Determination of the effective elastic moduli of inhomogeneous materials

1986 ◽  
Vol 26 (5) ◽  
pp. 739-746 ◽  
Author(s):  
V. V. Novikov
Keyword(s):  
Elastic Moduli ◽  
Effective Elastic Moduli ◽  
Inhomogeneous Materials

Viscoelastic Behavior of Heterogeneous Media

1965 ◽  
Vol 32 (3) ◽  
pp. 630-636 ◽  
Author(s):  
Zvi Hashin
Keyword(s):  
Linear Viscoelasticity ◽  
Elastic Moduli ◽  
Heterogeneous Media ◽  
Correspondence Principle ◽  
Viscoelastic Behavior ◽  
Effective Elastic Moduli ◽  
Macroscopic Behavior ◽  
Linear Viscoelastic

The macroscopic viscoelastic behavior of linear viscoelastic heterogeneous media is defined in terms of effective relaxation moduli and creep compliances. It is shown that these effective relaxation and creep functions are related to effective elastic moduli of elastic heterogeneous media by the correspondence principle of the theory of linear viscoelasticity. This analogy is applied to the determination of macroscopic behavior of some special kinds of viscoelastic heterogeneous media, in dilatation and shear.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

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