ABSTRACT
The mechanical response of materials such as fiber and particle composites, rocks, concrete, and granular materials, can be profoundly influenced by the existence of voids. The aim of the present work is to study the dynamic behavior of hexagonal microstructured composites with voids by using a discrete model and homogenizing materials, such as micropolar and classical Cauchy continua. Three kinds of hexagonal microstructures, named regular, hourglass, and skew, are considered with different length scales. The analysis of free vibration of a panel described as a discrete system, as a classical and as a micropolar continuum, and the comparison of results in terms of natural frequencies and modes show the advantage of the micropolar continuum in describing dynamic characteristics of orthotropic composites (i.e., regular and hourglass microstructures) with respect to the Cauchy continuum, which gives a higher error in frequency evaluations for all three hexagonal microstructured materials. Moreover, the micropolar model also satisfactorily predicts the behavior of skewed microstructured composites. Another advantage shown here by the micropolar continuum is that, like the discrete model, this continuum is able to present the scale effect of microstructures, while maintaining all the advantages of the field description. The effect of void size is also investigated and the results show that the first six frequencies of the current problem decrease by increasing in void size.
ABSTRACT
It has been demonstrated that materials with microstructure, such as particle composites, show a peculiar mechanical behavior when discontinuities and heterogeneities are present. The use of non-local theories to solve this challenge, while preserving memory of the microstructure, particularly of internal length, is a challenging option. In the present work, composite materials made of rectangular rigid blocks and elastic interfaces are studied using a Cosserat formulation. Such materials are subjected to dynamic shear loads. For anisotropic media, the relative rotation between the local rigid rotation and the microrotation, which corresponds to the skewsymmetric part of strain, is crucial. The benefits of micropolar modeling are demonstrated, particularly for two orthotropic textures of different sizes.
ABSTRACT
This work aims to present the dynamic character of microstructured materials made of hexagonal-shape particles interacting with elastic interfaces. Several hexagonal shapes are analyzed to underline the different constitutive behavior of each texture. The mechanical behavior at the macro scale is analyzed by considering a discrete model assumed as a benchmark of the problem and it is compared to a homogenized micropolar model as well as a classical one. The advantages of the micropolar description with respect to the classical one are highlighted when internal lengths and anisotropies of microstuctured materials are taken into consideration. Comparisons are presented in terms of natural frequencies and modes of vibrations.
