The first approximation (N=1) of a three-dimensional micropolar elastic prismatic body in moments of displacement and rotation, obtained via Legendre polynomial expansion, is applied to two related problems: field reconstruction and damage identification. In the first problem, two- and three-dimensional field distributions are reconstructed for a simply supported square prismatic body under three loading configurations, with first-order moment loading as the primary case. Two distinct resonances are identified within the N=1 framework. At the material cutoff ωc=4α/J, micro-rotation amplitudes are amplified while translational amplitudes are suppressed (displacement locking). At the geometric cutoff ωgeo∝h−1, the bending mode is resonantly excited while micro-rotation remains near its quasi-static level. In the second problem, a scalar damage model αeff=α(1−D) is introduced. The material cutoff follows ωc(D)=ωoc1−D, confirmed numerically for all four decoupled subsystems and different prismatic body thicknesses. Geometric branches remain insensitive to damage, producing a spectral separation that may serve as a damage indicator. A critical thickness h* is identified where ωgeo=ωoc, leading to role reversal between material and geometric branches. Numerical results are presented for the polyurethane foam of Lakes.
Armine Ulukhanyan (Wed,) studied this question.