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Homogenization Methods in Materials and Structures

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Civil Engineering".

Deadline for manuscript submissions: closed (31 August 2020) | Viewed by 41805

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Special Issue Editors

Prof. Dr. Angelo Luongo

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Department of Civil, Construction-Architectural and Environmental Engineering, University of L’Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, 67100 L’Aquila, Italy
Interests: continuum and structural mechanics; linear and nonlinear dynamics; stability and bifurcation of dynamical systems; buckling and postbuckling of elastic structures; localization phenomena; aeroelasticity; perturbation methods; computational mechanics
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Prof. Dr. Francesco dell’Isola

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International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy
Interests: continuum mechanics; porous media; piezo-electro-mechanical structures; nonlinear elasticity; second gradient materials; metamaterials; mechanics of living tissue; smart materials; composite materials; experimental mechanics; numerical mechanics
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Prof. Dr. Giuseppe Piccardo

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Dipartimento di Ingegneria Civile, Chimica e Ambientale, Università di Genova, 16126 Genova, Italy
Interests: dynamics; aerodynamics; structural engineering; finite element analysis turbulence modeling; mechanical engineering; wind tunnel testing; coding; engineering, applied and computational mathematics; numerical analysis

Dr. Daniele Zulli

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Department of Civil, Construction-Architectural and Environmental Engineering, University of L’Aquila, 67100 L’Aquila, Italy
Interests: stability and nonlinear oscillations of elastic structures; perturbation methods and reduced order models; aeroelasticity; homogeneous models of structures
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Prof. Dr. Francesco D’Annibale

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Department of Civil, Construction-Architectural and Environmental Engineering, University of L’Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, 67100 L’Aquila, Italy
Interests: control of elastic systems via added piezoelectric devices; stability and nonlinear oscillations of elastic systems under conservative and non-conservative actions; perturbation methods; damage constitutive models; computational mechanics; homogenization of beam-like structures
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Dr. Manuel Ferretti

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International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy
Interests: stability and nonlinear oscillations of elastic systems under conservative and non-conservative loads; dynamics of strings and beams with traveling masses; perturbation methods; mechanics of generalized continua; mechanics of woven fibrous composite reinforcements; homogenization of beam-like structures

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to academic researchers who want to propose studies on the homogenization of complex materials and structures, covering the whole process, from the idealization and design, to the real application.

The subject has received great attention in the last few years, involving researchers whose expertise exploits different scientific areas, including continuum mechanics, structural mechanics, acoustics, materials design, and 3D printing techniques.

Some of the topics considered for this Special Issue include, but are not limited to, the following:

The formulation of homogenous models of micro-structured materials and periodic structures;
The static, dynamic, and stability behavior of homogenous models of lattice members;
Analytical and numerical methods in materials and structures design;
Wave propagation in periodic media;
The experimental validation of the homogenization.

Prof. Dr. Angelo Luongo
Prof. Dr. Francesco dell’Isola
Prof. Dr. Giuseppe Piccardo
Prof. Dr. Daniele Zulli
Dr. Francesco D’Annibale
Dr. Manuel Ferretti
Guest Editors

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Homogenization
Structural design
Material design
Statics
Dynamics
Stability

Published Papers (12 papers)

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Research

19 pages, 698 KiB

Open AccessArticle

Static Response of Double-Layered Pipes via a Perturbation Approach

by Daniele Zulli, Arnaldo Casalotti and Angelo Luongo

Appl. Sci. 2021, 11(2), 886; https://doi.org/10.3390/app11020886 - 19 Jan 2021

Cited by 4 | Viewed by 1676

Abstract

A double-layered pipe under the effect of static transverse loads is considered here. The mechanical model, taken from the literature and constituted by a nonlinear beam-like structure, is constituted by an underlying Timoshenko beam, enriched with further kinematic descriptors which account for local effects, namely, ovalization of the cross-section, warping and possible relative sliding of the layers under bending. The nonlinear equilibrium equations are addressed via a perturbation method, with the aim of obtaining a closed-form solution. The perturbation scheme, tailored for the specific load conditions, requires different scaling of the variables and proceeds up to the fourth order. For two load cases, namely, distributed and tip forces, the solution is compared to that obtained via a pure numeric approach and the finite element method. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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18 pages, 929 KiB

Open AccessArticle

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

by Jarosław Latalski and Daniele Zulli

Appl. Sci. 2020, 10(21), 7802; https://doi.org/10.3390/app10217802 - 03 Nov 2020

Cited by 11 | Viewed by 4221

Abstract

The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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23 pages, 13725 KiB

Open AccessArticle

A Transitional Connection Method for the Design of Functionally Graded Cellular Materials

by Shihao Liang, Liang Gao, Yongfeng Zheng and Hao Li

Appl. Sci. 2020, 10(21), 7449; https://doi.org/10.3390/app10217449 - 23 Oct 2020

Cited by 6 | Viewed by 1787

Abstract

In recent years, the functionally graded materials (FGM) with cellular structure have become a hot spot in the field of materials research. For the continuously varying cellular structure in the layer-wise FGM, the connection of gradient cellular structures has become the main problem. Unfortunately, the effect of gradient connection method on the overall structural performance lacks attention, and the boundary mismatch has enormous implications. Using the homogenization theory and the level set method, this article presents an efficient topology optimization method to solve the connection issue. Firstly, a simple but efficient hybrid level set scheme is developed to generate a new level set surface that has the partial features of two candidate level sets. Then, when the new level set surface is formed by considering the level set functions of two gradient base cells, a special transitional cell can be constructed by finding the zero level set of this generated level set surface. Since the transitional cell has the geometric features of two gradient base cells, the shape of the transitional cell fits perfectly with its connected gradient cells on both sides. Thus, the design of FGM can have a smooth connectivity with C¹ continuity without any complex numerical treatments during the optimization. A number of examples on both 2D and 3D are provided to demonstrate the characteristics of the proposed method. Finite element simulation has also been employed to calculate the mechanical properties of the designs. The simulation results show that the FGM devised by the proposed method exhibits better mechanical performances than conventional FGM with only C⁰ continuity. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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12 pages, 1319 KiB

Open AccessArticle

On Effective Bending Stiffness of a Laminate Nanoplate Considering Steigmann–Ogden Surface Elasticity

by Victor A. Eremeyev and Tomasz Wiczenbach

Appl. Sci. 2020, 10(21), 7402; https://doi.org/10.3390/app10217402 - 22 Oct 2020

Cited by 11 | Viewed by 2026

Abstract

As at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related phenomena. In this paper, we derive an expression for the effective bending stiffness of a laminate plate, considering the Steigmann–Ogden surface elasticity. To this end, we consider plane bending deformations and utilize the through-the-thickness integration procedure. As a result, the calculated elastic bending stiffness depends on lamina thickness and on bulk and surface elastic moduli. The obtained expression could be useful for the description of the bending of multilayered thin films. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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20 pages, 824 KiB

Open AccessArticle

Static and Dynamic Responses of Micro-Structured Beams

by Francesco D’Annibale, Manuel Ferretti and Angelo Luongo

Appl. Sci. 2020, 10(19), 6836; https://doi.org/10.3390/app10196836 - 29 Sep 2020

Cited by 6 | Viewed by 1676

Abstract

In this study, we developed a one-dimensional Timoshenko beam model, embedded in a 3D space for static and dynamic analyses of beam-like structures. These are grid cylinders, that is, micro-structured bodies, made of a periodic and specifically designed three-dimensional assembly of beams. Derivation is performed in the framework of the direct 1D approach, while the constitutive law is determined by a homogenization procedure based on an energy equivalence between a cell of the periodic model and a segment of the solid beam. Warping of the cross-section, caused by shear and torsion, is approximatively taken into account by the concept of a shear factor, namely, a corrective factor for the constitutive coefficients of the equivalent beam. The inertial properties of the Timoshenko model are analytically identified under the hypothesis, and the masses are lumped at the joints. Linear static and dynamic responses of some micro-structured beams, taken as case studies, are analyzed, and a comparison between the results given by the Timoshenko model and those obtained by Finite-Element analyses on 3D frames is made. In this framework, the effectiveness of the equivalent model and its limits of applicability are highlighted. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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24 pages, 8804 KiB

Open AccessArticle

Homogenization of Ancient Masonry Buildings: A Case Study

by Simona Di Nino and Daniele Zulli

Appl. Sci. 2020, 10(19), 6687; https://doi.org/10.3390/app10196687 - 24 Sep 2020

Cited by 5 | Viewed by 1733

Abstract

With the aim of evaluating local and global dynamic mechanisms of a vast and historical masonry building, a homogeneous structural model is proposed here. It is realized with the assembly of othotropic plates and Timoshenko and pure shear beams as well. The identification of the constitutive parameters is carried out after realizing refined finite element models of building portions, and imposing energy or displacement equivalence with the corresponding homogeneous versions, depending on the complexity of the involved schemes. The outcomes are compared with those provided by experimental investigations, and help to give insight and interpretation on the dynamic behavior of the building. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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16 pages, 663 KiB

Open AccessArticle

Buckling of Planar Micro-Structured Beams

by Manuel Ferretti and Francesco D’Annibale

Appl. Sci. 2020, 10(18), 6506; https://doi.org/10.3390/app10186506 - 18 Sep 2020

Cited by 2 | Viewed by 1695

Abstract

In this paper, a Timoshenko beam model is formulated for buckling analysis of periodic micro-structured beams, uniformly compressed. These are planar grid beams, whose micro-structure consists of a square lattice of equal fibers, modeled as Timoshenko micro-beams. The equivalent beam model is derived in the framework of a direct one-dimensional approach and its constitutive law, including the effect of prestress of the longitudinal fibers, is deduced through a homogenization approach. Accordingly, micro–macro constitutive relations are obtained through an energy equivalence between a cell of the periodic model and a segment of the equivalent beam. The model also accounts for warping of the micro-structure, via the introduction of elastic and geometric corrective factors of the constitutive coefficients. A survey of the buckling behavior of sample grid beams is presented to validate the effectiveness and limits of the equivalent model. To this purpose, results supplied by the exact analyses of the equivalent beam are compared with those given by finite element models of bi-dimensional frames. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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20 pages, 25911 KiB

Open AccessArticle

Impacts of Compaction Load and Procedure on Stress-Deformation Behaviors of a Soil Geosynthetic Composite (SGC) Mass—A Case Study

by Meenwah Gui, Truc Phan and Thang Pham

Appl. Sci. 2020, 10(18), 6339; https://doi.org/10.3390/app10186339 - 11 Sep 2020

Cited by 2 | Viewed by 3026

Abstract

Fill compaction in the construction of Geosynthetic Reinforced Soil (GRS) mass is typically performed by operating a vibratory or roller compactor, which in turns imposed a compaction load in direction perpendicular to the wall face. The compaction process resulted in the development of the so-called compaction-induced stress (CIS), which may subsequently increase the stiffness and strength of the fill material. Compaction process is normally simulated using one of the following compaction procedures—(i) a uniformly distributed load acting on the top surface of each soil lift, (ii) a uniformly distributed load acting on the top and bottom surface of each soil lift, and (iii) a moving strip load with different width. Uncertainties such as compaction procedures, compaction and surcharge loads led to the disparity in studying the mechanism of GRS mass. This paper aimed to study the impact of compaction load, compaction procedure, surcharge load and CIS on the stress-deformation behavior of GRS mass via the simulation of a 2 m high Soil Geosynthetic Composite (SGC) mass and a 6 m high GRS mass. The results were examined in terms of reinforcement strains, wall lateral displacements, and net CIS. Results from the analysis show the important impacts of compaction conditions on the stress-deformation behavior of SGC mass and the CIS. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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23 pages, 8098 KiB

Open AccessFeature PaperArticle

An Equivalent Non-Uniform Beam-Like Model for Dynamic Analysis of Multi-Storey Irregular Buildings

by Annalisa Greco, Ilaria Fiore, Giuseppe Occhipinti, Salvatore Caddemi, Daniele Spina and Ivo Caliò

Appl. Sci. 2020, 10(9), 3212; https://doi.org/10.3390/app10093212 - 05 May 2020

Cited by 18 | Viewed by 2669

Abstract

Dynamic analyses and seismic assessments of multi-storey buildings at the urban level require large-scale simulations and computational procedures based on simplified but accurate numerical models. For this aim, the present paper proposes an equivalent non-uniform beam-like model, suitable for the dynamic analysis of buildings with an asymmetric plan and non-uniform vertical distribution of mass and stiffness. The equations of motion of this beam-like model, which presents only shear and torsional deformability, were derived through the application of Hamilton’s principle. The linear dynamic behaviour was evaluated by discretizing the continuous non-uniform model according to a Rayleigh–Ritz approach based on a suitable number of modal shapes of the uniform shear-torsional beam. In spite of its simplicity, the model is able to reproduce the dynamic behaviour of low- and mid-rise buildings with a significant reduction of the computational burden with respect to that required by more general models. The efficacy of the proposed approach was tested, by means of comparisons with linear Finite Element Model (FEM) simulations, on three multi-storey buildings characterized by different irregularities. The satisfactory agreement, in terms of natural frequencies, modes of vibration and seismic response, proves the capability of the proposed approach to reproduce the dynamic response of complex spatial multi-storey frames. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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20 pages, 6942 KiB

Open AccessArticle

Experimental Study on the Flexural Behavior of over Reinforced Concrete Beams Bolted with Compression Steel Plate: Part I

by Shatha Alasadi, Payam Shafigh and Zainah Ibrahim

Appl. Sci. 2020, 10(3), 822; https://doi.org/10.3390/app10030822 - 23 Jan 2020

Cited by 12 | Viewed by 4688

Abstract

The purpose of this paper is to investigate the flexural behavior of over-reinforced concrete beam enhancement by bolted-compression steel plate (BCSP) with normal reinforced concrete beams under laboratory experimental condition. Three beams developed with steel plates were tested until they failed in compression compared with one beam without a steel plate. The thicknesses of the steel plates used were 6 mm, 10 mm, and 15 mm. The beams were simply supported and loaded monotonically with two-point loads. Load-deflection behaviors of the beams were observed, analyzed, and evaluated in terms of spall-off concrete loading, peak loading, displacement at mid-span, flexural stiffness (service and post-peak), and energy dissipation. The outcome of the experiment shows that the use of a steel plate can improve the failure modes of the beams and also increases the peak load and flexural stiffness. The steel development beams dissipated much higher energies with an increase in plate thicknesses than the conventional beam. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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14 pages, 1364 KiB

Open AccessArticle

Free Damping Vibration of Piezoelectric Cantilever Beams: A Biparametric Perturbation Solution and Its Experimental Verification

by Zhi-Xin Yang, Xiao-Ting He, Dan-Dan Peng and Jun-Yi Sun

Appl. Sci. 2020, 10(1), 215; https://doi.org/10.3390/app10010215 - 26 Dec 2019

Cited by 7 | Viewed by 6460

Abstract

As an intelligent material, piezoelectric materials have been widely used in many intelligent fields, especially in the analysis and design of sensors and actuators; however, the vibration problems of the corresponding structures made of the piezoelectric materials are often difficult to solve analytically, because of their force–electric coupling characteristics. In this paper, the biparametric perturbation method was used to solve the free damping vibration problem of piezoelectric cantilever beams, and the perturbation solution of the problem solved here was given. A numerical example was given to discuss the influence of the piezoelectric properties on the vibration of piezoelectric cantilever beams. In addition, related vibration experiments of the piezoelectric cantilever beams were carried out, and the experimental results were in good agreement with the theoretical results. The results indicated that the biparametric perturbation solution obtained in this study is effective, and it may serve as a theoretical reference for the design of sensors and actuators made of piezoelectric materials. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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21 pages, 33223 KiB

Open AccessArticle

An Experimental and Numerical Study on the Flexural Performance of Over-Reinforced Concrete Beam Strengthening with Bolted-Compression Steel Plates: Part II

by Shatha Alasadi, Zainah Ibrahim, Payam Shafigh, Ahad Javanmardi and Karim Nouri

Appl. Sci. 2020, 10(1), 94; https://doi.org/10.3390/app10010094 - 20 Dec 2019

Cited by 7 | Viewed by 9042

Abstract

This study presents an experimental investigation and finite element modelling (FEM) of the behavior of over-reinforced simply-supported beams developed under compression with a bolt-compression steel plate (BCSP) system. This study aims to avoid brittle failure in the compression zone by improving the strength, strain, and energy absorption (EA) of the over-reinforced beam. The experimental program consists of a control beam (CB) and three BCSP beams. With a fixed steel plate length of 1100 mm, the thicknesses of the steel plates vary at the top section. The adopted plate thicknesses were 6 mm, 10 mm, and 15 mm, denoted as BCSP-6, BCSP-10, and BCSP-15, respectively. The bolt arrangement was used to implement the bonding behavior between the concrete and the steel plate when casting. These plates were tested under flexural-static loading (four-point bending). The load-deflection and EA of the beams were determined experimentally. It was observed that the load capacity of the BCSP beams was improved by an increase in plate thickness. The increase in load capacity ranged from 73.7% to 149% of the load capacity of the control beam. The EA was improved up to about 247.5% in comparison with the control beam. There was also an improvement in the crack patterns and failure modes. It was concluded that the developed system has a great effect on the parameters studied. Moreover, the prediction of the concrete failure characteristics by the FE models, using the ABAQUS software package, was comparable with the values determined via the experimental procedures. Hence, the FE models were proven to accurately predict the concrete failure characteristics. Full article

(This article belongs to the Special Issue Homogenization Methods in Materials and Structures)

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