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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Shape transitions in a network model of active elastic shells.

Ajoy Maji1, Kinjal Dasbiswas2, Yitzhak Rabin3

  • 1Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel.

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This study introduces a minimal active elastic model that mimics biological shape changes. The model demonstrates how mechanical forces and pressure regulation can autonomously transition spherical shells into complex 3D shapes like ellipsoids.

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Area of Science:

  • Biophysics
  • Mechanobiology
  • Materials Science

Background:

  • Morphogenesis involves complex 3D shape transformations from simpler forms.
  • Mechanical forces, including motor-generated forces and hydrostatic pressure, drive these shape changes via mechano-chemical feedback.
  • Living matter exhibits autonomous biophysical shape changes, exemplified by organisms like Hydra.

Purpose of the Study:

  • To introduce a minimal, active, elastic model inspired by autonomous biophysical shape change.
  • To investigate the role of active regulation of mechanical properties in morphogenesis.
  • To explore how pressure influences shape transitions in active elastic shells.

Main Methods:

  • Developed a minimal active elastic model using a network of springs in a spherical shell geometry.
  • Implemented a mechano-chemical feedback mechanism where local curvature affects spring elastic constants.
  • Combined spring excitation with hydrostatic pressure regulation to observe shape dynamics.

Main Results:

  • The active elastic shell model demonstrated autonomous shape transitions from spheroidal to ellipsoidal or other spheroidal forms.
  • Shape transformation was dependent on the regulated hydrostatic pressure.
  • A critical pressure threshold was identified, inducing an abrupt switch between ellipsoidal and spheroidal shapes.

Conclusions:

  • Active regulation of mechanical properties and pressure are key to autonomous morphogenesis.
  • Hydrostatic pressure acts as a sensitive switch controlling material shape transitions.
  • The model provides biologically inspired design principles for creating autonomous shape-changing materials.