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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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Replacement relations for a viscoelastic material containing multiple inhomogeneities.

E Vilchevskaya1,2, V Levin3, S Seyedkavoosi4

  • 1Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Bolshoy Pr., 61, V.O., St.Petersburg 199178, Russia.

International Journal of Engineering Science
|March 15, 2021
PubMed
Summary
This summary is machine-generated.

This study extends classical replacement relations to viscoelastic materials, enabling predictions of fluid-filled porous material properties. The findings are crucial for understanding complex material behaviors in geophysics and engineering.

Keywords:
Gassmann equationReplacement relationsfraction-exponential operatorproperty contribution tensorsviscoelasticity

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Area of Science:

  • Geophysics
  • Materials Science
  • Continuum Mechanics

Background:

  • Classical replacement relations link elastic properties of porous materials to their infill.
  • Existing models primarily address purely elastic materials.

Purpose of the Study:

  • To derive viscoelastic replacement relations for porous materials with viscoelastic infill.
  • To extend the applicability of Gassmann-type equations to more complex material behaviors.

Main Methods:

  • Utilized compliance/stiffness contribution tensors for anisotropic materials.
  • Applied the elastic-viscoelastic correspondence principle and Laplace transform.
  • Employed Scott-Blair-Rabotnov fractional-exponential operators for viscoelastic properties.

Main Results:

  • Derived generalized replacement relations for viscoelastic porous materials.
  • Demonstrated that the derived relations reduce to the classical Gassmann equation for isotropic elastic materials.
  • Obtained explicit analytical expressions for viscoelastic properties.

Conclusions:

  • The developed framework accurately describes the effective viscoelastic properties of fluid- or solid-filled porous materials.
  • This work provides a powerful tool for analyzing wave propagation and material response in complex heterogeneous media.
  • The findings have implications for seismic exploration and material characterization.