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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
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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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Normal stresses in elastic networks.

Adrian R Cioroianu1, Cornelis Storm1

  • 1Department of Applied Physics and Institute for Complex Molecular Systems, Eindhoven University of Technology, P. O. Box 513, NL-5600 MB Eindhoven, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
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Summary
This summary is machine-generated.

Geometric nonlinearities in filamentous networks generically produce negative normal stresses, even with linear springs. This study explores how elastic nonlinearities and other factors modify this behavior in polymer networks.

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Area of Science:

  • Polymer physics
  • Soft matter physics
  • Materials science

Background:

  • Polymeric materials under shear can exhibit normal stresses, perpendicular to the applied shear.
  • These normal stresses are intrinsically nonlinear, appearing at the second order of shear strain (O(γ(2))).
  • While often positive (outward), negative normal stresses (inward) are observed in biopolymer networks like fibrin and actin gels, attributed to fiber elasticity.

Purpose of the Study:

  • To investigate the origin of negative normal stresses in filamentous networks.
  • To demonstrate that geometric nonlinearities, not solely elastic ones, can cause negative normal stresses.
  • To analyze the impact of elastic nonlinearities, nonaffine deformations, and filament persistence on this phenomenon.

Main Methods:

  • Analytical derivation of model nonlinear network behavior.
  • Expansion of theoretical models to the required nonlinear order.
  • Numerical simulations to complement analytical findings.

Main Results:

  • Geometric nonlinearities in filamentous networks generically lead to negative normal stresses.
  • This effect occurs even in networks composed of linear, Hookean springs.
  • The study quantifies how elastic nonlinearities, nonaffine deformations, and cross-linker-induced persistence influence normal stress behavior.

Conclusions:

  • Negative normal stresses in filamentous networks can arise from geometric effects, independent of material's elastic nonlinearity.
  • The findings provide a fundamental explanation for anomalous negative normal stresses observed in biopolymer networks.
  • Further investigation into combined geometric and elastic nonlinearities offers deeper insights into polymer network mechanics.