Effective Properties of Discrete Random Composites Wherein the Host and Inclusion Phases Obey Different Constitutive Relations

1991 ◽  
Vol 253 ◽  
Author(s):  
V V. Varadan ◽  
R. T. Apparao ◽  
V. K. Varadan
Keyword(s):  
Wave Propagation ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Effective Medium ◽  
Acoustic Wave Propagation ◽  
Piezoelectric Composites ◽  
Inclusion Phase ◽  
Random Composites ◽  
Polarization Study ◽  
Effective Medium Theories

ABSTRACTIn studying the effective medium theories, polarization is hardly given a consideration in deciding the effective properties of a composite where the host and inclusion phases follow different constitutive equations. A significant conclusion of this paper is that eventhough the composite has discrete inclusions, with the inclusion phase obeying different constitutive properties than the host, the effective medium shows a preference for the inclusion behavior rather than the host which is continuous. As an example, results on polarization study are detailed for the specific case of chiral composites. Application of similar principles is presently explored in more complex problems like the elastic wave propagation through piezoelectric composites and the acoustic wave propagation through sediments.

scholarly journals Homogenization of piezoelectric planar Willis materials

2021 ◽  
Author(s):  
Alan Muhafra ◽  
Majd Kosta ◽  
Daniel Torrent Martí ◽  
René Pernas Salomón ◽  
Gal Shmuel
Keyword(s):  
Heterogeneous Media ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Piezoelectric Composites ◽  
Long Wavelength ◽  
Equivalent Models ◽  
Homogenized Model ◽  
Arbitrary Frequency ◽  
Momentum Coupling ◽  
Physical Laws

Homogenization theories provide models that simplify the constitutive relations of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain-momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green’s function method predicted analogous electro-momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source- driven approach that delivers a unique set of effective properties for arbitrary frequency-wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws.

Effective Dynamic Constitutive Relations for 3-D Periodic Elastic Composites

2013 ◽  
Vol 1508 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Constitutive Relation ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Bloch Wave ◽  
Ensemble Averaging ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Elastic Composites

ABSTRACTCentral to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. Recent advances in the theory of dynamic homogenization have established the coupled form of the constitutive relation (Willis constitutive relation). This coupled form of the constitutive relation naturally emerges from ensemble averaging of the dynamic fields and automatically satisfies the dispersion relation in the case of periodic composites. Its importance is also notable due to its invariance under transformational acoustics. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

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