  Second-order structured deformations of continua provide an extension of the
multiscale geometry of first-order structured deformations by taking into
account the effects of submacroscopic bending and curving. We derive here an
integral representation for a relaxed energy functional in the setting of
second-order structured deformations. Our derivation covers inhomogeneous
initial energy densities (i.e., with explicit dependence on the position);
finally, we provide explicit formulas for bulk relaxed energies as well as
anticipated applications.
