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Related Concept Videos

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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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.
Dynamic Modulus of Elasticity of Concrete01:16

Dynamic Modulus of Elasticity of Concrete

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.
The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x 4 x 20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by a...
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

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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 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...

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Soft random solids and their heterogeneous elasticity.

Xiaoming Mao1, Paul M Goldbart, Xiangjun Xing

  • 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

Vulcanization theory reveals spatial heterogeneity in soft random solids due to synthesis fluctuations. This heterogeneity impacts elastic properties, with large residual stresses and long-ranged disorder found in the equilibrium state.

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Area of Science:

  • Materials Science
  • Soft Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Soft random solids exhibit spatial heterogeneity in their structure and elastic properties.
  • This heterogeneity originates from quenched-in fluctuations during synthesis.
  • Understanding this disorder is crucial for predicting material behavior.

Purpose of the Study:

  • To investigate spatial heterogeneity in the elastic properties of soft random solids.
  • To apply vulcanization theory and replica field theory to model quenched disorder.
  • To characterize the statistics of elasticity disorder in these materials.

Main Methods:

  • Utilizing vulcanization theory and replica field theory to model random-solid-forming systems.
  • Analyzing the Goldstone sector of fluctuations associated with the liquid-to-random-solid transition.
  • Reinterpreting free energy to derive statistics of quenched disorder in elasticity.

Main Results:

  • Elastic deformations are described by the Goldstone sector, linked to spontaneous symmetry breaking.
  • The free energy of the Goldstone sector corresponds to a phenomenological elastic medium with quenched disorder.
  • Identified statistics of quenched disorder in terms of residual stress and Lamé-coefficient fields.

Conclusions:

  • Soft random solids possess significant residual stresses in their equilibrium state.
  • Disorder correlators of residual stress are long-ranged and governed by a universal parameter.
  • This universal parameter also determines the mean shear modulus of the material.