Instability of soft matters

Growing soft tissue with a confined boundary is accompanied by a large strain and stress which lead to instability and the formation of surface wrinkling, folding or creasing. This paper presents the morphological evolution of the growth of a biological tube composed of a neo-Hookean hyperelastic material within a confined environment. Critical growth ratios for the triggering of creases or detachment from the contacting boundary have been investigated both analytically and numerically. Results show that compressive residual stresses induced by confined growth of the tubular tissue can lead to a variety of surface folding patterns which strongly depend on the thickness of the tube. In thick tube creases begin to form at the inner surface of the tube and in thin tube the structure detaches from the confining wall. Between these two extremes there is a transitional area wherein the tube starts to crease at first and then detaches from the confining wall. Further modeling reveals that a gap between the tube and the confinement can tune the shape evolution of the growing biological tube. These findings may provide some fundamental understanding to growth modeling of complicated biological phenomena such as cortical folding of the brain and the growth of solid tumors.

confinement growth
Expansion, crease formation and detaching of a biological tube induced by the continuous growth.

Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as its morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability, therefore non-linear finite element simulations are carried out to replicate the post-stability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

interfacial crease
Morphological evolution of a growing bi-layer structure with different initial interface radii.

Creasing in soft polymeric films is a result of substantial compressive stresses that trigger instability beyond a critical strain and have been directly related to failure mechanisms in polymeric films. However, it has been shown that programming these instabilities into soft materials can lead to new applications, such as particle sorting, deformable capillaries, and stimuli-responsive interfaces. In this work, we present a method for fabricating reproducible nanoscale surface instabilities using reactive micro-contacting printing (μCP) on activated ester polymer brush layers of poly(pentafluorophenyl acrylate). The sizes and structures of the nanoscale creases can be changed by varying the grafting density of the substrate and pressure used during μCP. Stress is generated in the film under confinement due to the molecular weight increase of the side chains during post-polymerization modification, which results in a substantial in-plane growth in the film, and leads to the observed nanoscale creases.

polymer creasing
Top: AFM topography images of PFPA films functionalized with Jeffamine® M-2070. (A) From solution, (B) μCP with a pressure of 18.3 Pa, and (C) μCP with a pressure of 1.15 kPa. Bottom: Morphological simulations of the low grafting density substrate after post-polymerization modification using μCP for. A). 18.3Pa and B). 1.15kPa.


M. J. Razavi, R. Pidaparti and X. Wang, "Surface and Interfacial Creases in a Bilayer Tubular Soft Tissue", Physical Review E, 94: 022405, 2016.

K. Brooks, M. J. Razavi, X. Wang and J. Locklin, "Nanoscale Surface Creasing Induced by Post-polymerization Modification", ACS Nano, 9 (11): 10961–10969, 2015.

M. J. Razavi and X. Wang, "Morphological Patterns of a Growing Biological Tube in a Constrained Environment with Contacting Boundary", RSC Advances, 5: 7440-7449, 2015.


Dr. Jason Locklin (UGA College of Engineering and Department of Chemistry)

Dr. Leonid Ionov (UGA College of Engineering and College of Family & Consumer Sciences)