Three-dimensional internal deformation measurement methods for hydrogels based on optical coherence tomography

Abstract Depth-resolved, non-contact, full-field three-dimensional (3D) deformation measurement is essential for the application of hydrogels in biomimicry, soft robotics, and optical components. However, current methods are constrained to surface measurements and encounter difficulties in underwater settings. Leveraging the 3D and depth-resolved imaging capabilities of optical coherence tomography (OCT), we propose an OCT-based method for measuring 3D deformation of hydrogels in water. This method integrates underwater electrically driven devices with a Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) based digital volume correlation (DVC) algorithm for 3D strain measurement. We conducted virtual tensile tests and underwater rigid body translation tests to validate the method. The results demonstrated that the strain calculation algorithm had an error of less than 80 μ ϵ and the system error for underwater strain measurement was less than 800 μ ϵ . Utilizing this innovative approach, we measured the 3D displacement and strain distributions within carbon nanotube (CNT)/Poly (acrylic acid/acrylamide) (CNT/P(AA/AM)) electro-responsive hydrogel samples. These samples were immersed in solutions of differing ionic concentrations and exposed to a range of direct current electric fields. We discovered that when subjected to electric fields ranging from 1 to 3 volts, the central region of the hydrogel experiences tensile deformation along the direction from electrode to another. However, when the electric field strength is increased to between 4 and 5 volts, the deformation transitions to a compressive state. Additionally, an increase in NaCl concentration results in a decrease in the overall deformation of the hydrogel. In addition, uniaxial tensile tests were carried out on polyvinyl alcohol (PVA) hydrogels underwater to further verify the method. It was demonstrated that the method can accurately capture the internal deformation field of notched PVA hydrogels in solution under uniaxial tension. The integrated OCT-DVC method offers a novel experimental framework for precise 3D deformation measurement and analysis of semi-transparent hydrogel mechanical behavior in liquid environments.