Transient hoop-stress relocation and inverse identification in radially graded viscoelastic cylinders with independent bulk and shear relaxation spectra

Abstract

Bulk and shear relaxation functions need not have proportional time dependence. This study develops a quasi-static framework for pressurized, radially graded viscoelastic cylinders in which the two spectra are specified separately. A generalized-plane-strain formulation uses radial displacement, radial stress, and an axial-force integral as state variables, avoiding radial derivatives of the material functions. The transformed problem is solved by the complementary functions method and verified against an independent time-domain finite-element model. The examples show that spatial variation in relaxation times can temporarily change which wall governs the maximum hoop stress. This behaviour reflects competition between stress maxima rather than continuous motion of a single peak. Cross-solver identification tests use outer-surface displacement and axial strain. Repeated-noise tests show that the reduced model can retain useful response predictions as measurement noise increases, although individual material parameters become substantially less precise. Adding radial-profile coefficients worsens conditioning and can prevent convergence under the same measurement and optimization protocol. A separate Gaver–Stehfest audit identifies sensitivity to transform-sample errors and reduced accuracy near a pressure-ramp corner. A material-informed epoxy example illustrates the errors caused by proportional bulk–shear approximations. These results support numerical analysis and experiment design, but not unrestricted parameter recovery or laboratory validation. Axial measurements must be interpreted as gauge averages, and the opposing radial gradients used in the examples remain hypothetical material profiles.