Higher-order moduli of elasticity for an isotropic elastic body

Sekoyan, S. S.

doi:10.1007/bf00882127

Cited by 1 publication

(1 citation statement)

References 10 publications

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“…When considering nonlinear elastic material, Equation (86) can be generalized by means of higher order elastic moduli taking into account the deviation from the stress-strain proportionality [87,88]

\begin{matrix} true \\ right T_{i j} = C_{i j k h} ϵ_{k h} + \frac{1}{2} L_{i j k h n m} ϵ_{k h} ϵ_{n m} + . . . = ([] {scriptC}_{i j k h} + \frac{1}{2} {scriptL}_{i j k h n m} ϵ_{n m} + . . .) ϵ_{k h} = {scriptC}_{i j k h}^{N L} ((), \overset{false^}{ϵ}) ϵ_{k h} \end{matrix}

where

{\overset{C}{true}}^{N L} (\overset{ϵ}{true})

is the nonlinear (strain dependent) stiffness tensor. It can be noticed that the tensor

\overset{C}{true}

has 21 independent entries, while the second order tensor

\overset{L}{true}

has 56 independent components.…”

Section: Nonlinear Elastic Constitutive Equationsmentioning

confidence: 99%

Dielectric and Elastic Characterization of Nonlinear Heterogeneous Materials

Giordano

2009

Materials

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This review paper deals with the dielectric and elastic characterization of composite materials constituted by dispersions of nonlinear inclusions embedded in a linear matrix. The dielectric theory deals with pseudo-oriented particles shaped as ellipsoids of revolution: it means that we are dealing with mixtures of inclusions of arbitrary aspect ratio and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. Each ellipsoidal inclusion is made of an isotropic dielectric material described by means of the so-called Kerr nonlinear relation. On the other hand, the nonlinear elastic characterization takes into consideration a dispersion of nonlinear (spherical or cylindrical) inhomogeneities. Both phases are considered isotropic (actually it means polycrystalline or amorphous solids). Under the simplifying hypotheses of small deformation for the material body and of small volume fraction of the embedded phase, we describe a theory for obtaining the linear and nonlinear elastic properties (bulk and shear moduli and Landau coefficients) of the overall material.

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