Morphology of residually-stressed tubular tissues: Beyond the elastic multiplicative decomposition

TL;DR

This paper investigates how residual stresses in elastic tubes can induce buckling and wrinkling, introducing a new model that prescribes residual stress fields directly and validating predictions with finite element simulations.

Contribution

A novel modeling approach that directly prescribes residual stress in elastic tubes, enabling analysis of buckling and wrinkling without assuming a virtual stress-free state.

Findings

Residual stress can cause buckling in elastic tubes.

Wrinkles can form on inner or outer surfaces depending on residual hoop stress.

Finite element simulations match theoretical predictions and reveal crease shapes and amplitudes.

Abstract

Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.