Elephant trunk wrinkles: A mathematical model of function and form

TL;DR

This paper presents a mathematical model explaining the formation and distribution of skin wrinkles in elephant trunks, linking morphogenesis, mechanical properties, and geometric factors to the pattern of wrinkles.

Contribution

It introduces a nonlinear morphoelasticity-based model that predicts wrinkle patterns based on skin thickness, stiffness, growth, and curvature, providing new insights into elephant trunk morphology.

Findings

Fewer wrinkles near the trunk base where curvature is lower.

More wrinkles develop distally with higher curvature.

Ventral side exhibits less wrinkling compared to dorsal side.

Abstract

A notable feature of the elephant trunk is the pronounced wrinkling that enables its great flexibility. Here, we devise a general mathematical model that accounts for the characteristic skin wrinkles formed during morphogenesis in the elephant trunk. Using physically realistic parameters and operating within the theoretical framework of nonlinear morphoelasticity, we elucidate analytically and numerically the effect of skin thickness, relative stiffness, and differential growth on the physiological pattern of transverse wrinkles distributed along the trunk. We conclude that since the skin and muscle components have similar material properties, geometric parameters, such as curvature, play an important role. In particular, our model predicts that, in the proximal region close to the skull, where the curvature is lower, fewer wrinkles form and will form sooner than in the distal narrower region, where more wrinkles develop. Similarly, less wrinkling is found on the ventral side, which is flatter, compared to the dorsal side. In summary, the mechanical compatibility between the skin and the muscle enables them to grow seamlessly, while the wrinkled skin acts as a protective barrier that is both thicker and more flexible than the unwrinkled skin.