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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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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...
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The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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The relationship between viscoelasticity and elasticity.

J H Snoeijer1, A Pandey1, M A Herrada2

  • 1Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 28, 2020
PubMed
Summary
This summary is machine-generated.

This review explores the connection between viscoelasticity and elasticity in soft materials. Understanding this relationship helps predict material behavior, like the stability of elastic threads.

Keywords:
capillarityelasticitygelsinstabilityviscoelasticity

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Area of Science:

  • Soft Matter Physics
  • Continuum Mechanics
  • Polymer Science

Background:

  • Soft materials exhibit complex behaviors between fluids and solids.
  • Continuum descriptions use either solid (Lagrangian) or fluid (Eulerian) mechanics.
  • Viscoelastic liquids, like polymer solutions, have a characteristic relaxation time (λ).

Purpose of the Study:

  • To connect theories of viscoelasticity and elasticity for soft matter.
  • To analyze polymer models in the limit of infinite relaxation time (λ→∞).
  • To understand the role of elastic limits in material behavior.

Main Methods:

  • Reviewing principles of viscoelastic liquid models.
  • Examining kinematics and elastic response under large deformations.
  • Analyzing polymer models' correspondence to nonlinear elastic solids.
  • Splitting elastic stress work into reversible and dissipative components.
  • Establishing the conservation law for total energy.

Main Results:

  • Identified polymer models that behave as nonlinear elastic solids as λ→∞.
  • Differentiated reversible and dissipative work contributions from elastic stresses.
  • Established a general energy conservation law.
  • Demonstrated how elastic limits influence capillary instability in elastic threads.

Conclusions:

  • The elastic correspondence provides a valuable framework for soft matter problems.
  • The presence or absence of an elastic limit is crucial for phenomena like capillary instability.
  • Connecting viscoelasticity and elasticity offers insights into soft material mechanics.