  Differential evolution indicators are introduced for 3D spatiotemporal
imaging of micromechanical processes in complex materials 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 segment-wise scattering signatures of the domain's internal structure
through carefully constructed, non-iterative 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 and bubbles. This gives birth to differential
indicators that specifically recover the 3D support of micromechanical
evolution within a network of unknown scatterers. The direct scattering problem
is formulated in the frequency domain where the background is comprised of a
random distribution of monolithic fragments. The constituents are connected via
highly heterogeneous interfaces of unknown elasticity and dissipation which are
subject to spatiotemporal evolution. The support of internal boundaries are
sequentially 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 spatiotemporal reconstruction of progressive damage zones
featuring randomly distributed cracks and bubbles.
