Third-order bound of nonlinear composites and porous media under hydrostatic deformation

•3rd-Order bound derived for nonlinear composites under hydrostatic deformation.•Hashin’s sphere assemblage not an optimal microstate in nonlinear cases.•Distinctive behaviors of a dry porous medium from a saturated one.

In this study the third-order variational bound is explicitly derived for nonlinear composites subject to hydrostatic deformation. By formulating the stochastic extreme principle for nonlinear boundary value problems, the third-order upper bound of the potential is derived for nonlinear two-phase composites, which is further explicitly specialized to porous media. Examples of application are provided by applying the derived bound to various cases of composites and porous media characterized with power law nonlinearity.