopped once the examined orientation is close to any previously found maximum.
To ensure that the optimization routine works, the user has to include the Optimize option in the setup of the related methods.
There are following methods implemented in PragTic, that utilize the MSSR concept:
* McDiarmid method v. 91 – the user can switch to the MD method in its setup
* Wang & Brown method – the user can switch to the MD method in its setup
* Matake method – this is the same damage parameter as in Findley method, which nevertheless utilizes the MD concept
To ensure that the optimization routine works, the user has to include the Optimize option in the setup of the related methods.
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© PragTic, 2007
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