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

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.

References in corpus (3)

• Initial stresses in elastic solids: Constitutive laws and acoustoelasticity
• Bending instabilities of soft tissues
• On deforming a sector of a circular cylindrical tube into an intact tube: existence, uniqueness, and stability

Cited by in corpus (6)

• Modified multiplicative decomposition model for tissue growth: Beyond the initial stress-free state
• Influence of initial residual stress on growth and pattern creation for a layered aorta
• Prescribing patterns in growing tubular soft matter by initial residual stress
• Rayleigh-Taylor instability in soft elastic layers
• Electro-mechanically guided growth and patterns
• Basis functions for residual stresses