Disentangling geometrical, viscoelastic and hyperelastic effects in force-displacement relationships of folded biological tissues

  • Francesco Atzeni
  • Flavio Lanfranconi
  • Christof M. AegerterEmail author
Open Access
Regular Article


Drosophila wing discs show a remarkable variability when subject to mechanical perturbation. We developed a stretching bench that allows accurate measurements of instantaneous and time-dependent material behaviour of the disc as a whole, while determining the exact three-dimensional structure of the disc during stretching. Our experiments reveal force relaxation dynamics on timescales that are significant for development, along with a surprisingly nonlinear force-displacement relationship. Concurrently our imaging indicates that the disc is a highly heterogeneous tissue with a complex geometry. Using image-based 3D finite element modelling we are able to identify the contributions of size, shape and materials parameters to the measured force-displacement relations. In particular, we find that simulating the stretching of a disc with stiffness patterns in the extra-cellular matrix (ECM) recapitulates the experimentally found stretched geometries. In our simulations, linear hyperelasticity explains the measured nonlinearity to a surprising extent. To fully match the experimental force-displacement curves, we use an exponentially elastic material, which, when coupled to material relaxation also explains time-dependent experiments. Our simulations predict that as the disc develops, two counteracting effects, namely the discs foldedness and the hardening of the ECM lead to force-relative displacement curves that are nearly conserved during development.

Graphical abstract


Living systems: Multicellular Systems 


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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Francesco Atzeni
    • 1
    • 2
    • 3
  • Flavio Lanfranconi
    • 1
  • Christof M. Aegerter
    • 1
    • 2
    Email author
  1. 1.Physics InstituteUniversity of ZurichZurichSwitzerland
  2. 2.Institute of Molecular Life SciencesUniversity of ZurichZurichSwitzerland
  3. 3.Life Science Zurich Graduate SchoolETH Zurich and University of ZurichZurichSwitzerland

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