A formulation of variational principles in terms of functional integrals is
proposed for any type of local plastic potentials. The minimization problem is
reduced to the computation of a path integral. This integral can be used as a
starting point for different approximations. As a first application, it is
shown how to compute to second-order the weak-disorder perturbative expansion
of the effective potentials in random composite. The three-dimensional results
of Suquet and Ponte-Casta\~neda (1993) for the plastic dissipation potential
with uniform applied tractions are retrieved and extended to any space
dimension, taking correlations into account. In addition, the viscoplastic
potential is also computed for uniform strain rates.Comment: 20 pages, accepted for publication in JMP
