Fig. 5

Mean circumferential Cauchy stress–circumferential stretch relationships with load partitioning between layers and layer-specific circumferential load bearing for the three cases analysed in this study: (1) full tri-layered model with residual stresses (A and B), (2) tri-layered model neglecting residual stresses (C and D), and (3) tri-layered model neglecting \({\mathbf{F}}_{1}\) (E and F). Circumferential stretch at the inner radius was computed as \({\lambda }_{\theta }\)=\({r}_{\mathrm{internal}}\)/\({R}_{\mathrm{internal}}\). In Panels A, C and E, the intimal line was obtained using Eq. 11 with \({{\varvec{\upsigma}}}^{{\mathrm{m}}}=\varvec{0}\) and \({{\varvec{\upsigma}}}^{{\mathrm{a}}}=\varvec{0}\), and the media line with \({{\varvec{\upsigma}}}^{{\mathrm{a}}}=\varvec{0}\). The adventitial line was obtained using the full version of Eq. 14. This means that, for any given \({\lambda }_{\theta }\)/pressure, the amplitude of each coloured area is given by the corresponding layer’s circumferential stress multiplied by its loaded relative thickness (i.e. \({\sigma }_{\theta \theta }^{k}\frac{{h}^{k}}{{h}^{{\mathrm{wall}}}}\) where k indicates a generic layer)