Reciprocity, passivity and causality in Willis materials

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.