A discrete-time approach to the formulation of constitutive models for viscoelastic soft tissues

This paper presents a novel approach to constitutive modeling of viscoelastic soft tissues. This formulation combines an anisotropic strain energy function, accounting for preferred material directions, to define the elastic stress-strain relationship, and a discrete time black-box dynamic model, borrowed from the theory of system identification, to describe the time-dependent behavior. This discrete time formulation is straightforwardly oriented to the development of a recursive time integration scheme that calculates the current stress state by using strain and stress values stored at a limited number of previous time instants. The viscoelastic model and the numerical procedure are assessed by implementing two numerical examples, the simulation of a uniaxial tensile test and the inflation of a thin tube. Both simulations are performed using parameter values based on previous experiments on preserved bovine pericardium. Parameters are then adjusted to investigate the sensitivity of the model. The hypotheses the model relies upon are discussed and the main limitations are stated.