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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...
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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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Elasticity from the force network ensemble in granular media.

Srdjan Ostojic1, Debabrata Panja

  • 1Institute for Theoretical Physics, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.

Physical Review Letters
|December 13, 2006
PubMed
Summary

Force transmission in granular materials shows nonlinear behavior near overloads and elastic behavior at larger scales. Friction influences this transition, impacting how forces propagate through granular systems.

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Area of Science:

  • Physics
  • Materials Science
  • Engineering Mechanics

Background:

  • Granular materials exhibit complex force transmission behaviors.
  • Understanding force networks is crucial for predicting material response.
  • Previous studies have explored various aspects of granular mechanics.

Purpose of the Study:

  • To investigate force transmission in static granular materials.
  • To analyze the mechanical response of different granular packing configurations.
  • To explore the influence of friction and overload on force propagation.

Main Methods:

  • Numerical evaluation of mechanical response.
  • Utilizing the force network ensemble framework.
  • Simulating hexagonal packings of frictionless grains.
  • Simulating rectangular packings of frictional grains.

Main Results:

  • Force transmission is nonlinear with two peaks near overload application.
  • At larger length scales, the response is linear and elasticlike.
  • A crossover depth exists between nonlinear and linear behaviors.
  • This depth increases with overload magnitude and decreases with friction.

Conclusions:

  • Granular materials exhibit scale-dependent mechanical responses to force transmission.
  • Friction plays a significant role in modulating the transition between nonlinear and elastic behaviors.
  • The force network ensemble provides a framework for understanding these complex phenomena.