Constitutive modelling of PMMA-based bone cement: a functional model of viscoelasticity and its approximation for time domain investigations

Abstract

To represent the mechanical behaviour of polyethylmethacrylate-based bone cement, a constitutive approach of finite linear viscoelasticity is formulated and identified. Motivated by the experimental data of storage and loss modulus, the model is based on a three-dimensional functional in integral representation. In the investigated frequency range, the master curve of the loss modulus is constant and that of the storage modulus increases linearly with the logarithm of the frequency. This behaviour corresponds to a viscoelastic fluid, and can be described by a continuous relaxation spectrum. For numerical simulations which are planned in future, the constitutive functional is approximated by a discrete spectrum. To this end, an earlier-developed method to approximate continuous relaxation spectra in limited time or frequency ranges by discrete ones is applied.