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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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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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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Analysis of a viscoelastic phase separation model.

Aaron Brunk1, Burkhard Dünweg2,3, Herbert Egger4

  • 1Institute of Mathematics, Johannes Gutenberg University Mainz, Staudingerweg 9, 55128 Mainz, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 2, 2021
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A new viscoelastic phase separation model ensures thermodynamic consistency. Numerical simulations align well with physical experiments and mesoscopic models, validating its effectiveness.

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dynamic structure factorrelative energyviscoelastic phase separationweak-strong uniqueness

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Area of Science:

  • Physics
  • Materials Science
  • Chemical Engineering

Background:

  • Phase separation is crucial in materials science and fluid dynamics.
  • Existing models may not fully capture viscoelastic effects during phase separation.
  • Thermodynamic consistency is essential for accurate modeling.

Purpose of the Study:

  • To propose a novel model for viscoelastic phase separation.
  • To ensure the model's consistency with the second law of thermodynamics.
  • To analyze the model's mathematical properties and validate its performance.

Main Methods:

  • Systematic derivation from a conservative two-fluid model.
  • Inclusion of phenomenological viscoelastic terms for dissipative effects.
  • Mathematical analysis of well-posedness (existence, weak-strong uniqueness, stability) using relative energy estimates.
  • Numerical simulations to compare with experimental and mesoscopic data.

Main Results:

  • A new, thermodynamically consistent viscoelastic phase separation model.
  • Proof of well-posedness in two space dimensions.
  • Numerical simulations show good agreement with physical experiments.
  • Qualitative agreement observed with mesoscopic simulations.

Conclusions:

  • The proposed model accurately describes viscoelastic phase separation.
  • The model's mathematical rigor is established.
  • It offers a reliable tool for simulating and understanding phase separation phenomena in viscoelastic fluids.