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Related Concept Videos

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

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.
Bending of Members Made of Several Materials01:11

Bending of Members Made of Several Materials

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.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Hooke's Law01:26

Hooke's Law

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.
Elasticity in Concrete01:20

Elasticity in Concrete

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 portion of...
Strain and Elastic Modulus01:15

Strain and Elastic Modulus

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...
Generalized Hooke's Law01:22

Generalized Hooke's Law

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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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Published on: April 25, 2019

Morphology and linear-elastic moduli of random network solids.

Susan Nachtrab1, Sebastian C Kapfer, Christoph H Arns

  • 1Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany.

Advanced Materials (Deerfield Beach, Fla.)
|June 18, 2011
PubMed
Summary

This study uses finite element analysis to model disordered network solids, finding that solid volume fraction dictates effective elastic moduli. Collagen and Poisson-Voronoi networks show similar behavior, suggesting a unified modeling approach.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Computational Modeling

Background:

  • Disordered network solids, such as collagen fiber networks, exhibit complex mechanical properties.
  • Understanding the relationship between structure and effective linear-elastic moduli is crucial for predicting material behavior.

Purpose of the Study:

  • To analyze the effective linear-elastic moduli of disordered network solids using voxel-based finite element calculations.
  • To investigate the influence of solid volume fraction on bulk and shear moduli in different network structures.
  • To compare the mechanical behavior of collagen fiber networks and Poisson-Voronoi processes.

Main Methods:

  • Voxel-based finite element calculations were employed to determine effective moduli.
  • Network solids were generated using Poisson-Voronoi processes and derived from confocal microscopy images of collagen fiber networks.
  • The solid volume fraction was systematically varied by adjusting fiber radius.

Main Results:

  • Empirical power-laws approximated the bulk (K) and shear (G) moduli for intermediate solid volume fractions (ϕ), yielding exponents n≈1.4 and m≈1.7.
  • Exponents for collagen and Poisson-Voronoi networks were similar and deviated from analytical values for low-density structures.
  • A proposed functional form successfully modeled the crossover from low-density power-law behavior to high-density porous solid behavior, yielding an asymptotic exponent n≈1.00.
  • Effective moduli were primarily dependent on the solid volume fraction, irrespective of underlying network characteristics.

Conclusions:

  • The solid volume fraction is the dominant factor governing the effective linear-elastic moduli of disordered network solids.
  • Poisson-Voronoi processes can quantitatively model network solids with structures similar to collagen networks.
  • The findings provide a unified framework for understanding the mechanical properties of diverse disordered network materials.