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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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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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Stress: General Loading Conditions01:15

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To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
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Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
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Elastic Strain Energy for Shearing Stresses

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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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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
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Osteocyte lacunar strain determination using multiscale finite element analysis.

Sravan K Kola1, Mark T Begonia2, LeAnn M Tiede-Lewis3

  • 1Department of Civil and Mechanical Engineering, University of Missouri-Kansas City, 350L Flarsheim Hall, 5100 Rockhill Road, Kansas City, MO 64110, United States of America.

Bone Reports
|June 2, 2020
PubMed
Summary
This summary is machine-generated.

Osteocyte lacunae size and orientation influence bone strain responses. Variations in lacunar size and alignment explain heterogeneous osteocyte activation under mechanical load, impacting bone remodeling.

Keywords:
Finite element modelLacunaeOsteocytePerilacunar matrixStrain

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Area of Science:

  • Biomechanical Engineering
  • Cellular Mechanobiology
  • Skeletal Biology

Background:

  • Osteocytes are key mechanosensors in bone, regulating resorption and formation.
  • Osteocyte activation by mechanical forces, including Wnt/β-catenin signaling, is heterogeneous.
  • Previous finite element models often used simplified geometries and single osteocytes.

Purpose of the Study:

  • To investigate how osteocyte lacunae size and orientation affect micro-heterogeneity in bone strain.
  • To explain the observed heterogeneous patterns of osteocyte activation under mechanical loading.
  • To develop multi-scale computational models of osteocyte mechanotransduction.

Main Methods:

  • Developed microscale and nanoscale finite element (FE) models of osteocytes.
  • Analyzed lacunar and perilacunar strain responses based on lacunar orientation and size.
  • Utilized 3D confocal image stacks of mouse femur osteocytes for realistic geometries.
  • Performed parametric analysis by varying perilacunar modulus.

Main Results:

  • Lacunar strains decreased with increased perilacunar modulus, indicating stress shielding.
  • Osteocytes aligned with the loading axis experienced lower strains than those perpendicular.
  • Larger lacunae resulted in increased lacunar strains.
  • FE models with multiple osteocytes, including realistic geometries, were employed.

Conclusions:

  • Osteocyte lacunae orientation and size are critical factors in heterogeneous strain distribution.
  • These factors contribute to the observed varied osteocyte activation patterns following mechanical loading.
  • Understanding lacunar-level strain mechanics enhances knowledge of osteocyte mechanotransduction and bone adaptation.