Closure to “Discussion of ‘Variational Methods for Dispersion Relations and Elastic Properties of Composite Materials’” (1973, ASME J. Appl. Mech., 40, pp. 317–318)

1973 ◽  
Vol 40 (1) ◽  
pp. 318-318
Author(s):  
W. Kohn ◽  
J. A. Krumhansl ◽  
E. H. Lee
Keyword(s):  
Composite Materials ◽  
Variational Methods ◽  
Elastic Properties ◽  
Dispersion Relations

Variational Methods for Dispersion Relations and Elastic Properties of Composite Materials

1972 ◽  
Vol 39 (2) ◽  
pp. 327-336 ◽  
Author(s):  
W. Kohn ◽  
J. A. Krumhansl ◽  
E. H. Lee
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Elastic Waves ◽  
Variational Principles ◽  
Lattice Structure ◽  
Dispersion Relations ◽  
Bravais Lattice ◽  
Layered Composites ◽  
Crystal Lattices ◽  
Ritz Procedure

The propagation of harmonic elastic waves through composite media with a periodic structure is analyzed. Methods utilizing the Floquet or Bloch theory common in the study of the quantum mechanics of crystal lattices are applied. Variational principles in the form of integrals over a single cell of the composite are developed, and applied in some simple illustrative cases. This approach covers waves moving in any direction relative to the lattice structure, and applies to structures of the Bravais lattice groups which include, for example, parallel rods in a square or hexagonal pattern, and an arbitrary parallelepiped cell. More than one type of inclusion can be considered, and the elastic properties and density of the inclusion and matrix can vary with position, as long as they are periodic from cell to cell. The Rayleigh-Ritz procedure can be applied to the solution of the variational equations, which provides a means of calculating dispersion relations and elastic properties of specific composite materials. Detailed calculations carried out on layered composites confirm the effectiveness of the method.

scholarly journals Modeling of the electromagnetic and elastic properties of composite materials

2020 ◽  
Vol 934 ◽  
pp. 012016
Author(s):  
Yu I Dimitrienko ◽  
K M Zubarev ◽  
Yu V Yurin ◽  
V I Yakovlev
Keyword(s):  
Composite Materials ◽  
Elastic Properties

scholarly journals Multi-scale identification of the elastic properties variability for composite materials through a hybrid optimisation strategy

2019 ◽  
Vol 176 ◽  
pp. 107193 ◽  
Author(s):  
Lorenzo Cappelli ◽  
Georgios Balokas ◽  
Marco Montemurro ◽  
Frédéric Dau ◽  
Laurent Guillaumat
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Multi Scale

Elastic Properties of Artificially Layered Thin Films

1987 ◽  
Vol 103 ◽  
Author(s):  
Robert C. Cammarata
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Composite Materials ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Metallic Thin Films ◽  
Theoretical Understanding ◽  
Composition Modulation

ABSTRACTEnhancements in the elastic moduli by factors of two or more in compositionally modulated metallic thin films have been observed for a certain range of composition modulation wavelengths. The experimental and theoretical understanding of this phenomenon, known as the supermodulus effect, is reviewed. Also, the mechanical properties of other artificially layered and composite materials are discussed and compared with the behavior of metallic superlattice thin films.

Elastic Behaviors of Stitched Multi-Axial Warp Knit Fabric Composites

2006 ◽  
Vol 306-308 ◽  
pp. 817-822 ◽  
Author(s):  
Heoung Jae Chun ◽  
H.W. Kim ◽  
Joon Hyung Byun
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Structural Integrity ◽  
Experimental Results ◽  
Fiber Volume ◽  
Representative Volume ◽  
Fabric Composites ◽  
Out Of Plane ◽  
Stress States ◽  
Warp Knitted Fabric

The purposes of stitching multi-axial warp knitted fabric preform prior to the fabrication of the composite materials by resin-transfer molding technique are to improve the resistance to delamination and to increase the out-of-plane properties of the composite materials for structural integrity. The influence of the through-the-thickness stitching on the elastic properties and behaviors of the multi-axial warp knit fabric composites is studied. An analytical model based on the representative volume is proposed to predict the elastic properties of the stitched multi-axial warp knit fabric composite materials. The fiber volume ratios determined by geometric parameters set by the representative volume and elastic behaviors of the in-situ constituent materials are used for the predictions. The crucial step in the analysis is to correlate the averaged stress states in the constituents by adopting bridging matrix. The predicted results are compared with the experimental results. It is found that the predicted results are in reasonably good agreement with the experimental results.

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