Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

Abstract

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials.

Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation

“…For homogenization of discrete structures possessing strong anisotropy as orthotropic textures, a full micropolar model is needed (for more discussion on the topic see [ 31 , 54 , 75 ]). In this case, the non-symmetries (skew-symmetries) of the strain and stress tensors play a relevant role.…”

“…Classical theory of elasticity (Cauchy of Grade 1), on the other hand, fails to accurately homogenize the discrete nature into a continuum medium for a structure having comparable internal and external lengths [ 22 , 23 ]. This drawback can be overcome by means of non-classical (non-local) continuum theories which simultaneously utilize field description at coarse level, and preserve the memory of material’s underlying structure at fine level through internal scale parameters [ 24 , 25 , 26 , 27 , 28 , 29 ] that can refer to different physical features ranging from nano order (e.g., distance between atoms in a nanoscopic structure) up to meso/macro orders (size of particle/grain in a composite medium) as demonstrated in different studies [ 30 , 31 , 32 , 33 ].…”

New insights on homogenization for hexagonal-shaped composites as Cosserat continua

“…These models, which present additional degrees of freedom, can be classified as 'implicit/ weak' non-local models [11,28,29]. The literature shows that they have been satisfactorily applied to various composites [10,13,[30][31][32][33][34][35][36][37][38][39][40]. Different works moreover, [41][42][43][44][45][46] proposed multiscale computational homogenization with 'explicit' non-local or higher order deformation gradient theories in composite materials [47][48][49][50][51].…”

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

“…In general, different nonlocal theoretical frameworks can be developed. Examples of nonlocal approaches that should be mentioned for completeness purposes are the strain and stress gradient theories [ 58 , 59 , 60 ], the modified couple stress theory [ 61 , 62 , 63 , 64 ], and the ones based on micropolar formulations [ 65 , 66 , 67 ]. A comprehensive literature review concerning nonlocal elasticity can be found in the paper by Zhao et al [ 68 ] for completeness purposes.…”