Viscoelastic mechanical behavior of periodontal ligament: Creep and relaxation hyper-viscoelastic constitutive models

Abstract

In this contribution, creep and relaxation hyper-viscoelastic constitutive models of periodontal ligament (PDL) was proposed to define PDL as a steady state rheology (linear)-nonlinear viscoelastic fluid biomaterial. The physical elements of the hyperelastic spring, non-Newtonian fluid damper and strain gap were proposed. The hyperelastic spring, linear elastic spring, linear viscous damper, stress lock, and strain gap constituted the creep and relaxation models. The qualitative energy analysis was made in the viscoelastic zone between the instantaneous elastic element and the infinite elastic element in the creep and relaxation models. The mechanical behavior of viscoelastic materials is qualitatively unified. The universal static, creep, and relaxation mechanical behaviors of materials were explained from the energy point of view (graphische viscoelastic). After defining a virtual “infinite elastic curve of viscoelastic solid” in the viscoelastic fluid model, the universal creep recovery mechanical behavior was analyzed. The unity of the opposites between viscoelastic solid and viscoelastic fluid was clarified. In addition, A physical thinking of “anchored” was proposed to qualitatively modify the Boltzmann superposition principle. Instantaneous/infinite elastic-plastic-fracture curve, yield curve and fracture curve were defined to distinguish viscoelastic zone and viscoplastic zone. Finally, the unsteady-rheological (nonlinear) behavior of nonlinear viscoelastic fluid materials and the hyper-viscoelastic-plastic behavior of nonlinear viscoelastic solid materials were predicted.