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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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When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
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A Fractional Order Standard Linear Solid Model for Extracting the Elastic Moduli of Internal Cell Structures.

Haoping Yu1, Heng Li1, Wei Zhang1

  • 1State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China.

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Summary
This summary is machine-generated.

This study introduces a new fractional-order model to measure the elastic moduli of cell structures. This simplified method accurately determines cell mechanics without complex experiments.

Keywords:
atomic force microscopeelasticityinternal cell structuremodel

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Area of Science:

  • Biophysics
  • Cell Mechanics
  • Materials Science

Background:

  • Cellular mechanical properties, or elastic moduli, are key indicators of cell behavior.
  • Measuring these properties typically involves complex micro/nano-scale experimental procedures.

Purpose of the Study:

  • To propose a novel fractional-order standard linear solid model for determining the elastic moduli of internal cell structures.
  • To simplify the experimental measurement of cell mechanics.

Main Methods:

  • A fractional-order standard linear solid model was developed, treating the nucleus, cytoskeleton, and cytoplasm as load-bearing components.
  • The model was fitted to cell creep curves obtained via atomic force microscopy (AFM).

Main Results:

  • The model successfully extracted elastic moduli for the nucleus, intermediate filaments, microtubules, and a composite membrane-cytoplasm-actin cortex element.
  • Fitted elastic moduli were of appropriate magnitude, independent of loading, and showed good agreement (R²: 0.95-0.98) with existing data.
  • The proposed model demonstrated lower Akaike Information Criterion (AIC) values compared to traditional Prony models.

Conclusions:

  • The developed fractional-order model offers a simplified and effective method for measuring the mechanical properties of internal cell structures.
  • This approach eliminates the need for complex experimental setups and can monitor cellular responses to various stimuli.