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

Abstract

Increasing application of composite structures in engineering field inherently speed up the studies focusing on the investigation of non-homogeneous bodies. Due to their capability on capturing the size effects, and offering solutions independent of spatial discretization, enriched non-classical continuum theories are often more preferable with respect to the classical ones. In the present study, the sample problem of a plate with a circular inclusion subjected to a uniform tensile stress is investigated in terms of both 'implicit'/'weak' and 'explicit'/'strong' non-local descriptions: Cosserat (micropolar) and Eringen theories, by employing the finite element method. The material parameters of 'implicit' model is assumed to be known, while the nonlocality of 'explicit' model is optimized according to stress concentration factors reported for infinite Cosserat plates. The advantages/disadvantages, and correspondence/noncorrespondence between both non-local models are highlighted and discussed apparently for the first time, by comparing the stress field provided for reference benchmark problem under various scale ratios, and material parameter combinations for matrix-inclusion pair. The results reveal the analogous character of both non-local models in case of geometric singularities, which may pave the way for further studies considering problems with noticeable scale effects and load singularities. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation 'Explicit' and 'implicit' non-local continuous descriptions for a circular plate with an inclusion in tension †Meral Tuna,

Scale dependent continuum approaches for discontinuous assemblies: ‘Explicit’ and ‘implicit’ non-local models

“…Non-classical theories are used to study the various kinds of material problems [28,29], but recently, a special attention is paid to comparison of various continuum models which can shed light on the proper description of physical phenomena of the underlying discrete system [30,31,32,33]. To this end, possible correspondences and differences between 'implicit' Cosserat and 'explicit' Eringen theories are studied through a common problem of a two-dimensional (2D) square masonry, fixed at the bottom edge and subjected to loads at the top edge (as in [34]).…”

“…To this end, possible correspondences and differences between 'implicit' Cosserat and 'explicit' Eringen theories are studied through a common problem of a two-dimensional (2D) square masonry, fixed at the bottom edge and subjected to loads at the top edge (as in [34]). As in the previous exercise of the authors, focused on geometric singularity [33], Eringen's theory is not here specifically used to model solids at atomistic scale, but rather the focus is on larger structures dominated by a mesoscale internal lenght, l, that does not significantly differ from the macroscopic length, L ( l L 1). A block masonry wall has been considered, although the actual discrete structure of the materials is non-homogeneous, it has been described as a homogeneous and orthotropic linear elastic equivalent continuum models, exploiting a coarse-graining procedure.…”

A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method

“…Lately, researchers have explored the possibility of combining nonlocal strain effects with strain gradient theory in a single higher-order theory [14][15][16] referred to as nonlocal strain gradient theory. These size-dependent theories were exploited to model nanorods [2], nanobeams [1,17,18] and nanoplates [19][20][21][22]. These simple structures are conventionally modeled based on Euler-Bernoulli beam theory (EBT) and classical plate theory (CPT), respectively.…”

‘Explicit’ and ‘Implicit’ Non-local Continuum Descriptions: Plate with Circular Hole

“…In accordance with authors' previous publication [89], the simulations are repeated considering two different mesh configurations of different refinement (see Fig. 5), both characterized by three different scale ratios: L/a = 3.0 (Model 1), L/a = 10.0 (Model 2) and L/a = 20.0 (Model 3).…”

“…Although the application fields of Cosserat (micropolar) and Eringen's theories seem to be quite different due to distinct kinematic and dynamic descriptors they possess, comparison between various non-classical theories has the utmost significance in increasing the accuracy and precision of the modelling and design studies. Following the previous works of authors [89,90], the possible correspondences and differences between 'implicit' type Cosserat and 'explicit' type Eringen non-local models are investigated through a different example problem of pratical importance; a plate with a circular hole subjected to tensile loads. The results are obtained by employing standard displacement based finite element method (FEM) within the linearised kinematical framework.…”