On Determination of Wave Velocities through the Eigenvalues of Material Objects

The statement of the eigenvalue problem for a tensor–block matrix of any order and of anyeven rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrixare invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities ofwave propagation of some medias through the eigenvalues of the material objects. In particular, weconsider the classical and micropolar materials with the different anisotropy symbols and for themwe determine the expressions for the velocities of wave propagation through the eigenvalues of thematerial objects.

Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.