Non-linear waves in heterogeneous elastic rods via homogenization

Numerical Homogenization of Heterogeneous Anisotropic Linear Elastic Materials

Abstract. The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of trabecular bone tissue. In our previous work [1], the orthotropic case was considered. The homogenized anisotropic tensor is transformed according to the principle directions of anisotropy (PDA). This provides opp...

Homogenization methods for anisotropic linear elastic polycrystals

The elastic properties of uniform polycrystalline materials without defects depend on both the constitutive properties of the constituents and the microstructural characteristics like the distribution of grain orientations and grain shapes. For an overview concerning the homogenization of elastic properties see, e.g., [1]. The elementary bounds by Voigt and Reuss take into account only the volu...

Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization

Wave propagation in periodic elastic composites whose phases may have not only highly contrasting but possibly also (in particular) highly anisotropic stiffnesses and moderately contrasting densities is considered. A possibly inter-connected (i.e. not necessarily isolated) ‘‘inclusion” phase is assumed generally much softer than that in the connected matrix, although some components of its stif...

A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium

Non-Linear Analysis of Asymmetrical Eccentrically Stiffened FGM Cylindrical Shells with Non-Linear Elastic Foundation

In this paper, semi-analytical method for asymmetrical eccentrically stiffened FGM cylindrical shells under external pressure and surrounded by a linear and non-linear elastic foundation is presented. The proposed linear model is based on two parameter elastic foundation Winkler and Pasternak. According to the von Karman nonlinear equations and the classical plate theory of shells, strain-displ...