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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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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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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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Nonlinear Rheological Behavior of Polyacrylamide Solutions under Large-Amplitude Oscillatory Shear.

Rishav Agrawal1,2, William N Sharratt1, Robert J Poole1

  • 1School of Engineering, University of Liverpool, The Quadrangle, Liverpool L69 3GH, United Kingdom.

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|April 20, 2026
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This summary is machine-generated.

This study reveals how polymer concentration affects the nonlinear rheology of polyacrylamide solutions, showing a transition from viscous to elastic behavior with increasing concentration. Advanced rheology and imaging highlight microstructural changes and instabilities in concentrated solutions.

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Area of Science:

  • Polymer Physics
  • Rheology
  • Soft Matter Science

Background:

  • Understanding the relationship between polymer concentration, network structure, and nonlinear rheological response is crucial but challenging.
  • Polymer solutions exhibit complex flow behaviors that are highly dependent on molecular weight and concentration.
  • Previous studies have explored linear viscoelasticity, but a comprehensive understanding of nonlinear dynamics across various concentrations is needed.

Purpose of the Study:

  • To investigate the nonlinear rheological behavior of aqueous polyacrylamide (PAAm) solutions across a wide concentration range.
  • To correlate bulk rheological measurements with microstructural observations using rheomicroscopy.
  • To elucidate the influence of normalized polymer concentration (c_w/c_e) on flow properties and structural evolution.

Main Methods:

  • Steady shear, small-amplitude oscillatory shear (SAOS), and large-amplitude oscillatory shear (LAOS) measurements were performed on PAAm solutions.
  • Nonlinear analyses included Fourier transform (FT) rheology, intrinsic nonlinearity (³Q₀), energy dissipation ratio (ϕ), and sequence of physical processes (SPP).
  • Rheomicroscopy was employed to visualize flow-induced microstructural changes.

Main Results:

  • A transition from viscous-dominated to elastic-dominated behavior was observed with increasing PAAm concentration, alongside enhanced shear thinning.
  • All samples exhibited a concentration-independent plastic-like dissipation plateau (ϕ ≈ 0.85) beyond the moduli crossover.
  • Rheomicroscopy revealed homogeneous flow at low concentrations, while highly entangled solutions showed structural disruption, banding, and fracture.

Conclusions:

  • Bulk rheological measurements combined with advanced LAOS tools and imaging provide a comprehensive understanding of polymer solution nonlinear rheology.
  • Localized microstructural instabilities can occur in concentrated polymer solutions, which may not be apparent from bulk measurements alone.
  • The findings offer insights for designing and formulating soft materials for applications in printing, flow processing, and biomedical gels.