Towards the design of meta-materials with enhanced damage sensitivity: second gradient porous materials.

Numerous computational and conceptual diffculties are often encountered when conceiving techniques which are effective in detecting damage intensity, localization and onset. Actually, also when the semi-inverse or the material characterization problems which are commonly formulated in this context can be recognized to be well posed, the numerical and computational obstacles which need to be overcome can render useless the conceived methodology. In the present paper we propose to change the paradigm used up to now when addressing the problem of damage assessment in engineering materials. In fact, we propose to conceive a meta-material the properties of which make more expedite and effective the detection of cracks onset and damage evolution via the study of reflection and transmission of waves. More particularly, porous materials with underlying heterogeneous micro- structure may magnify the effects of reflection and transmission of waves at damaged sites depending on the considered boundary conditions. Materials of this type would make easier the structural health monitoring via non destructive evaluation of local damage and would permit to detect incipient structural failure in a more efficient way. By analyzing the characteristic patterns of the reflection and transmission properties of surfaces where damage is concentrated, we show that,in the considered meta-materials, slow incident waves can be used to detect the onset and evolution of first gradient macroscopic damage ($\delat_e$), while fast incident waves can be used to reveal loss of contact at the microscopic level ($\delat_r$).