A viscoelastic model to simulate soft tissue materials

Abstract

Continuum mechanic theories are frequently used to simulate the mechanical behavior of elastic and viscous materials, specifically soft tissues typically showing incompressibility, nonlinear deformation under stress, fading memory and insensitivity to the strain-rate. The time dependence of a viscoelastic material could be better understood by considering it as composed by an elastic solid and a viscous fluid. Different types of mechanical devices can be constructed provided a particular configuration of elastic springs and dashpots. In this work our aim is to probe many of the soft tissue mechanical behavior, by considering a Kelvin's device coupled to a set of in parallel Maxwell's devices. Then, the resulting model composed of a long series of modified Kelvin bodies must span a broad range of characteristic times resulting in a suitable model for soft tissue simulation. Under driving static and dynamic stress applied to a 2-Dim system, its time dependence strain response is computed. We obtain a set of coupled Volterra integral equations solved via the extended trapezoidal rule scheme, and the Newton-Raphson method to solve nonlinear coupled equations.