International audienceIn this paper, a new plastic potential for porous solids with von Mises perfectly-plastic matrix containing spherical cavities is derived using a rigorous limit analysis approach. For stress-triaxialities different from 0 and ±∞, the dilatational response depends on the signs of the mean stress and the third invariant of the stress deviator. The classic Gurson potential is an upper-bound of the new criterion. A full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is also used to generate numerical gauge surfaces for the porous material. The numerical calculations confirm the new features of the dilatational response, namely: a very specific dependence with the signs of the mean stress and the third invariant that results in a lack of symmetry of the yield surface
Starting from flat two-dimensional gauge potentials we propose the notion of W-gauge structure in terms of a nilpotent BRS differential algebra. The decomposition of the underlying Lie algebra with respect to an SL(2) subalgebra is crucial for the discussion conformal covariance, in particular the appearance of a projective connection. Different SL(2) embeddings lead to various W-gauge structures.We present a general soldering procedure which allows to express zero curvature conditions for the W-currents in terms of conformally covariant differential operators acting on the W gauge fields and to obtain, at the same time, the complete nilpotent BRS differential algebra generated by W-currents, gauge fields and the ghost fields corresponding to W-diffeomorphisms. As illustrations we treat the cases of SL(2) itself and to the two different SL(2) embeddings in SL(3) , viz. the W (1) 3 -and W (2) 3 -gauge structures, in some detail. In these cases we determine algebraically W-anomalies as solutions of the consistency conditions and discuss their Chern-Simons origin.
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