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Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
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Effective Governing Equations for Viscoelastic Composites.

Laura Miller1, Ariel Ramírez-Torres1, Reinaldo Rodríguez-Ramos2,3

  • 1School of Mathematics & Statistics, University of Glasgow, Glasgow G12 8QQ, UK.

Materials (Basel, Switzerland)
|July 29, 2023
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Summary
This summary is machine-generated.

This study presents a new homogenized model for linear viscoelastic composites with multiple elastic phases and a fluid. The model accurately captures microscale fluid-structure interactions for heterogeneous materials.

Keywords:
fluid–structure interactionhomogenizationviscoelasticity

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Area of Science:

  • Multiphase flow
  • Composite materials science
  • Continuum mechanics

Background:

  • Understanding the macroscopic behavior of complex composites with fluid interactions is crucial.
  • Existing models often simplify microscale phenomena, limiting their applicability to highly heterogeneous systems.

Purpose of the Study:

  • To derive a new homogenized model for linear viscoelastic composites with multiple elastic phases and an incompressible Newtonian fluid.
  • To upscale microscale fluid-structure interactions (FSI) using asymptotic homogenization.
  • To provide a model applicable to systems with small distances between phases.

Main Methods:

  • Asymptotic (periodic) homogenization method (AHM) to decouple spatial scales.
  • Upscaling of the fluid-structure interaction problem at the microscale.
  • Derivation of a Kelvin-Voigt viscoelastic model from partial differential equations.

Main Results:

  • A novel homogenized model for linear viscoelastic composites with multiple elastic phases and fluid.
  • The model's coefficients are determined by solving a single local FSI problem.
  • The model reduces to the Burridge and Keller (1981) case for a single elastic phase.

Conclusions:

  • The derived model accurately represents the overall behavior of complex composites.
  • This model is suitable for highly heterogeneous materials found in biological and geological contexts.
  • The approach provides a robust framework for analyzing microscale fluid-structure interactions in composites.