An investigation of coupled solution algorithms for finite‐strain poroviscoelasticity applied to soft biological tissues

Abstract

Poroviscoelastic models have been widely employed to the modeling of hydrated biological tissues, since they allow to investigate the biomechanical responses associated with the interstitial fluid flow. Such problems present strong physical couplings arising from material and geometrical nonlinearities. In this regard, the present study investigates the numerical performance of five biphasic solution algorithms within the context of soft biological tissues: monolithic, drained, undrained, fixed-strain, and fixed-stress scheme. To this end, two classical tests were studied within a finite element framework: confined and unconfined compression tests. Since these tests behave differently in terms of biphasic coupling, the sensitivity of different permeability values and time increments to the algorithms' performance were assessed. The results highlight that iterative techniques perform well over the monolithic one for weak coupling cases but suffer from lack of convergence when the coupling strength increases. This means that, in contrast to what is recommended in the vast majority of geomechanics papers, the iteratively-coupled schemes are not always well-suited methods for problems related to soft biological tissues mechanics. The monolithic scheme thus emerges as the most reliable choice to solve biphasic problems in a biomechanics context, specifically when high coupling strength problems and small time increments take place.

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

“…• large deformation theory of porous media 15,16,22,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] • inertial effects [11][12][13]15,16,18,22,23,[25][26][27][29][30][31][33][34][35][36][38][39][40][41][42][43][44] • non-linear constitutive theory 13,16,19,24,25,[27]…”

“…The three‐field formulation is not new, see, for example, Zienkiewicz et al 17 for the initial theory and others 18–23 for various numerical implementations. However, to the best of our knowledge, this work is one of the first (if not the first) to consider the following novel contributions simultaneously : large deformation theory of porous media 15,16,22,24–41 inertial effects 11–13,15,16,18,22,23,25–27,29–31,33–36,38–44 non‐linear constitutive theory 13,16,19,24,25,27–29,31,33–39,42 compressible constituents 11,13,16,23,26,30,31,33,35,38,43,45 high strain‐rate loading to large strains with nonlinear geometric effects (this is the primary contribution of the paper) …”