Characterization of two-scale gradient Young measures and application to   homogenization
  This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures. 
Jean-Francois Babadjian, Margarida Baia, Pedro M. Santos