Fig. 1

Schematic representation of the different configurations and linking deformation gradients analysed in this study: (1) isolated layers (\({\kappa }_{\mathrm{isolated}}\)), (2) composite wall (\({\kappa }_{\mathrm{composite}}\)), (3) unloaded cylindrical vessel (\({\kappa }_{\mathrm{unloaded}}\)), and (4) pressurised axially stretched cylindrical vessel (\({\kappa }_{{\mathrm{tension}}-{\mathrm{inflation}}}\)). Note that the deformation from \({\kappa }_{\mathrm{isolated}}\) to \({\kappa }_{\mathrm{unloaded}}\), mapped by the deformation gradient \({\mathbf{F}}_{{\mathrm{residual}},k}\), defines the layer-specific residual deformations. Deformation gradients were differentially defined in the three analysed scenarios \(s\in\{\mathrm{1,2},3\}\) (Table 1) as indicated. Note the use of different coordinate systems in the respective configurations. Superscript \(k\in \left\{{\mathrm{i}},{\mathrm{m}},{\mathrm{a}}\right\}\) indicates the intimal (\({\mathrm{i}}\)), medial (\({\mathrm{m}}\)), or adventitial (\({\mathrm{a}}\)) layer, respectively