Numerical Algorithm for Simulation of Soft Tissue Swelling and Shrinking in a Total Lagrangian Explicit Dynamics Framework

We present an algorithm for modelling swelling and shrinking of soft tissues based on the total Lagrangian formulation of the finite element (FE) method. Explicit time integration with adaptive dynamic relaxation is used to compute the steady state solution. The algorithm can easily handle geometric and material nonlinearities, and is very efficient because it allows pre-computation of important solution parameters and does not require solution of large systems of equations. Swelling and shrinking behaviour is modelled by applying a multiplicative decomposition of the deformation gradient to separate the total deformation into swelling/shrinking and elastic components. A hyperelastic constitutive law is used to model the elastic behaviour of the material. Accuracy of the algorithm is confirmed by successful verification against an established FE code. The algorithm involves only vector operations and is well suited for parallel implementation for increased computational speed.