Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak-and strong-form finite element solutions

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 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

The strong formulation finite element method: stability and accuracy

The Strong Formulation Finite Element Method (SFEM) is a numerical solution technique for solving arbitrarily shaped structural systems. This method uses a hybrid scheme given by the Differential Quadrature Method (DQM) and the Finite Element Method (FEM). The former is used for solving the differential equations inside each element and the latter employs the mapping technique to study domains of general shape. A general brief review on the current methodology has been reported in the book [1] and recalled in the works [2,3], where a stress and strain recovery procedure was implemented. The aim of this manuscript is to present a general view of the static and dynamic behaviors of one- and two-dimensional structural components solved by using SFEM. It must be pointed out that SFEM is a generalization of the so-called Generalized Differential Quadrature Finite Element Method (GDQFEM) presented by the authors in some previous papers [4-8]. Particular interest is given to the accuracy, stability and reliability of the SFEM when it is applied to simple problems. Since numerical solutions - of any kind - are always an approximation of physical systems, all the numerical applications are compared to well-known analytical and semi-analytical solutions of one- and two-dimensional systems. Ultimately, this work presents typical aspects of an innovative domain decomposition approach that should be of wide interest to the computational mechanics community

Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

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

A Study on the Effect of Doping Metallic Nanoparticles on Fracture Properties of Polylactic Acid Nanofibres via Molecular Dynamics Simulation

All-atom molecular dynamics simulations are conducted to elucidate the fracture mechanism of polylactic acid nanofibres doped with metallic nanoparticles. Extensional deformation is applied on polymer nanofibres decorated with spherical silver nanoparticles on the surface layer. In the ob-tained stress–strain curve, the elastic, yield, strain softening and fracture regions are recognized, where mechanical parameters are evaluated by tracking the stress, strain energy and geometrical evolutions. The energy release rate during crack propagation, which is a crucial factor in fracture mechanics, is calculated. The results show that the presence of doping nanoparticles improves the fracture properties of the polymer nanofibre consistently with experimental observation. The na-noparticles bind together polymer chains on the surface layer, which hinders crack initiation and propagation. The effect of the distribution of nanoparticles is studied through different doping decorations. Additionally, a discussion on the variation of internal energy components during uniaxial tensile loading is provided to unravel the deformation mechanism of nanoparticle-doped nanofibres

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

In this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials

Computational approach for form-finding optimal design

In this paper, an optimization strategy for a canopy, based on computational modelling approaches is presented. The design approach is applied to a realistic roof structure of an ecological island (waste collection centre) and has been completely redesigned with the aid of a Genetic Algorithm and a Dynamic Relaxation Algorithm. The preliminary design of the roof structure can be formulated as a shape optimization problem, involving functional needs and constraints at different scales of the structure. The proposed hypothesis solution was studied by using an optimization procedure through algorithms in the software Rhinoceros3D®/Grasshopper®. The main aim of this work is to explore different modelling approaches for form-finding that can be built from the use of numerical simulations based on algorithms. To this aim, the need to meet various requirements (structural, functional, formal) involving a team of architects and engineers can be interpreted as a matter of structural optimizatio

Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic

A comparative SFEM- and IGA-based numerical prediction of the stress concentration factor in plates with discontinuities

In this contribution we present a numerical analysis of the Stress Concentration Factor (SCF) KT and the stress distribution around holes and discontinuities in plane state structures. The stress concentration in discontinuous zones is known to be a very significant issue in strength problems. Indeed, the presence of a discontinuity makes even a simple structure model complicated to analyze, regardless of the method being used. The Finite Element Method (FEM) is the most common tool in engineering for treating such problems. However, a very fine mesh is generally required for a realistic prediction of stresses around critical zones as cracks or discontinuities. Despite the large use of the FEM as numerical approach to predict stress concentrations, the problem is still open. Here two innovative numerical techniques are proposed as computationally more efficient alternatives to determine the SCFs with a limited number of degrees of freedom, which may significantly decrease the computation time. A limited number of degrees of freedom is due to a higher order scheme carried out by the SFEM. On the contrary, the standard FEM employs local low order polynomials for the approximation of solution, and special functions are generally implemented for stress concentration problems. More in detail, the local and global strong formulation finite element method (SFEM), and the isogeometric approach (IGA) based on quadratic Non-Uniform Rational B-Spline (NURBS) basis functions, are herein applied for the purpose, as proposed for other applications in [1,2] for the SFEM, and [3-5] for IGA, respectively. In order to demonstrate the accuracy of the two proposed methodologies, some classical examples are studied, which consider rectangular plates with different discontinuities, e.g. circular holes, U-holes, or V-notches. All the numerical results obtained in terms of stress distribution and KT are compared with the theoretical predictions from the literature as well as the numerical solutions provided by FEM. The numerical solutions for the KT are based on a linear interpolation of the stresses near the discontinuities within a certain distance of interpolation, and agree very well with the exact computations available in the handbooks. A comparative evaluation of numerical results based on the IGA, SFEM and FEM approaches is illustrated in Figures 1 and 2, in terms of stress distributions and KT for a U-notched plate subjected to a uniform loading and for different degrees of freedoms (DOFs). The numerical results provided by SFEM and IGA methods are very close to the ones found with FEM, thus confirming the potentials and accuracy of the two proposed methods to capture the stress concentrations in fracture mechanics, also for coarse mesh discretizations

Application of column buckling theory to steel aluminium foam sandwich panels

In steel structures, a lot of attention is paid to lightweight structures, i.e. reduction of dead load without compromising structural safety, integrity and performance. Thanks to modern steel aluminium foam sandwich panel manufacturing technology a new possibility became available for lightweight structural design. Assessment and understanding of the behaviour of this sandwich panel under in-plane compression or flexure is crucial before its application in steel structures. Column buckling theory is considered and applied to the steel aluminium foam sandwich panel to evaluate its behaviour under in-plane compressive load. In this work, various assumptions are made to generalise Euler’s buckling formula. The generalisation requires modification of the buckling stiffness expression to account for sandwich panel composite properties. The modified analytical expression is verified with finite element simulation employing various material models specific to steel faceplates and aluminium foam as well as various geometric imperfections. Based on this study, it can be concluded that Euler’s buckling formula can be successfully modified and used in the prediction of the load-carrying capacity of a sandwich panel