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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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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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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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The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
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On the Interplay Between Roughness and Elastic Modulus at the Nanoscale: A Methodology Study with Bone as Model

Alessandro Gambardella1, Gregorio Marchiori1, Melania Maglio1

  • 1Scienze e Tecnologie Chirurgiche, IRCCS Istituto Ortopedico Rizzoli, 40136 Bologna, Italy.

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Atomic force microscopy nanoindentation can reliably measure the elastic modulus (E) of biological tissues. Accurately accounting for local sample roughness (γs) is crucial for precise nanoscale mechanical property quantification.

Keywords:
atomic force microscopycortical boneimage analysisnanoindentationroughnesstissue biomechanics

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Area of Science:

  • Biophysics
  • Materials Science
  • Nanotechnology

Background:

  • Atomic force microscopy (AFM) nanoindentation is vital for subcellular mechanical analysis.
  • Nanoscale elastic modulus (E) measurements are often unreliable due to unaddressed sample roughness.
  • Understanding roughness influence is key to improving AFM nanoindentation accuracy.

Purpose of the Study:

  • To rigorously re-examine roughness interpretation in AFM nanoindentation.
  • To validate a method for extracting local roughness (γs) at each indentation site.
  • To establish an accurate correlation between local roughness and elastic modulus (E) values.

Main Methods:

  • Performed 80 nanoindentations on murine tibia cortical bone using two AFM tips.
  • Maintained a maximum penetration depth of 10 nm for all measurements.
  • Quantified local roughness (γs) at each nanoindentation site.

Main Results:

  • A slight decreasing trend observed between elastic modulus (E) and local roughness (γs).
  • 90% of E values were deemed reliable when local roughness (γs) was below 10 nm (R² > 0.90).
  • Significant dispersion in E values (over 50%) observed even at low roughness (γs = 0).

Conclusions:

  • Accurate correlation of elastic modulus (E) with local roughness (γs) is achievable.
  • Local roughness significantly impacts nanoscale mechanical property measurements.
  • A tip-to-sample contact model explains roughness heterogeneity effects on bone's nanoscale topography.