A rate-insensitive linear viscoelastic model for soft tissues

Abstract

It is well known that many biological soft tissues behave as viscoelastic materials with hysteresis curves being nearly independent of strain rate when loading frequency is varied over a large range. In this work, the rate-insensitive feature of biological materials is taken into account by a generalized Maxwell model. To minimize the number of model parameters, it is assumed that the characteristic frequencies of Maxwell elements form a geometric series. As a result, the model is characterized by five material constants: micro(0), tau, m, rho and beta, where micro(0) is the relaxed elastic modulus, tau the characteristic relaxation time, m the number of Maxwell elements, rho the gap between characteristic frequencies, and beta=micro(1)/micro(0) with micro(1) being the elastic modulus of the Maxwell body that has relaxation time tau. The physical basis of the model is motivated by the microstructural architecture of typical soft tissues. The novel model shows excellent fit of relaxation data on the canine aorta and captures the salient features of vascular viscoelasticity with significantly fewer model parameters.