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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...
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Buckling by disordered growth.

Rahul G Ramachandran1,2, Ricard Alert1,2,3, Pierre A Haas1,2,4

  • 1<a href="https://ror.org/01bf9rw71">Max Planck Institute for the Physics of Complex Systems</a>, Nöthnitzer Straße 38, 01187 Dresden, Germany.

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This summary is machine-generated.

Tissue growth variability can surprisingly alter buckling instabilities, crucial for brain folding. This study reveals that growth variability can either lower or raise the buckling threshold, offering insights into biological development.

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Area of Science:

  • Biophysics
  • Developmental Biology
  • Mechanical Engineering

Background:

  • Buckling instabilities driven by tissue growth are fundamental to biological development, such as brain folding.
  • Cell-to-cell variability in tissue growth is common, but its impact on buckling instabilities remains poorly understood.

Purpose of the Study:

  • To investigate the effects of growth variability on the buckling instabilities of an elastic rod with fixed ends.
  • To determine how spatial variations in growth influence the critical growth threshold for buckling.

Main Methods:

  • Analytical calculations were performed for simple, symmetric growth fields.
  • Numerical simulations were used to sample random growth fields and analyze their effects.
  • The study analyzed the buckling of a simplified elastic rod model with fixed ends.

Main Results:

  • Tissue growth variability can either increase or decrease the growth threshold for buckling.
  • These effects occur even in the absence of residual stresses caused by growth variability.
  • For random growth fields, the shift in the buckling threshold correlates with spatial moments of the growth field.

Conclusions:

  • The spatial arrangement of growth variability can be exploited by biological systems to either initiate or prevent buckling.
  • Understanding growth variability is key to comprehending developmental processes involving tissue morphogenesis.
  • This research provides a framework for analyzing mechanical instabilities in biological tissues with inherent variability.