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On the origins of the idea of the multiplicative decomposition of the deformation gradient
Usually the multiplicative decomposition of deformation gradient in finite plasticity is (incorrectly) attributed to Lee and Liu (1967). This short note discusses the origins of this idea, which go back to the late 1940s. We explain that the first explicit mention of this decomposition appeared a decade earlier in the work of Bilby, et al. (1957) and Kröner (1959). While writing this note I found out that Bruce Bilby passed away a couple of years ago at the age of 91.
| Attachment | Size |
|---|---|
 MultDecompSaYa15.pdf | 150.55 KB |
| B.A. Bilby.pdf | 1.19 MB |
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Comments
Eckart
Dear Arash,
Thanks for your note. I liked it twice. First, it is short. Second, you start with Eckart's work.
I have a comment. It is true that Eckart's approach can be called the trigger of the multiplicative decomposition because it introduces the metric evolution. However and this is important, following the Eckart's work one does not need to directly introduce the controversial multiplicative decomposition - it can be elegantly avoided as in works by Leonov, Rubin, and myself.
Best,
Kosta
Re: Eckart
Dear Kosta:
Thanks for your interest and kind words. And thank you for your comment. This note simply explains what the origins of the idea of F=FeFp are and who significantly contributed to this decomposition. It neither promotes this idea in finite plasticity, nor it claims that this is the only approach to finite plasticity. Of course, there are other methods some of which you just mentioned.
Regards,
Arash
Arash, Thank you
For posting the biographical memoir of Bilby. Much appreciated.
I wonder if there is something similar on the life of Roland DeWit who passed away a few years ago.
Many thanks for this thorough
Many thanks for this thorough analysis. However, if I recall correctly, in [Humphrey and Rajagopal, 2002] it is said that the multiplicative decomposition of the deformation was first used to model tissue growth in [Skalak et al., 1982]. Martin
Re: Martin's comment
Dear Martin:
Thanks for your message. I had read the paper by Skalak, et al. a few years ago and looked at it again. They do not mention the decomposition of the deformation gradient. I also looked at the paper by Humphrey and Rajagopal that you mentioned here. They do not give Skalak, et al. credit for this decomposition.
Regards,
Arash
Many thanks for the
Many thanks for the clarification. I guess I was confused by the part "It is remarkable, however, that it was not until the papers by Skalak and Skalak et al. that there was an attempt to model growth in soft tissues within the context of nonlinear mechanics, and in particular finite strain elasticity. Among others, Rodriquez et al. built upon the ideas of Skalak." Plus the fact that I was never able to access the papers by Skalak. I would be very grateful if you could send them to me. Thanks again. Martin