Mechanics-based measurement of one-dimensional deformation using multilayer embedded distributed optical-fibre strain sensing

Abstract

Self-sensing structures require methods that convert internally measured strain into deformation with explicit mechanical meaning. This study presents a mechanics-based method for reconstructing two one-dimensional responses in 3D-printed polymer specimens containing embedded optical fibres: axial elongation under quasi-static tension and single-plane beam deflection under three-point bending. Baseline-subtracted distributed optical fibre sensing (DOFS) strain is integrated over a prescribed tensile gauge; under bending, multilayer strains are fitted through the section to identify curvature and then integrated between fixed physical supports. Coordinate signs, sensing-layer positions and boundary conditions are prescribed independently of digital image correlation (DIC), which is introduced only after reconstruction as an external validation measurement. Tensile reconstruction gave a DOFS–DIC slope of 1.059, R2=0.999 817 and a direct root-mean-square error (RMSE) of 9.045 μm. In bending, the median sectional-fit R2 was 0.9949 and the unscaled reconstructed profile followed DIC with a median correlation of 0.9974; the direct RMSE of 0.462 mm and amplitude ratio of 0.582 retained the observed absolute-amplitude underestimation. Downsampling distinguished the minimum testable information supplied by three layers from the additional diagnostic redundancy of five and nine layers. The resulting method combines high-accuracy axial reconstruction, high-spatial-fidelity bending measurement and residual-based multilayer diagnostics in one traceable internal-sensing framework. The present validation covers one resin batch and one-dimensional dominant loading cases, while multidirectional or non-collinear sensing paths provide a testable route towards future three-dimensional reconstruction.