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Related Concept Videos

Shearing Strain01:20

Shearing Strain

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The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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Strain and Elastic Modulus01:15

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

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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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Elastic Strain Energy for Shearing Stresses01:20

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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Hooke's Law01:26

Hooke's Law

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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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Problem Solving on Stress and Strain01:22

Problem Solving on Stress and Strain

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Stress is a quantity that describes the magnitude of a force that causes deformation, generally defined as internal force per unit area. When forces pull on an object and cause its elongation, like the stretching of an elastic band, it is called tensile stress. When forces cause the compression of an object, it is known as compressive stress. When an object is being squeezed uniformly from all sides, like a submarine in the depths of the ocean, we call this kind of stress bulk stress (or volume...
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Investigating Stress-relaxation and Failure Responses in the Trachea
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Simple average expression for shear-stress relaxation modulus.

J P Wittmer1, H Xu2, J Baschnagel1

  • 1Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.

Physical Review. E
|February 13, 2016
PubMed
Summary
This summary is machine-generated.

We present a new formula, G(t)=μ_{A}-h(t), for calculating the shear-stress relaxation modulus in elastic materials. This method simplifies computations by relating it to the mean-square displacement of shear stress over time.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Rheology

Background:

  • Determining the shear-stress relaxation modulus (G(t)) is crucial for understanding the mechanical behavior of elastic solids and fluids.
  • Existing computational methods may have limitations or pitfalls.

Purpose of the Study:

  • To propose a novel and simplified expression for the computational determination of G(t).
  • To offer an alternative approach for calculating the shear-stress relaxation modulus.

Main Methods:

  • Development of a simple-average expression: G(t) = μ_{A} - h(t).
  • Utilizing the initial shear modulus (μ_{A}) and the mean-square displacement of shear stress (h(t)).
  • Analysis of sampling time and ensemble effects.

Main Results:

  • The proposed expression G(t) = μ_{A} - h(t) provides a direct computational route to the shear-stress relaxation modulus.
  • Identified potential issues with alternative methods relying on shear-stress autocorrelation functions.

Conclusions:

  • The new relation offers a computationally efficient method for determining G(t) in isotropic elastic networks.
  • The approach is adaptable for calculating other general linear response functions.