A new mathematical model of compressive stress-strain behaviour of low viscosity and high viscosity bone cement with different strain rates

Abstract

A new mathematical model of compressive stress-strain behaviour of low viscosity (LV) and high viscosity (HV) bone cement has been proposed to capture large uniaxial deformation under constant applied strain rate by incorporating three-term power law. The modeling capacity of the proposed model has been validated using uniaxial compressive test under eight different low strain rates ranging from 1.39 × 10-4 s-1 to 3.53 × 10-2 s-1 for low viscosity and high viscosity bone cement. The well agreement between the model and experimental response suggests that the proposed model can successfully predict rate dependent deformation behavior for Poly(methyl methacrylate) (PMMA) bone cement. Additionally, the proposed model was compared with the generalized Maxwell viscoelastic model and found to be in good agreement. The comparison of compressive responses over low strain rates for LV and HV bone cement reveals their rate-dependent compressive yield stress behaviour along with a higher value of compressive yield stress of LV bone cement compared to HV bone cement. For example, at the strain rate of 1.39 × 10-4 s-1 the mean value of compressive yield stress of LV bone cement was found to be 64.46 MPa, whereas for HV bone cement it was 54.00 MPa. Moreover, the modeling of experimental compressive yield stress with the Ree-Eyring molecular theory suggests that the variation of yield stress of PMMA bone cement can be predicted using two processes Ree-Eyring theory. The proposed constitutive model might be useful to characterize large deformation behaviour with high accuracy for PMMA bone cement. Finally, both variants of PMMA bone cement also exhibit ductile-like compressive behaviour below the strain rate of 2.1 × 10-2 s-1, whereas above this threshold strain rate, brittle-like compressive failure behavior is observed.