Some Novel Numerical Applications of Cosserat Continua

Abstract

Cosserat continua demonstrated to have peculiar mechanical properties, with respect to classic Cauchy continua, because they are able to more accurately describe heterogeneous materials, as particle composites and masonry-like material, taking into account size effects. Many studies have been devoted to their numerical implementation. In this paper, some reference benchmarks, referred to an isotropic heterogeneous sample, are shown by comparing the solutions provided by strong and weak formulations. The strong formulation finite element method (SFEM), implemented in MATLAB®, is compared to the finite element method (FEM), given by COMSOL® Multiphysics, and the advantages of the two approaches are highlighted and discussed.

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

“…The above-mentioned results are in accordance with the existing literature [32,48]. In the following subsections, the comments about each model with different scale ratios will be detailed with focusing on the conducted non-local theory.…”

“…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.…”

“…From a different point of view, Dong, Wang and Rubin [47], treated the interface as a finite thickness Cosserat shell/membrane medium and compared their results with explicit solutions. More recently, Atroshchenko et al [48], modelled the matrix-inclusion structure as Cosserat media considering various material properties and showed the effect of imperfect and perfect interfaces via employing boundary element method (BEM), while Fantuzzi et al, [32] investigated the classical matrix-inclusion problem considering micropolar theory using both strong and standard forms of the finite element method.…”

Mechanical Behavior of Anisotropic Composite Materials as Micropolar Continua

“…The same coarse-graining procedure is used which can be shown to be actually dependent both on the brick size, shape and texture of the original (fine) lattice model. The simulations have been carried out for a panel under localized loads, using a standard finite element approach based on a micropolar finite element implementation, with quadratic and linear interpolation functions for the displacement and rotation fields, developed in Fantuzzi et al (2018) following the approach in Providas and Kattis (2002) and implemented within Comsol Multiphysics© framework (Comsol, 2017). The results are presented in terms of contour plots of displacement, stress and relative rotation, the significant strain measure related to the non-symmetrical part of the strain.…”