Differential Tomography of Micromechanical Evolution in Elastic Materials of Unknown Micro/Macrostructure

Abstract

Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in elastic solids where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of a priori unknown or uncertain structure. In this vein, a three-tier imaging platform is established where (1) the domain is periodically (or continuously) subject to illumination and sensing in an arbitrary configuration; (2) sequential sets of measured data are deployed to distill far-field signatures of the domain's internal structure through carefully constructed, noniterative solutions to the scattering equation; and (3) the resulting solution sequence is then used to rigorously construct an imaging functional carrying appropriate invariance with respect to the unknown stationary components of the background, e.g., pre-existing interstitial boundaries. This gives birth to differential indicators that specifically recover the 3D support of evolution within a network of unknown scatterers. The direct scattering problem is formulated in the frequency domain where the background consists of a random distribution of monolithic fragments. The constituents are connected through highly heterogeneous interfaces of unknown elasticity and dissipation spanning from perfectly bonded to traction-free contacts which are subject to evolution in time and space. The support of interfacial boundaries is periodically illuminated by a set of incident waves and thus-induced scattered fields are captured over a generic observation surface. The performance of the proposed imaging indicator is illustrated through a set of numerical experiments for sequential reconstruction of evolving damage zones featuring randomly distributed cracks and bubbles.