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Table 1 Description of the three modelling scenarios analysed in this study

From: The Role of Layer-Specific Residual Stresses in Arterial Mechanics: Analysis via a Novel Modelling Framework

Scenario \({\mathbf{F}}_{{\mathrm{residual}},k}\) Description
1 \({\mathbf{F}}_{1}{\mathbf{G}}^{k}\) Layer-specific residual stresses in the unloaded cylindrical vessel (\({\kappa }_{\mathrm{unloaded}}\)) arise from two subsequent deformations of the isolated layers (\({\kappa }_{\mathrm{isolated}}\)): (1) into a tri-layered flat wall (\({\kappa }_{\mathrm{composite}}\)) that is (2) then bent into \({\kappa }_{\mathrm{unloaded}}\)
2 \({\mathbf{I}}\) Residual stresses in \({\kappa }_{\mathrm{unloaded}}\) are completely neglected as no deformation occurs from \({\kappa }_{\mathrm{isolated}}\) to \({\kappa }_{\mathrm{unloaded}}\)
3 \({\mathbf{G}}^{k}\) Layer-specific residual stresses in \({\kappa }_{\mathrm{unloaded}}\) arise solely from the deformation of the isolated layers (\({\kappa }_{\mathrm{isolated}}\)) into \({\kappa }_{\mathrm{composite}}\). Hence, \({\kappa }_{\mathrm{composite}}\) is used as an approximation of \({\kappa }_{\mathrm{unloaded}}\)