Cordial saludo,
In the last months, I have working in the theory of
expansion of cavities of Vesic, for linear
elastic/perfectly plastic materials in spherical and
cylindrical cavities.
I am working in a strain-stress relationship in the
plastic zone. That relationship is based on the
equation of equilibrium, equation of compatibility, a
yield function, and the normality. It is similar, to
a certain extent, to the positions made by Chakrabarty
in his book of plasticity and for the work of Hendrom
and Aiyer (1975) for tunnels.
I obtain a differential equation.
This is a relation between plastic normal strain in
direction radial (sigma-r) and the stress normal
equivalent: (p=(sigma-r+2sigma-teta)/3 and q=sigma-r
-sigma-teta)
I annex this equation. This equation is easy to solve.
The main hypothesis is that the material will behave
in a linear elastic way from r=Ri until r=Ru (I am
using the same nomenclature of Vesic). When r=Ru and
the radial effort reaches the pu value, then the
material will have a perfectly plastic behaviour.
I have other problem. This theory should be work whit
the finite strains (Lubliner, 1990: Chakrabarty) and I
believe that the up of Vasic (1972) is integrate of
infinitesimal strain.
What do you think? And, I need to know if the
hypothesis to obtain this equation are valid and if
anybody has made this before.
Best wishes,
Isabel Cristina Gómez Gutiérrez
PD/ If somebody recommends me some paper I request
your, please, that indicates me the internet place
where it can down load; because at the moment I am
living in Riohacha (Guajira - Colombia) and my only
communication with the external world is by means of
the Internet
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