Conclusions

When defining the properties required for a homogeneous medium to be the static equivalent of a layered heterogeneous medium the following conditions are sufficient to uniquely define the homogeneous medium.

• Identical thickness (volume).
• Identical mass.
• Either one of the following two equivalent conditions

  1.

  Identical thickness integral of discontinuous stress and strain components.

  2.

  Identical thickness (volume) integral of elastic energy.

Either condition leads to the Schoenberg/Muir averaging rule.