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

Abstract

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.

Mechanical Behavior of Anisotropic Composite Materials as Micropolar Continua

“…The role of scale effects in orthotropic media under the action of a load applied on portions of variable size of the boundary of the body and the consequences in terms of strain and stress diffusion have been highlighted by the parametric analyses performed in the recent work (Leonetti et al, 2019). The present work, does not accounts for size effects but focuses on the response of anisotropic micropolar media, under localized loads, in the presence of an increasing degree of anisotropy.…”

“…The two-dimensional problem of micropolar continua is solved through the finite element implementation proposed in Leonetti et al (2019), where displacement/rotation components are ordered in the vectors u = u 1 u 2 T , φ = [φ], and the stress and strain components in the vectors σ = σ 11 σ 22 σ 12 σ 21 T , The weak form of the present problem has to be formulated in order to carry out the finite element implementation, and, considering a domain with boundary Ŵ N , writes:…”

“…Finite element approximation though interpolation functions N u and N φ is given by u = N uũ , φ = N φφ , where the over tilde vectors indicate the kinematic parameters correspondent to in-plane displacements and rotations at the nodes. Quadratic interpolation functions for the displacements and linear ones for the rotations have been assumed, as it was introduced in Leonetti et al (2019). Thus, displacements are modeled with nine nodes, whereas micro-rotation are related to the four corner nodes.…”

“…In a recent work (Leonetti et al, 2019), by adopting the coarse-graining procedure presented in Masiani and Trovalusci (1996); Trovalusci and Masiani (1999), the behavior of orthotropic brick/block masonry panels under compressive loads at the top, described as equivalent micropolar continua, has been investigated by varying the brick size and the load footprint, showing the capability of the micropolar model to distribute the load depending on the brick size. In the present work, the effect of the degree of anisotropy of the (coarse) continuum micropolar model on the strain/stress diffusion is studied.…”

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].…”