Mechanical Behavior of Anisotropic Composite Materials as Micropolar Continua

Abstract

The macroscopic behavior of materials with anisotropic microstructure described as micropolar continua is investigated in the present work. Micropolar continua are characterized by a higher number of kinematical and dynamical descriptors than classical continua and related stress and strain measures, namely the micro-rotation gradient (curvature) and the relative rotation with their work conjugated counterparts, the micro-couple, and the skew-symmetric part of the stress, respectively. The presence of such enriched strain and stress fields can be detected especially when concentrated forces and/or geometric discontinuities are present. The effectiveness of the micropolar model to represent the mechanical behavior of materials made of particles of prominent size has been widely proved in the literature, in this paper we focus on the capability of this model to grossly capture the behavior of anisotropic solids under concentrated loads for which the relative strain, that is a peculiar strain measure of the micropolar model, can have a salient role. The effect of material anisotropy in the load diffusion has been investigated and highlighted with the aid of numerical parametric analyses, performed for two dimensional bodies with increasing degrees of anisotropy using a finite element approach specifically conceived for micropolar media with quadratic elements implemented within Comsol Multiphysics© framework. The present studied cases show that a significant diffusion and redistribution of the load is due to an increasing in the level of material anisotropy.

‘Explicit’ and ‘implicit’ non-local continuous descriptions for a plate with circular inclusion in tension

“…N is employed for interpolation of nodal in-plane displacements and consists of quadratic interpolation functions, while  N is employed for nodal out-of-plane micro-rotations, and includes linear type shape functions. As it was mentioned in Fantuzzi et al, [32], and Fantuzzi et al, [33], and clearly showed in the Fig. 1(a), all the nodes of the nine-node Lagrange element possess displacement-type DOFs, whereas micro-rotation DOFs are attached only to the four corner nodes:…”

“…Among 'implicit' non-local models, many papers showed the advantages of micropolar theory, which has been widely exploited for describing heterogeneous materials with microstructures (e.g. masonry-like structures, granular, blocked and layered materials, rock assemblages, reinforced composites, and so on [26][27][28][29][30][31][32][33]). The micropolar model was first developed by Cosserat brothers [17], and improved by many researchers over the years such as, Eringen [18], Nowacki [19], etc.…”

Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

“…For the sake of conciseness, boundary terms are not reported. For further details and reading, strong form equations can be found in [50,60,61].…”

“…In the present work, micropolar theory is considered which introduces the rotation of the material point, termed microrotation, to be distinguished with the macrorotation of the body (local rigid rotation). The effects of this local rotation have been widely investigated in [38,39,[48][49][50] for masonry-like materials.…”

Micromodels for the in-plane failure analysis of masonry walls: Limit Analysis, FEM and FEM/DEM approaches

“…regular) masonries, for which a suitably defined unit cell plays the role of RVE, but there exist also different homogenization techniques for both linear and nonlinear analyses of random microstructures, already applied or directly applicable to irregular masonry structures [21][22][23]. Other multiscale strategies have been proposed that exploit different homogenization techniques based on the so-called Cauchy rule, and its, generalizations [24] that allowed the derivation of both classical and generalized continua able to properly represent scale effects, that in masonry materials are prominent [25][26][27][28][29]. In this work the attention is mainly focused on the category of micromodels particularly focusing on Limit Analysis, which represents a very effective tool to estimate the collapse load and collapse mechanism for one-leaf masonry structures [30][31][32][33][34][35].…”