A viscoelastic model to simulate soft tissue materials

[摘要] 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.

[发布机构] Departamento de Física, IFQC, Universidade Federal de Goiás, Catalão, Goiás; 75704/020, Brazil^1;Departamento de Física, IGCE, UNESP, Rio-Clãro, São Paulo; 13500/970, Brazil^2

[效力级别] 数学

[关键词] Mechanical behavior;Mechanical device;Nonlinear deformations;Soft tissue simulation;Visco-elastic material;Viscoelastic modeling;Viscous materials;Volterra integral equations