Bulge initiation in tubes of time-dependent materials

This work considers the inflation and extension of an elastomeric tubular membrane when its material exhibits a time-dependent response. Three different models for time-dependent response are considered: finite linear viscoelasticity, Pipkin–Rogers non-linear viscoelasticity, and thermally induced chemorheological degradation. The first two are based on different assumptions about stress relaxation effects while the third accounts for time-dependent microstructural changes due to simultaneous scission and re-cross-linking of macromolecular network junctions. Each of these models describes a material response that softens with time. It is shown that the constitutive equations for all three models are included in a general non-linear single-integral constitutive equation.

In previous work, for elastic membranes, the material is fixed and a localized bulge may form as the load increases. In this work, the load is specified, and a localized bulge may form as the membrane material undergoes a time-dependent response. It is assumed that the extension and inflation histories are initially uniform, but there may be a time when a localized bulge-like deformation starts to form. This is treated as branching from the uniform extension and inflation history. For times beyond this ‘branching time’, the governing equations are satisfied by both the continuation of the initial uniform deformation history and the branched deformation history for the bulge. A unified condition for determining this branching time, applicable to all three models, is derived in terms of the general non-linear single-integral constitutive equation. Post-branching response is not considered here.