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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "D1: Advanced Energy Materials".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 27194

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Special Issue Editors

Prof. Dr. Tomasz Garbowski

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Department of Biosystems Engineering, Poznan University of Life Sciences, ul. Wojska Polskiego 28, 60-637 Poznań, Poland
Interests: computational mechanics; structural optimization; mathematical programming; inverse problems; mechanics of materials; paper physics

Prof. Dr. Zbigniew Pozorski

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Institute of Structural Analysis, Faculty of Civil and Transport Engineering, Poznan University of Technology, ul. Piotrowo 5, 60-965 Poznań, Poland
Interests: mechanics of sandwich panels; composites; local instability; structure identification; dynamics; optimization
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Prof. Dr. Katarzyna Rzeszut

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Guest Editor

Institute of Building Engineering, Poznan University of Technology, 60965 Poznan, Poland
Interests: metal structures; nonlinear sensitivity analysis; optimal design; thin-walled steel structures; passive and energy-saving buildings; design methods in fire conditions

Special Issue Information

Dear Colleagues,

This Special Issue of Energies is devoted to the deformation energy of composite structures. Composites, including corrugated and sandwich structures, are increasingly used as construction materials or load-bearing elements in various engineering fields. Due to their specific composition, their load capacity to section weight ratio is much higher than that of traditional solid sections. In addition, the geometries of the corrugated or soft-core structures are constantly being modified to improve their mechanical properties. This Special Issue will enable scientists and engineers to exchange the latest knowledge on advances in theoretical and computational approaches for composite structures.

Among others, the following topics are the main fields of interest for this Special Issue: deformation energy in composite structures such as beams, plates and shells, corrugated boards and sandwich panels; its mechanical characterization and strength estimation methods, numerical, and analytical homogenization techniques; laboratory testing methods; linear and nonlinear analysis of any structures made of composites.

There are no particular restrictions on the thematic areas of this Special Issue as long as the submitted works relate to strain energy in composites. Energies readers and authors are encouraged to send their latest research work in these areas, with an emphasis on experimental validations and empirical proofs.

Prof. Dr. Tomasz Garbowski
Prof. Dr. Zbigniew Pozorski
Prof. Dr. Katarzyna Rzeszut
Guest Editors

Manuscript Submission Information

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Keywords

Composite structures
Strain energy
Sandwich plates
Shells
Finite element method
Homogenization
Material characterization
Inverse problems
Thin-wall structures
Local instability
Dynamics
Sensitivity analysis

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Published Papers (7 papers)

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Research

19 pages, 4920 KiB

Open AccessArticle

Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes

by Tomasz Gajewski, Tomasz Garbowski, Natalia Staszak and Małgorzata Kuca

Energies 2021, 14(14), 4321; https://doi.org/10.3390/en14144321 - 17 Jul 2021

Cited by 18 | Viewed by 2728

Abstract

As long as non-contact digital printing remains an uncommon standard in the corrugated packaging industry, corrugated board crushing remains a real issue that affects the load capacity of boxes. Crushing mainly occurs during the converting of corrugated board (e.g., analog flexographic printing or laminating) and is a process that cannot be avoided. However, as this study shows, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision of ±10 μm) in the range from 10 to 70% on different laboratory measurements was checked. The typical mechanical tests—i.e., edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc.—were performed on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions. The proposed measurement technique was successfully used to precisely estimate and thus control the crushing of corrugated board, while the proposed numerical and analytical techniques was used to estimate the load capacity of corrugated board packaging. A good correlation between the measured reduced stiffness of the corrugated cardboard and the proposed analytical predictive models was obtained. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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16 pages, 5727 KiB

Open AccessArticle

Crushing of Single-Walled Corrugated Board during Converting: Experimental and Numerical Study

by Tomasz Garbowski, Tomasz Gajewski, Damian Mrówczyński and Radosław Jędrzejczak

Energies 2021, 14(11), 3203; https://doi.org/10.3390/en14113203 - 30 May 2021

Cited by 10 | Viewed by 3831

Abstract

Corrugated cardboard is an ecological material, mainly because, in addition to virgin cellulose fibers also the fibers recovered during recycling process are used in its production. However, the use of recycled fibers causes slight deterioration of the mechanical properties of the corrugated board. In addition, converting processes such as printing, die-cutting, lamination, etc. cause micro-damage in the corrugated cardboard layers. In this work, the focus is precisely on the crushing of corrugated cardboard. A series of laboratory experiments were conducted, in which the different types of single-walled corrugated cardboards were pressed in a fully controlled manner to check the impact of the crush on the basic material parameters. The amount of crushing (with a precision of 10 micrometers) was controlled by a precise FEMat device, for crushing the corrugated board in the range from 10 to 70% of its original thickness. In this study, the influence of crushing on bending, twisting and shear stiffness as well as a residual thickness and edge crush resistance of corrugated board was investigated. Then, a procedure based on a numerical homogenization, taking into account a partial delamination in the corrugated layers to determine the degraded material stiffness was proposed. Finally, using the empirical-numerical method, a simplified calculation model of corrugated cardboard was derived, which satisfactorily reflects the experimental results. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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14 pages, 1113 KiB

Open AccessArticle

Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Perforations

by Tomasz Garbowski, Tomasz Gajewski and Jakub Krzysztof Grabski

Energies 2021, 14(4), 1095; https://doi.org/10.3390/en14041095 - 19 Feb 2021

Cited by 36 | Viewed by 5276

Abstract

This paper presents a modified analytical formula for estimating the static top-to-bottom compressive strength of corrugated board packaging with different perforations. The analytical framework is based here on Heimerl’s assumption with an extension from a single panel to a full box, enhanced with a numerically calculated critical load. In the proposed method, the torsional and shear stiffness of corrugated cardboard, as well as the panel depth-to-width ratio is implemented in the finite element model used for buckling analysis. The new approach is compared with the successful though the simplified McKee formula and is also verified with the experimental results of various packaging designs made of corrugated cardboard. The obtained results indicate that for boxes containing specific perforations, simplified methods give much larger estimation error than the analytical–numerical approach proposed in the article. To the best knowledge of the authors, the influence of the perforations has never been considered before in the analytical or analytical–numerical approach for estimation of the compressive strength of boxes made of corrugated paperboard. The novelty of this paper is to adopt the method presented to include perforation influence on the box compressive strength estimation. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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13 pages, 4019 KiB

Open AccessArticle

Analytical Models of Axially Loaded Blind Rivets Used with Sandwich Beams

by Robert Studziński

Energies 2021, 14(3), 579; https://doi.org/10.3390/en14030579 - 23 Jan 2021

Cited by 1 | Viewed by 2224

Abstract

The paper presents the novel use of analytical models of a beam on an elastic foundation. The one-parameter model (Winkler model) and the two-parameter models (Filonenko-Borodich and Pasternak models) were investigated. These models were used to describe the elastic response of axially loaded blind rivets used with sandwich structures. The elastic response related to the elastic strain energy is mentioned in the paper as the resilience modulus of the connection. The databases from laboratory pull-out tests were used to verify these models. One type of blind rivet (aluminum, with three clamping arms) and one type of sandwich beam were used. The sandwich beams used in the experiments consisted of two thin-walled and stiff external facings (zinc-coated steel) and a thick, soft core (polyisocyanurate foam—PIR). In the test the sandwich beams were subjected to static, axial pull-out loading. The research provides the quantitative comparison between the laboratory experiment and the analytical solutions from models adopted for this type of connection. Additionally, the failure mechanisms, the secant stiffness at the ultimate capacity, and the strain energy capacity of the elastic foundation at failure are considered. To the author’s knowledge, this approach has not been described in the literature so far. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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12 pages, 809 KiB

Open AccessArticle

Designing of Dynamic Spectrum Shifting in Terms of Non-Local Space-Fractional Mechanics

by Krzysztof Szajek, Wojciech Sumelka, Krzysztof Bekus and Tomasz Blaszczyk

Energies 2021, 14(2), 506; https://doi.org/10.3390/en14020506 - 19 Jan 2021

Cited by 2 | Viewed by 1938

Abstract

In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1D material bodies with a specific dynamic eigenvalue spectrum is discussed. Such a formulated problem is based on the proper spatial distribution of material length scale, which maps the information about the underlying microstructure (it is important that the material length scale is one of two additional material parameters of sFCM compared to the classical local continuum mechanics—the second one, the order of fractional continua—is treated herein as a scaling parameter only). Technically, the design process for finding adequate length scale distribution is not trivial and requires the use of an inverse optimization procedure. In the analysis, the objective function considers a subset of eigenvalues reduced to a single value based on Kreisselmeier–Steinhauser formula. It is crucial that the total number of eigenvalues considered must be smaller than the limit which comes from the ratio of the sFCM length scale to the length of the material body. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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23 pages, 38090 KiB

Open AccessArticle

A New Blast Absorbing Sandwich Panel with Unconnected Corrugated Layers—Numerical Study

by Hasan Al-Rifaie, Robert Studziński, Tomasz Gajewski, Michał Malendowski, Wojciech Sumelka and Piotr W. Sielicki

Energies 2021, 14(1), 214; https://doi.org/10.3390/en14010214 - 3 Jan 2021

Cited by 32 | Viewed by 4217

Abstract

The need for more effective defence systems is of critical importance because of the rising risk of explosive attacks. Sandwich panels are used as plastically deforming sacrificial structures, absorbing blast wave energy. To the authors’ knowledge, the blast behaviour of sandwich panels with connected (welded/bolted/riveted) corrugated layers has been well covered in literature. Hence, the aim of this numerical study was to develop new, easy-to-build, non-expensive, graded sandwich panel with ‘unconnected’ corrugated layers that can be used as a multipurpose sacrificial protective structure against wide range of blast threats. The proposed sandwich panel is composed of six unconnected aluminium (AL6063-T4) core layers encased in a steel (Weldox

460

E) frame with 330 × 330 × 150 mm overall dimensions. The numerical analysis was conducted using Abaqus/Explicit solver. First, the performance of four different nongraded layer topologies (trapezoidal, triangular, sinusoidal, and rectangular) was compared, when subjected to ~16 MPa peak reflected over-pressure (M = 0.5 kg of TNT at R = 0.5 m). Results showed that the trapezoidal topology outperformed other topologies, with uniform progressive collapse, lower reaction force, and higher plastic dissipation energy. Then, the trapezoidal topology was further analysed to design a ‘graded’ sandwich panel that can absorb a wide range of blast intensities (~4, 7, 11, 13, and 16 MPa peak reflected over-pressures) by using a (0.4, 0.8, 1.2 mm) stepwise thickness combination for the layers. In conclusion, the superior performance of the proposed sandwich panel with unconnected graded layers can be considered as a novel alternative to the conventional costly laser-welded sandwich panels. Applications of the new solution range from protecting civil structures to military facilities. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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20 pages, 2754 KiB

Open AccessFeature PaperArticle

Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Openings

by Tomasz Garbowski, Tomasz Gajewski and Jakub Krzysztof Grabski

Energies 2021, 14(1), 155; https://doi.org/10.3390/en14010155 - 30 Dec 2020

Cited by 43 | Viewed by 5215

Abstract

This paper presents mixed analytical/numerical method for estimating the static top-to-bottom compressive strength of corrugated packaging with different ventilation openings and holes, in which the torsional and shear stiffness of corrugated cardboard as well as the panel depth-to-width ratio are included. Analytical framework bases on Heimerls assumption with a modification to a critical force, which is here computed by a numerical algorithm. The proposed method is compared herein with the successful McKee formula and is verified with the large number of experiment results of various packaging designs made of different qualities of corrugated cardboard. The results show that, for various hole dimensions or location of openings in no-flap and flap boxes, the estimation error may be reduced up to three times than in the simple analytical approach. Full article

(This article belongs to the Special Issue Strain Energy in Composite Structures)

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