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

Abstract

AbstractPoroviscoelastic 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.