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<p dir="ltr">Terahertz Time Domain Spectroscopy (THz-TDS) is a powerful non-destructive, non-ionizing spectroscopic technique utilized for evaluating the optical properties of materials within the terahertz frequency range, spanning from 0.1 to 10 terahertz or wavelengths of 300 micron to 3000 micron. It effectively bridges the gap between microwave and infrared regions on the electromagnetic spectrum and its high resolution which avoiding scattering can quantify small changes in dielectric properties of media. It has high transmission through visibly opaque polymers and its ability to record both magnitude and phase information makes it a strong spectroscopic technique with applications in security, chemistry, electronics and telecommunication and non-destructive evaluation methods for solid mechanics.</p><p><br></p><p dir="ltr">This work introduces a polarization-dependent analytical model employing THz-TDS for computing strain in materials. The model establishes a correlation between volumetric strain and the change in time of arrival for a THz pulse, leveraging dielectrostrictive properties, variations in doping particle density, and changes in sample thickness due to Poisson’s effects. Validation of the analytical model is achieved through strain mapping of polydimethylsiloxane doped with highly dielectrostrictive strontium titanate (STO). Two experiments, including open-hole tensile and circular edge-notch specimens, demonstrate the efficacy of the model. Additionally, the study accounts for stress relaxation behavior to ensure measurement accuracy. Comparison of THz strain mapping results with finite element model (FEM) and surface strain measurements using digital image correlation (DIC) method highlights the technique's sensitivity to material features such as particle clumping and edge effects, while showcasing strong agreement with FEM and DIC results.</p><p><br></p><p dir="ltr">This analytical model is further expanded for experimentally mapping subsurface stress and strain in the adhesive layer of a single lap shear test. This in-situ non-destructive testing method pioneers the use of THz-TDS for stress estimation in the adhesive layer. Validation through strain mapping of STO doped Araldite 2011 epoxy adhesive with the analytical formulation is presented.</p><p dir="ltr">Finally, THz-TDS is applied for fracture front mapping in a double cantilever beam test with high-density polyethylene bonded with STO doped Araldite 2011. The phase-dependent model for mapping fracture fronts in the sub-surface adhesive layer involves analyzing convoluted waves due to interface resonances in a multi-layer structure using THz-TDS in transmission mode. The technique evaluates changes in dielectrostrictive properties and degree of separation to delineate fracture fronts. THz image enhancement algorithms facilitate crack front delineation. Error analysis on measured crack thickness is conducted to evaluate signal-to-noise ratio for THz-TDS. Additionally, an approach employing THz-TDS measured fracture propagation information for determining sub-surface stress maps in the adhesive layer and computing fracture toughness (G_Ic) is proposed. This work highlights the versatility and efficacy of THz-TDS in material characterization and stress/strain mapping in solid mechanics applications.</p>

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