The principal objective of this study is to assess the hierarchical effects of defects on the elastic stiffness properties at different levels of observation. In particular, quantitative damage measures which characterize the fundamental mode of degradation in the form of elastic damage provide quite insightful meanings at the level of constitutive relations and at the level of structures. For illustration, a total of three model problems of increasing complexity, a 1-D bar structure, a 2-D stress concentration problem, and a heterogeneous composite material made of a matrix with particle inclusions. Considering a damage scenario for the particle inclusions the material system degrades from a composite with very stiff inclusions to a porous material with an intact matrix skeleton. In other damage scenario for the matrix, the material system degrades from a composite made of a very stiff skeleton to a disconnected assembly of particles because of progressive matrix erosion. The trace-back and forth of tight bounds in terms of the reduction of the lowest eigenvalues are extensively discussed at different levels of observation.