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Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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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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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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An Optimized O9-1/Hydrogel System for Studying Mechanical Signals in Neural Crest Cells
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The Ogden model for hydrogels in tissue engineering: Modulus determination with compression to failure.

David S Nedrelow1, Jakob M Townsend1, Michael S Detamore1

  • 1Stephenson School of Biomedical Engineering, University of Oklahoma, Norman, OK, USA.

Journal of Biomechanics
|April 29, 2023
PubMed
Summary

The Ogden model accurately describes hydrogel mechanical properties across the full strain range, offering a better alternative to the traditional elastic modulus for tissue engineering applications.

Keywords:
BiomechanicsChondrogenicElasticNonlinearStem cellSwelling

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Area of Science:

  • Biomaterials Science
  • Tissue Engineering
  • Mechanical Engineering

Background:

  • Traditional methods for assessing hydrogel mechanical properties, like compressive elastic modulus, often fail to capture non-linear behavior across the full strain range.
  • Tissue engineering requires accurate characterization of hydrogel mechanics for optimal construct design and performance.

Purpose of the Study:

  • To evaluate the Ogden model as an alternative to the compressive elastic modulus for characterizing the mechanical properties of tissue engineering hydrogels.
  • To quantify the non-linear mechanical behavior of different hydrogel formulations, including pentenoate-modified hyaluronic acid (PHA) and composite hydrogels with devitalized cartilage (DVC).

Main Methods:

  • Mechanical testing of PHA, PHA-PEGDA, and DVC hydrogels (5-15% w/v) to failure.
  • Fitting stress-strain data using both linear regression (5-15% strain) and the Ogden model.
  • Analysis of gene expression to assess chondrogenesis support by DVC hydrogels.

Main Results:

  • The Ogden model accurately fitted the full strain range of hydrogel compression (R² = 0.998 ± 0.001).
  • DVC15 hydrogels exhibited significantly higher compressive elastic modulus (129 kPa) and shear modulus (37 kPa) compared to PHA hydrogels.
  • PHA hydrogels showed higher nonlinearity (α = 10) than DVC15 hydrogels (α = 1.4), indicating distinct material behaviors.

Conclusions:

  • The Ogden model provides a robust method for quantifying hydrogel mechanical properties, including non-linearity, across the entire strain range.
  • DVC hydrogels demonstrate potential for cartilage tissue engineering, with Ogden model parameters offering baseline targets for future studies.
  • The Ogden model is a valuable alternative to the traditional elastic modulus for characterizing tissue engineering hydrogels.