New rheological models of viscoelastic responses of LV and HV PMMA bone cement validated with experiments

Analytical descriptions of mechanical behaviour have established the Poly (methyl methacrylate) (PMMA) bone cement as a well-known time-dependent viscoelastic material . Assessing creep functions offers a dependable criterion for accomplishing its anchoring requirements in orthopaedic surgical applications. In this context, the present work proposed and validated the rheological mechanical models for the description of creep compliance and modulus relaxation responses of low viscosity (LV) and high viscosity (HV) PMMA bone cement through the nanoindentation technique. The analysis assumes that the Berkovich indentation occurring at the nanoscale behaves as linear viscoelastic deformation. An approach incorporating ramp loading deformation into analytical expressions for creep deformation and load relaxation during the holding period of an indentation cycle has been employed to estimate the creep and relaxation modulus behaviors. The mechanical interpretation of the shear creep compliance behavior was explored through the generalized Voigt (five-element) and extended Burger (six-element) models whereas; the generalized Maxwell model (five-element) was employed for the relaxation modulus function. The LV variant exhibits higher viscoelastic behaviour , showing a tendency to increase the measured value of the creep compliance/relaxation modulus established at ascending values of various constant peak loads (1.5, 2.5, 4.5, 6.5, and 8.5 mN)/maximum indentation depths (500, 600, 700, 800, and 900 nm). In addition, the elastic moduli of both variants were established using the creep deformation. The good correlations of indentation data with the rheological models yield relevant remarkable results of deformation and relaxation properties of both bone cements.