Eigenstrain tomography for resolving discontinuous and impotent inelastic strain fields

Accurate characterisation of complex residual stress requires resolving underlying inelastic strains, which often exhibit unobservable or discontinuous features. This study establishes the fundamental identifiability limits of eigenstrain tomography when mapping sparse diffraction measurements to volumetric discontinuous and impotent (stress-free null) strain states. The results demonstrate that the mechanics-informed inversion intrinsically isolates unobservable impotent modes without artificial mathematical smoothing, provided the acquisition path is geometrically complete. The key novelty lies in identifying a strict dimensional threshold for triaxial deformation. While uniaxial states are uniquely identifiable from single-component data, resolving fully triaxial fields inherently requires multi-component, orthogonal strain measurements to decouple structural cross-talk. This dimensional threshold advances the fundamental theory of ill-posed inverse problems in continuum mechanics by redefining data sufficiency requirements for multi-axial reconstruction. These findings provide mechanics-based observability criteria for experimental design, proving that sharp resolution of embedded boundaries is fundamentally limited by tomographic acquisition completeness.