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The V-W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V-W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.

Owing to fabrication defects in carbon fiber (CF) tows, the unevenness of fiber roves, such as local bends, misalignments, and skewness, results in irregular distribution of the electrical resistance in the transverse direction along the gauge length of a sensor, which affects its performance. In this study, a pre-tension approach was developed according to the creep mechanism of composites to straighten the CFs. In addition, the resin relaxation was controlled by tensioning the fibers during and after hardening of the epoxy resin using a double-tension method to enhance the electrical sensing properties of long gauge carbon fiber line (CFL) strain sensors. Different levels of sustained tensile stresses were studied to obtain the optimal tensile stress level both during and after hardening to be applied in the double-tension method. The results of static and dynamic tests showed that the double-tension technique could significantly straighten the fibers, and stabilize the transverse connections of CFL sensors in the case of tensioning the fibers during and after hardening under a sustained stress of 60% of the ultimate tensile stress of the CFs. The proposed double-tension method was utilized to improve the response of the CFL sensors with short gauge lengths.