  We consider problems of static equilibrium in which the primary unknown is
the stress field and the solutions maximize a complementary energy subject to
equilibrium constraints. A necessary and sufficient condition for the
sequential lower-semicontinuity of such functionals is symmetric ${\rm
div}$-quasiconvexity, a special case of Fonseca and M\"uller's
$A$-quasiconvexity with $A = {\rm div}$ acting on $R^{n\times n}_{sym}$. We
specifically consider the example of the static problem of plastic limit
analysis and seek to characterize its relaxation in the non-standard case of a
non-convex elastic domain. We show that the symmetric ${\rm div}$-quasiconvex
envelope of the elastic domain can be characterized explicitly for isotropic
materials whose elastic domain depends on pressure $p$ and Mises effective
shear stress $q$. The envelope then follows from a rank-$2$ hull construction
in the $(p,q)$-plane. Remarkably, owing to the equilibrium constraint the
relaxed elastic domain can still be strongly non-convex, which shows that
convexity of the elastic domain is not a requirement for existence in
plasticity.
