---

In this paper, the multiple scattering of obliquely incident elastic waves from fibers encased in a solid viscoelastic medium is studied. This problem has applications in ultrasonic nondestructive testing of composite materials. The fibers could be either isotropic or transversely isotropic. Based on the existing theory of elastic wave scattering from a single fiber, a mathematical model for multiple scattering of elastic waves from a number of parallel fibers embedded in a viscoelastic matrix is derived. This model incorporates all three kinds of longitudinal, horizontally polarized shear, and vertically polarized shear waves. The incident wave angle is arbitrarily chosen and the receiver can be considered to be at any desired location in space. The model is capable of handling any order of scattering from any number of cylinders. To validate the numerical results, a number of experiments were conducted on steel cylinders embedded in a polymeric block. With the aid of an ultrasonic probe, the scattered field was measured and analyzed. Comparing the analytical and experimental results, good agreement was observed between resonance frequencies observed in experiments and mathematical model

---

In this paper, behavior of functionally graded rubbers with large deformation has been modeled under different loading conditions. Rubbers have been assumed incompressible hyperelastic material. In the first section of this paper, behavior of isotropic FG rubber has been investigated in uniaxial extension, equibiaxial extension and pure shear. In the second section, behavior of isotropic FG rubber is investigated in mechanical and thermal loads, simultaneously. For this purpose, multiplicative decomposition of deformation gradient tensor has been used. At last, behavior of transversely isotropic FG rubber has been investigated in uniaxial extension, equibiaxial extension and pure shear. Material properties vary continuously in different specific direction in FG hyperelastic materials. For modeling nonlinear behavior of hyperelastic materials, strain energy functions are used. Strain energy functions are function of invariants of left Cauchy-Green stretch tensor. Modification in strain energy functions required in order to use them for FG rubbers. For this purpose, material constants of strain energy functions have been assumed to vary exponentially in the axial direction of bar. Moreover, stretches in different points of the bar are considered to be function of material properties variation in the length direction. Analytical solution have been compared with experimental data and good agreement has been found between them, therefore proposed constitutive law has been modeled material behavior with a proper approximation.

---

Accurate determination of the electro-elastic fields of quantum nanostructures within piezoelectric media is an important issue for realizing the electro-mechanical behavior of these nanostructures. In this paper, the governing partial differential equations corresponding to piezoelectric media containing quantum nanostructures are presented and subsequently, generalized analytical solutions based on Fourier series technique are developed for determination of the coupled electro-elastic fields in transversely isotropic piezoelectric barrier due to periodically distributed quantum nanostructures. The electro-elastic couplings of the piezoelectric barrier as well as the interactions between the quantum nanostructures are exhibited within the framework of the presented analytical solution. It is observed that no electric field and no electric potential will be induced anywhere in the medium for periodic distribution of quantum wires. The presented analytical solution is capable of treating different shapes and geometries of quantum wires/quantum dots. The electro-elastic fields of various shapes of sections of quantum wires and different geometries of quantum dots are studied and the effects of the geometry of periodically distributed quantum nanostructures are demonstrated. The results show that geometry of quantum nanostructures may highly affect the induced electro-elastic fields and therefore, accurate determination of the geometry of quantum nanostructures as well as the induced electro-elastic fields would be essential for employment of these nanostructures in different fields of research and technology.

---

Nowadays fracture behavior composites play an important role in geomechanics engineering. Also, it is common knowledge that all existing structural materials contain different inter- and intra-component defect (cracks, delaminations, etc.). On the other hand, analytical techniques can provide a better physical interpretation of problems. In this paper, by using an analytical approach, effects of the fracture modes (opening, shearing and tearing) on a penny-shaped crack in a layer of transversely isotropic solid has been studied. The layer surfaces are fixed from displacement and the system is loaded symmetrically in each mode. In each mode, by substituting the boundary conditions into the governing equations of the medium, the problem reduced to dual integral equations. With the aid some mathematical methods, the dual integral equations are converted to a Fredholm integral equation which is amenable to numerical solution. These Fredholm integral equations are the functions of the thickness of the layer, the radius of crack and the properties of the layer. To evaluate the effect of anisotropic materials on the stress intensity factors(SIFs), several synthetic types of isotropic and transversely isotropic materials are selected. By employing a numerical method the opening, shearing and tearing SIFs for different ratios of layer thickness are obtained. The results for the opening SIF show that by increasing the  the SIF decreases substasinaly. On the other hand, an increase in   leads to increments in opening SIF. Also, the results demonstrate that the variation in  has a negligible effect on the opening SIF. Moreover, an increasing in  leads reductions in SIF. For the shearing SIF,  has little effect on the results although by decreasing the  the shearing SIF increases. Unlike the , the modulus of the young in the plane ( ) of the isotropy has substantial effect on the shearing SIF.  An increase in  leads increments in the shearing SIF. Also, by increasing the  the SIF increases marginally. In the mode III, the tearing SIF is only the functions of  (the shear modulus for the plane normal to the plane of isotropy) and . The results show that by reduction in  the tearing SIF increases and by increasing  the tearing SIF increases. An important point that can be inferred from the results is that by increasing the ratio of layer thickness to the radius of the penny-shaped crack all of the three SIFs increase, this increase for the lower thicknesses is much more in comparison to the greater thicknesses. Additionally, when the layer thickness gets higher, the stress intensity factors for all the materials tend to a constant coefficient. This means that when the layer thickness gets greater and tends to infinity, the SIFs become independent of the material of the layer