GREEN’S FUNCTION AND EFFECTIVE ELASTIC STIFFNESS TENSOR FOR ARBITRARY AGGREGATES OF CUBIC CRYSTALS

A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic crystal and ?ve texture coe?cients, accounts for the e?ects of the orientation distribution function (ODF) up to terms linear in the tex- ture coe?cients. Thus it is expected that our formula would be applicable to arbitrary aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. Three examples are presented to compare predictions from our formula with those from Nishioka and Lothe’s formula and Synge’s contour integral through numerical integration. As an applica- tion of Green’s function, we brie?y describe the procedure of deriving the e?ective elastic sti?ness tensor for an orthorhombic aggregate of cubic crystallites. The comparison of the computational results given by the ?nite element method and our e?ective elastic sti?ness tensor is made by an example.

A RATE TYPE METHOD FOR LARGE DEFORMATION PROBLEMS OF NONLINEAR ELASTICITY

In this paper. we obtain the rate-tvpe constitutive expressions of the nonlinearisotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rgterespectively,Through analysing the simple shear deformation for Mooney-Rivlin material.three kinds of rate-type constitutive equations are verified to be equivalent to the original equation.Rate-type variational prineiples are also presented, and the Ritzmethod is used to obtain the numerical solution of a reetangular rubber membraneunder uniaxial streteh.

A BOUNDARY INTEGRAL METHOD FOR COMPUTING ELASTIC MOMENT TENSORS FOR ELLIPSES AND ELLIPSOIDS

The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites. In this paper, we compute the elastic moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the elastic moment tensors and the single layer potential.

Retrieval of Elastic Green’s Tensor near a Cylindrical Inhomogeneity from Vector Correlations

Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and S waves. Insuch diffusive regime the P to S energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the Green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic Greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand S waves uniform but such that the energy ratio ES/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact Green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.