Relaxation Time Determines Mechanical Signal Persistence in the Periodontal Ligament Under Sustained Loading

Mechanical loading of connective tissues is traditionally prescribed by force magnitude. In viscoelastic tissues, a constant external force does not produce a constant internal mechanical environment: stress and strain evolve continuously after load onset, creating a time-varying tissue-level mechanical history relevant to resident cells. This distinction is rarely accounted for in clinical loading protocols or scaffold design. The rate of evolution is governed by the stress relaxation time constant (τ). How τ controls the persistence of mechanical signals under force-controlled sustained loading remains poorly quantified. Thus, we developed a three-dimensional finite element model of the Wistar rat maxillary first molar tooth–periodontal ligament (PDL)–bone complex with a PDL geometry reconstructed from micro-CT imaging by original frame-by-frame manual segmentation and compared outcomes across three τ values spanning two orders of magnitude under identical 0.5 N sustained loading. Under the same applied force, stress retention at 100 s ranged from 68% to 97%, while concurrent deformation creep showed an inverse relationship. These results demonstrate that τ strongly governs the persistence of mechanical signals under sustained force-controlled loading in this model. Supplementary simulations under oblique loading and perturbed PDL modulus confirmed that τ remains the dominant constitutive determinant of stress retention across altered loading directions and stiffness conditions.