Mixture rule for indentation derived Young's modulus in layered composites

The mixture rule for layered composites under the concentrated load condition has been formulated by the elastic energy method. Numerical boundary integral calculation reveals that the contour of strain is sensitive while that of stress is insensitive to the order and magnitude of elastic modulus, therefore stress could be an appropriate influence function for the present mixture rule. A simple mixture rule is obtained analytically by repeated integration of energy density, which is derived from Green's function of 2D and 3D half space. The prediction curve obtained by the present mixture rule shows good agreement with experimental indentation results.