Finite element formulation and analysis for an arterial wall with residual and active stresses

In this study, for predicting arterial function and pathogenesis from a mechanical viewpoint, we develop a continuum mechanical model of an arterial wall that embodies residual and active stresses following a traditional anisotropic passive constitutive law. The residual and active stresses are incorporated into finite element methods based on a two-field variational principle described in the Lagrangian form. The linearisation of nonlinear weak-form equations derived from this variational principle is then described for developing an original finite element algorithm. Numerical simulations reveal the following: (i) residual stresses lead to a reduction in stress gradient regardless of the magnitude of external load; (ii) active stresses help homogenise stress distribution under physiological external load, but this homogeneity collapses under pathological external load; (iii) when residual and active stresses act together, the effect of the residual stresses is relatively obscured by that of the active stresses. We conclude that residual stresses have minor but persistent mechanical effects on the arterial wall under both physiological and pathological external loads; active stresses play an important role in the physiological functions and pathogenesis of arteries, and the mechanical effect of residual stresses is dependent on the presence/absence of active stresses.