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Reciprocity, passivity and causality in Willis materials.

Michael B Muhlestein1, Caleb F Sieck2, Andrea Alù3

  • 1Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78701, USA; Applied Research Laboratories, The University of Texas at Austin, 10000 Burnet Rd, Austin, TX 78758, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|November 16, 2016
PubMed
Summary
This summary is machine-generated.

This study generalizes restrictions for Willis materials, which couple stress-strain and momentum-velocity relations. New formulations offer insights into subwavelength behavior and time-domain analysis for these advanced elastic materials.

Keywords:
Willis materialcausalityelastic metamaterialpassivityreciprocity

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Area of Science:

  • Physics
  • Materials Science
  • Continuum Mechanics

Background:

  • Willis materials, first proposed by Willis (1981), describe elastic materials with coupled stress-strain and momentum-velocity constitutive relations.
  • This coupling represents a generalization of standard elastodynamic theory, necessitating a re-evaluation of material property restrictions.

Purpose of the Study:

  • To derive generalized restrictions on material properties for Willis materials under assumptions of reciprocity, passivity, and causality.
  • To explore an alternative formulation of the standard Willis equations based on causality and low-order dispersion.
  • To investigate the subwavelength physical behavior and time-domain analysis of Willis materials.

Main Methods:

  • Derivation of generalized restrictions on material properties for reciprocal, passive, and causal Willis materials.
  • Formulation of an alternative Willis equation set considering causality and dispersion.
  • Specialization of results to the acoustic limit.

Main Results:

  • Established generalized restrictions for physically admissible Willis material properties.
  • Developed an alternative formulation of Willis equations offering improved insight into subwavelength physics.
  • Demonstrated the amenability of the alternative formulation to time-domain analyses.

Conclusions:

  • The generalized restrictions provide a more comprehensive understanding of Willis material behavior.
  • The alternative formulation enhances the physical interpretation of subwavelength phenomena.
  • The study advances the analysis of Willis materials, particularly in the acoustic regime.