I have seen plastic strain in terms of scalar values, mostly in Ramberg-Osgood, or Coffin-Manson models. But, is that expressed in tensor environment, in damage accumulation models, as well?
Yes. but in order to develop and use working models for multi-axial cases, for example in the case of fatigue, there is a need for plastic strain tensor. i don't think scalar values apply. Do they ?
Hi Arash Pourbagheri. The multi-axial theory for Ramberg-Osgood equation (or similar equation) is called deformation plasticity or Hencky's plasticity theory. It can be derived from a more general flow rule by assuming simple (proportional) loading. Please consult any book on theory of plasticity, for example, this book
https://books.google.de/books?id=l1FPaaY355gC&pg=PA177&lpg=PA177&dq=hencky+deformation+theory&source=bl&ots=bOnd5boHOw&sig=vjKRgcFlvjav5eZ3GDQDQClMEqE&hl=de&sa=X&ved=0ahUKEwiItbOjrq7NAhVKTSYKHdqNDVgQ6AEILTAA#v=onepage&q=hencky%20deformation%20theory&f=false
There are several multi-axial fatigue criteria including stress-tensor-based, strain-tensor-based or energy based. To select one you need to know about the kind of multi-axial cyclic loading (simple, non-proportional), loading and temperature ranges (LCF, HCF, creep-fatigue) and material responses.
Thanks a lot Konstantin for your good reference and response.
I know the multiaxial fatigue criteria of different type, in detail, well. but as far as i know, they take into account the total multiaxial strain in their damage side of the equation, and not just the plastic portion. Do you know any multiaxia fatigue model, critical plane approach specifically, that is based on the plastic multiaxial strains in its damage side of the equation of the model ?
In my view, in the LCF range the damage rate should be related to the inelastic strain rate tensor. We have good experience with continuum damage mechanics (it is more accurate than many empirical relations and works well in creep-fatigue regimes). Please have a look inside this book
https://books.google.de/books?id=WgeaXK6-ZgwC&printsec=frontcover&hl=de&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
In this paper we analyzed creep-fatigue and TMF applying a damage evolution equation
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