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This article introduces natural composite and nanocomposite panels of Luffa fibers–chitosan resin; and they are subjected to quasi-static penetration tests and compression experiments to discuss their penetration resistance and compression strength. Natural fibers of Luffa cylindrical sponge were used as the reinforcement and natural chitosan resin was produced from shrimp shells. Specimens with various characteristics were produced through hand layup method and they were subjected to penetration test of a blunt-nose punch. Results demonstrated that there is an optimum mass fraction for chitosan and magnetite nanoparticles to achieve the highest penetration strength; and the best layer configuration is as 0 and 90°, alternately. Furthermore, some glass-chitosan composite panels were produced and comparison of their penetration tests and the corresponding Luffa-chitosan composite experiments demonstrated that in a certain condition, the maximum loads of penetrating the punch into the both composite panels are the same. In second type experiments, quasi–static compression tests were performed on some cubic Luffa–chitosan specimens and results showed that the natural composite cube has significant specific absorbed energy; and by selecting its suitable dimensions, a natural energy absorber can be achieved. Development of the natural Luffa–chitosan composite is suggested, based on sustainability considerations; and using it in the bulletproof vests and armors is presented as a creative idea; due to its natural structure, compatibility with human skin, acceptable resistance against the penetration, its biodegradable ability and simple and low cost production process.

In the present research, vibration behavior is presented for a thermally postbuckled double-layered triangular graphene sheet (DLTGS). The DLTGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on the Kirchhoff’s plate theory, and a nonlinearity of von Karman-type is considered in strain–displacement relations. The thermal effects and van der Waals forces between layers are also included and some of the material properties are assumed to be temperature-dependent. A semi-analytical solution is obtained using the multiple time scales method. The effects of variation of small-scale parameter to the natural frequencies, deflections and response curve of DLTGS are analyzed, and the numerical results are obtained from the nonlocal plate model. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLTGS in thermal environments such as scale parameter and thermal load are presented. The stability and occurrence of the internal resonance between vibration modes around a stable buckled configuration is investigated.

This paper studies the flattening process of empty and polyurethane foam-filled composite-metal tubes, experimentally. To prepare these specimens, metal tubes were wrapped with a fiber-reinforced composite using hand layup method. For the metal tubes, two kinds of materials, aluminum and brass, were used, and the composite tubes were made of woven E-glass fiber and vinyl ester resin. A composite tube and a metal tube were tested to compare their flattening process with the results of composite-metal tubes. The specimens were laterally compressed between two rigid plates in quasi-static condition. According to the results, specific absorbed energy (SAE: absorbed energy to the specimen mass) by a studied composite tube is about 1.5 times bigger than the SAE by the metal tubes. However, the deformation mode of the metal tube is more regular than the composite tube. So, in composite-metal tubes, the metal part causes regularity in deformation, and the composite part causes higher energy absorption capacity and lower density at the same time. Finally, the effects of some parameters such as the tubes length, foam-filler, foam adhesion, and density on the energy absorption characteristics of composite-metal tubes are studied. The results indicate that wrapping the metal tubes by composite materials causes more regularity in deformation, higher energy absorption capacity, and lower density, simultaneously.

This article presents a novel general theory to estimate total absorbed energy (TAE) by two main absorber mechanisms: bending and plastic line. Furthermore, as case studies, some theoretical formulas are derived for predicting TAE of circular metal tubes during lateral flattening and indentation processes, based on three different material models of Rigid-perfectly plastic, Rigid-linear work hardening and Power hardening. Furthermore, some indentation and flattening tests are carried out on circular brazen and aluminum tubes to investigate correctness and accuracy of the derived theories. In the theoretical part, theoretical equations are derived for both thick-walled and thin-walled structures; and a multi criteria equation is derived to estimate TAE of two main energy absorbing mechanisms involving bending and plastic hinge line; and, then, based on the derived general formulas, some theoretical relations are calculated to predict TAE of indentation and flattening processes, as case studies. In the indentation process, circular tubes are considered between a slab rigid indenter and a rigid platen; and in the flattening process, circular tubes are laterally compressed between two rigid platens. To verify the derived equations, various experiments are performed on some circular brazen and aluminum specimens that are laterally indented and flattened in the quasi-static condition. In the indentation tests, different tubular samples with various wall thicknesses and radii of cross–section and material types are loaded under different slab rigid indenters with different widths. Then theoretical estimations of TAE by circular tubes during the indentation and flattening processes are compared with the corresponding experimental results. Also, effects of tube wall thickness and indenter width are investigated on TAE of tubes, experimentally and theoretically. Performed investigations illustrate that by increasing the wall thickness and indenter width, TAE of indented tubes increases. Also, the present research work affirms that TAE by circular tubes through the flattening process is higher than the corresponding value of their indentation process, theoretically; and upper limit of TAE of circular tubes through the indentation process occurs when, width of slab indenter reaches to half of tube initial perimeter.

To improve energy absorption performance of thin-walled sections, the present research work investigates energy absorption capability of a type of thin-walled profiles with H-shaped cross-section during quasi-static flattening process and optimizes its geometry, using the Taguchi method; and also derives some theoretical formulas to predict total absorbed energy by the H-shaped section. Two theoretical analyses are performed based on two different material models consist of Power hardening and Rigid-Linear work hardening. In each theoretical analysis, general formulations are derived to estimate absorbed energy by a plastic hinge line and an unbending process. In the optimization trend, design of experiment (DoE) is carried out by the Taguchi method. Due to experimental limitations in providing the various samples with different geometrical dimensions, ABAQUS/Explicit software is used. As control factors, influences of geometrical parameters and lateral loading angle are studies on specific energy absorption (SEA); and design of optimum geometry of the H-shaped profile is discussed. Contribution percentage of each control factor is determined on the SEA of the profile, which provides important reference for designing the H-shaped profile in practical energy absorption applications. Results show that wall thickness of the profile cross-section has the highest effect on the SEA of the H-shaped section with contribution ratio of 47.02%. Furthermore, loading angle has the smallest influence on the specific energy absorption capacity. Finally, optimum geometry of the profile is introduced. Also, comparison of the obtained results by theoretical predictions and numerical simulations illustrates precision and acceptable accuracy of the derived theories.

The main aim of the present research is to investigate the quasi-static penetration process of cylindrical indenters with different nose shapes into multilayered composite panels made of Dyneema and Glass woven fibers, and aluminum face sheets. For better understanding of the perforation mechanism of the composite panels, effects of indenter geometry, stacking sequences, and boundary conditions are studied and their effects on energy absorption, specific absorbed energy, maximum deformation, peak load, and failure modes are evaluated and discussed. Samples with different layering configurations loaded under quasi-static punch and indentation with loading rate of 5 mm/min using universal testing machine and cylindrical rigid indenters with different nose shapes geometries consist of blunt, hemispherical, conical, and ogival. Regarding the boundary condition effects, two different rigid fixtures are designed and manufactured with the same external square perimeter (250 × 250 mm) and two different internal perimeters of circular and square shapes respectively, with diameter of 15 mm and edge side of 100 mm. Results show that the hybrid composite panels composed of Dyneema sheets, exhibits significantly better load carrying capacity and specific absorbed energy under both loading conditions. Indenter nose shape significantly affects elastic load, peak load, and energy absorption and maximum deformation. Furthermore, from visual observations based on digital microscopic images, fiber breakage, fiber pull out, intralaminar delamination, and debonding between the composite layers within the damage zone were inspected and recognized as the main damage mechanisms of panels. Output data obtained from all the experimental investigation were reported, discussed, and commented upon.

In this paper, flattening process of polyurethane foam-filled aluminum columns with rectangular and square cross-sections subjected to lateral compression load is investigated, theoretically and experimentally. For this purpose, some flattening tests were performed on the foam-filled rectangular columns using a DMG machine, model 7166. Based on a new theoretical plastic deformation model, a relation is derived in order to predict instantaneous lateral load of the foam-filled rectangular columns during flattening process. Theoretical instantaneous lateral load versus lateral displacement diagrams of the specimens are compared with the experimental measurements, which shows a good agreement between them. Also, based on the experimental results, effects of different parameters such as load application directions, injection of polyurethane foam into columns, foam density and presence of the adhesion between the foam and the column inner wall are investigated on the flattening behavior of the structure. Furthermore, deformation modes of the specimens with different cross-sections are studied.

Nosing process of circular metal tubes in empty and polyurethane foam-filled conditions on a semispherical rigid die was analyzed by theoretical and experimental methods. A new theoretical model of plastic deformation of circular metal tubes was demonstrated during the nosing process on a rigid semispherical die. Based on the analytical model, some theoretical relations were calculated to estimate instantaneous forming load and dissipated energy of empty and foam-filled circular metal tubes versus axial displacement. Some circular brazen and aluminum tubes were prepared and shaped into semispherical nosed nozzles to verify the present theory. Comparison of theoretical predictions and the corresponding experimental measurements reveals that predicted load-displacement and dissipated energy-displacement diagrams by theoretical formulas have a good correlation with the corresponding experimental curves and it proves verity of the theory. Also, the present theory shows that dissipated energy and axial load of empty tubes depend on material type, wall thickness and diameter of the tubes and they are independent of tube initial length. Furthermore, the experimental results show that the presence of polyethylene Teflon-constraints increases ultimate axial displacement of the forming process.

In this article, absorbed energy per unit of initial tube length, initial peak force and mean folding force in empty and polyurethane foam-filled simple and grooved specimens with circular cross section are investigated, experimentally. Results demonstrate that in the empty and foam-filled simple specimens, absorbed energy per unit of initial tube length, initial peak force and mean folding force are larger than the corresponding values of the empty and foam-filled grooved specimens, respectively. But, increment of absorbed energy due to the foam-filler in the grooved tubes is more than the corresponding value in the simple specimens. Also, diagrams of absorbed energy and folding force versus the grooves distance have the minimum value. Therefore, there is a critical value for the grooves distance and according to the application viewpoint, to produce a good energy absorber, the grooves distance is selected far from the critical grooves distance. The experimental results show that when the grooves distance (λ) decreases, deformation mode inclines to the concertina (regular) mode and when λ increases, the deformation mode inclines to the diamond mode. Finally, a semiempirical relation is derived to predict the initial peak force of empty and foam-filled grooved tubes.

This paper is an attempt for introduction of new theoretical relations in order to predict energy absorption behavior of empty and polyurethane foam-filled composite tubes, which are made of woven fiber fabrics, during lateral compression between two rigid plates. Such theoretical relations can be used to specify portion of different deformations that are happened during crushing process in total energy absorption of the structures. Knowing these data may help the designers to reinforce the energy absorbers more effectively. Also, several experiments are conducted on empty and polyurethane foam-filled circular E-glass/Vinylester composite tubes in order to validate the theoretical relations. The specimens are laterally compressed between two rigid plates during a quasi-static process. According to experimental studies, the composite tubes collapse with different modes of deformation during lateral flattening. Different relations are introduced for prediction of the absorbed energy of tubes with different deformation modes. The theoretical and experimental energy-displacement diagrams and total absorbed energy by the composite tubes are compared and good agreements are found. Finally, theoretical relations are compared with each other and effects of different energy absorption mechanisms on total energy absorption are discussed based on the presented relations.

Cellular foams are a modern class of materials with unique mechanical properties that have wide ranging engineering applications, in the areas of biomedical, acoustic and thermal insulation, and crashworthiness. Recently, foam materials have received increased attention for vehicle crashworthiness due to their lightweight and excellent energy absorption capabilities that allow significant weight reduction without compromising structural safety aspects. Accordingly, this paper reviews the crush and energy absorption behaviour of foam-filled structures that can be used for crashworthy design in transport engineering. In addition, the mechanical and dynamic properties of cellular material and their role on the crashworthiness performance of filled structure are discussed. Particularly, the influences of foam density and interactions, between the foam and the tubes, on the deformation mode of the filled structures are clarified. The advantages offered by the innovative foam material, which contains a density gradient, on the crashworthiness behaviour are also highlighted. Also, a brief summary of optimisation studies involving the use of foam-filled structures are presented. It was found that the cellular materials improve the crashworthiness performance when they are used as filler material in thin-walled energy absorbers due to their capability of altering the deformation mode to a more favourable one.

This article performs theoretical and experimental studies on quadrangular metal columns during the indentation process. The samples are laterally compressed between a rigid platen and a solid cylindrical indenter under the quasi-static loading. Several columns are prepared with different cross sections, initial lengths, wall thicknesses and various alloy materials and are tested by indenters with different diameters. Effects of mentioned characteristics are investigated on crashworthiness parameters that have a key role in design of an energy absorber such as total absorbed energy and specific absorbed energy. Based on experimental observations, two theoretical models of plastic deformation are introduced. The theoretical equations are derived to predict energy–displacement diagram of quadrangular metal columns. Experimental results indicate that in a sample with a certain cross section, by increasing indenter diameter, total absorbed energy increases. Performed comparisons between theoretical predictions and the corresponding experimental measurements show that both of the theories and experiments illustrate the same trend for energy absorption capability by columns with respect to variations of initial length, wall thickness and material type of columns and diameter of rigid indenter.

This article introduces a novel energy absorber of sandwich tube with the agglomerated cork core and the composite tube during the indentation process under the applied quasi-static lateral loading by a solid cylindrical rigid indenter. Also, the corresponding cork specimens and the empty composite tubes are tested, too. The solid cylindrical cores made of agglomerated cork are prepared by punching a cork sheet with 200 kg/m 3 density and positioned into the composite tubes to manufacture the cork-filled tubes. The results show that the cork-filled composite tubes have an energy absorption capacity up to 5.65 times of the corresponding cork sample and up to 6.06 times of the corresponding empty tube. Also, it is found that total absorbed energy by a cork-filled composite tube is 174% higher than summation of absorbed energy by the corresponding empty tube and the cork sample. Also, specific absorbed energy by all the specimens is discussed.

Present research work introduces a novel composite material consists of agglomerated cork inserts as the stiffener particles and silicone rubber as the resin and uses it as an energy absorber during lateral flattening process under the quasi-static lateral loading in the form of solid cylinder by the experimental method. Solid cylindrical composite specimens were manufactured with different agglomerated cork insert conditions consist of different insert shapes of cylindrical and cubic, different diameters and heights of cylindrical insert, and various insert densities. Also, some composite specimens were produced with two different insert patterns of arranged and random and with two different agglomerated cork insert mass fractions that called MAX and MIN conditions. Furthermore, the composite specimens were manufactured with three different specimen diameters. All the samples were laterally compressed between two rigid platens and their energy absorptions were investigated. Also, effects of all the above mentioned parameters were discussed. In addition, spring-back rates of the samples were studied to investigate probability of using the introduced composite as both of reversible and irreversible energy absorbers. Experiments show that in the MAX condition, composite specimens with cylindrical inserts have higher specific absorbed energy respect to the specimens with cubic inserts and with cork powder.

In this article, a new manufacturing method is introduced to shape circular tubes into columns with triangular cross-section by the elastoforming process. Also, a theoretical analysis is performed to derive a theoretical formula for predicting total dissipated energy that is required for the forming process. For this purpose, V-shape dies with different angles are designed and some aluminum and brazen tubes with different characteristics are prepared. The circular tubes in the empty and filled conditions are compressed between a rigid V-shape die and a flat punch, and during the plastic deformation under the lateral loading, the tubes are shaped into the triangular sections. Considering different tube lengths, outer diameters and wall thicknesses, the specimens are categorized. Also, some of the samples are filled by cylindrical polyethylene Teflon with different thicknesses to investigate the effects of Teflon-filler on the shaping process of the triangular columns. The experiments show that using the cylindrical Teflon-filler, deformation mode of the triangular tubes improves, significantly. In addition, experimental observations of the deformation modes illustrate that there is an optimum value for wall thickness of cylindrical Teflon-filler and the tubes with the optimum Teflon-filler forms close to desirable triangular shape. The results show that by increasing tube wall thickness, probability of crack initiation and fracture reduces. Furthermore, comparison of estimations by the presented theory and the corresponding experimental measurements show an acceptable agreement, in both of empty and filled conditions.

In this article, some theoretical relations are derived to predict the instantaneous folding force and the absorbed energy by the empty and polyurethane foam-filled grooved tubes with circular cross-section during the first fold formation under the axial loading. Five different modes of deformation are considered in the theoretical model of deformation: bending around two internal circular hinge lines, bending around an external circular hinge line, extensional deformation in the folding arms, axial compression of the polyurethane foam, and interaction effects between polyurethane foam and inner wall of the grooved tube. Also, based on the experiments, a semi-empirical relation is suggested to predict the effective axial displacement at the end of a complete fold creation in the polyurethane foam-filled grooved tubes. To verify the theoretical analyses, some axial compression tests were carried out on the empty and filled grooved tubes. Comparison of the theoretical predictions with the corresponding experimental results showed a good correlation.

This article performs an experimental study on empty and polyurethane foam-filled thin-walled aluminium columns with quadrangular cross section in two different conditions: with or without centrally circular discontinuities on the longitudinal or latitudinal sides of column cross section during the folding process (local buckling). In each sample, two circular cut-outs were perforated into the opposite sides of specimens and the samples were axially compressed between two rigid platens under the quasi-static loading. The samples were prepared with different initial lengths, filling conditions and cut-out diameters. Effects of mentioned characteristics are investigated on total absorbed energy, specific absorbed energy, crush force efficiency, peak load and folding wavelength. Experimental observations show that by increasing the cut-out diameter and also by filling the column with the foam, folding wavelength decreases. Also, experiments show that there is an optimum diameter for the longitudinal side cut-outs which total absorbed energy by the filled rectangular specimen with the optimum cut-out is the highest. Furthermore, results illustrate that total absorbed energy increases due to increment of column length, but specific absorbed energy and crush force efficiency are independent of column length.

The present article introduces a new thin-walled specimen with longitudinal grooved section as an energy absorber during the flattening process. On the other hand, this paper examines lateral compression process and energy absorption behavior of grooved sections with special cross-section between two rigid platens. Influences of presence of polyurethane foam-filler and nesting the section by aluminum or brazen tube are studied on energy absorption capability by the structure under the lateral loading in the quasi-static condition. For this aim, seven groups of specimens are prepared and in each group, five similar specimens are tested with different loading angles of 0°, 30°, 45°, 60° and 90°, respect to the central line of two grooves of thin-walled section. Effects of presence of foam-filler into the grooved section of single samples and into inner aluminum or brazen tube of nested systems, effects of material type and wall thickness of inner tube of nested grooved sections, and influences of loading angle are investigated on energy absorption behavior and deformation mode of the structures during the flattening process. Based on experimental measurements and between all the tested specimens, the present research work suggest a grooved section with special cross-section that has been nested by an inner polyurethane foam-filled aluminum tube as the best energy absorber during the lateral compression. Finally, results of the present work are compared with represented results of some previous published works by other researchers to find out advantages of the introduced novel nested system of the present article.

The research investigates the axial splitting of E-glass/vinylester and E-glass/polyester composite columns with identical perimeters but different cross sections on polygonal aluminum dies, and the elimination of restrictions on the initial slit in the classical splitting process. A novel technique for the construction of mandrels using polystyrene foam is developed. Composite columns are produced by winding the fiber fabric layers around the mandrels using coarse and fine E-glass woven fibers. The deformation modes and energy absorption behavior of columns during the long stroke of the splitting process are compared. The effects of the initial slits, various cross sections, side lengths, number of fiber fabric layers, resin type, fiber fabric type and angle of polygon dies on the splitting and curling of the structures are investigated. The results of this study reveal that alternating cross sections of columns may affect deformation modes and energy absorption parameters.

This paper introduces a new method on cold metal forming of a circular metal tube into a structural profile and analyzes the process by theoretical and experimental methods. For this purpose, some thin-walled circular tubes of brass are laterally compressed on a U-shaped die with the quasi-static condition in two different conditions of empty and filled by polyethylene Teflon. A theoretical plastic deformation model is introduced, and an analytical relation is derived to predict required energy for performing the shaping process. To perform the experimental investigations, several specimens with different geometrical shapes and initial lengths of the Teflon filler and with different wall thicknesses, lengths, and diameters of circular tubes are prepared to study influences of each parameter on the forming process. Some deviation parameters are defined to check final cross-sectional shape of final productions. The cold forming process is performed by two different methods: single-stage and double-stage process. To investigate verity of the present theory, diagrams of forming energy-lateral displacement are compared with the corresponding theoretical predictions. The performed comparisons show that the theoretical relation estimates forming energy with a good accuracy. Finally, as an application, the produced thin-walled profiles are compressed between two rigid platens in the lateral direction and their energy absorption capacities are compared with the corresponding values of the simple circular tubes. The compared results show that when a circular metal tube is shaped into the structural profile, a new energy absorber part with higher energy absorption capability is achieved.

Teflon-pad shaping process of circular metal blanks into quasi-cup specimens is investigated by theoretical and experimental methods in the quasi-static condition. In the experiments, circular metal sheets are formed into the quasi-cup samples by compressing them between a Teflon-filled die and a rigid punch with desirable shape. To investigate influences of different parameters on the forming progress, 12 rigid punches with different dimensions, two blank material types of aluminum and galvanized iron, three blank thicknesses of 0.6, 1.1 and 1.5 mm, and two Teflon-fillers of PVC and polyurethane are used in several experimental tests. In the analytical part, theoretical deformation models of metal blank and Teflon-filler are introduced and based on energy method, energy absorptions by the blank and Teflon-filler are calculated to derive a theoretical formula for predicting total required energy of the forming process. For this purpose, several energy absorption mechanisms are considered in the blank and filler. Furthermore, predictions by theoretical equation are compared with the corresponding experimental tests to study the verity of the calculated formulas. Theoretical and experimental results illustrate change trend of forming energy with respect to blank thickness. Also, the performed forming tests show that when external cone angle of rigid punch with respect to the horizontal direction increases, forming energy increases nonlinearly; and when the depth of spherical part of rigid punch increases, the probability of rupture increases. Additionally, the experiments demonstrate that there is a direct relationship between the forming energy and flow stress of the blanks. Furthermore, experimental observations illustrate that forming energy of a certain blank with PVC Teflon-filler is higher than that of a similar specimen with polyurethane Teflon-filler; but, the probability of wrinkling decreases when PVC Teflon-pad is used as the filler; and it is advantage of PVC Teflon-filler with respect to polyurethane Teflon.

This article introduces a novel method to enhance energy absorption capability of thin-walled sections subjected to the quasi-static lateral loading by performing the saw cutting process on simple closed sections with rectangular columns and shaping them into open sections. For this purpose, some simple closed-sectional columns with square and rectangular cross-sections of aluminum were prepared and used to produce different types of open sections with different geometries and lip lengths through the saw cutting process on a face of the columns. Different paths were selected and performed for the saw cutting to obtain six types of square open section and five types of rectangular open sections with different forms of lips. Lateral compression tests between two rigid platens were employed to obtain variations of lateral load and absorbed energy versus lateral displacement and to calculate specific absorbed energy by thin-walled open sections during the flattening process. For each type of rectangular open sections, two similar specimens were prepared and one of them was compressed along the shorter edge and the other one was tested along the longer edge of the cross-section. Also, as benchmarks, some simple specimens with closed section were compressed in the lateral direction to compare their results with energy absorption capacity by the corresponding open sections. Experimental results show that in all types of square and rectangular open-sections, lip length has significant effects on energy absorption capability by the structure; and there is an optimum value for lip length of open section and the column with optimized length of the lips has the maximum absorbed energy. Furthermore, experiments reveal that rectangular open sections which are laterally compressed along their shorter edges absorb higher energy, in compression with the corresponding loaded specimens along the longer edges. Results show that maximum absorbed energy/mass belongs to a square open section of type A with rectangular lips and it is 2.68 times of the corresponding value of the similar closed section, as a valuable result.

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on Kirchhoff’s plate theory and nonlinearity of von Karman type is considered in strain–displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included, and some of the material properties are assumed to be temperature-dependent. A coupled system of equations is derived and a new semi-analytical solution is obtained using multiple time-scale methods. The effects of variation of small-scale parameter on the natural frequencies, deflections and response curve of DLGS are analyzed, and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics (MD) simulations are used to investigate different vibration behaviors of DLGS and calibration of the small-scale coefficient. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, environmental damping, length and thermal load are presented. The stability and occurrence of internal resonance between vibration modes around a stable buckled configuration are investigated.

This article studies on Teflon-pad forming process of circular metal blanks using a concave die by the experimental method. Influences of material type and thickness of sheets, depth and width of ring groove of the die and thickness of Teflon-pad on the forming process are investigated. For this purpose, several dies with different depths and widths of groove are machined from hardened steel. Some blanks were prepared from galvanized iron with thickness of 0.6 mm and the others were prepared from two different aluminum alloys with different thicknesses of 0.6, 1.1 and 1.5 mm. Blank is a circular sheet with diameter of 60 mm. Solid cylindrical Teflon pads with different thicknesses of 13, 15 and 23 mm are used in different tests. Blank is placed on a rigid die with a certain ring groove and solid cylindrical polyurethane Teflon is placed on top surface of the blank. Then, the mentioned system is placed between two rigid platens. During the test, punch moves with a constant velocity and polyurethane Teflon is compressed; so, the blank is shaped into desirable product. Experimental results show that when groove width of the die enhances, bending radius of a part of blank that is over the groove increases; so, required load for the forming process decreases. Also, the measurements indicate that at a certain punch displacement, required load for the forming process of thicker blanks are less than thinner one, and, created deformations in thicker samples are less than thinner blank.

This paper studies the ballistic limit velocity of empty rectangular columns under a blunt projectile penetration, theoretically and numerically. The deformation mechanism of the empty column is considered as plugging. The projectile is assumed to be a flat-ended cylinder without deformation. A new theoretical model of deformation is introduced, and based on the energy method, a theoretical formula is derived to estimate the ballistic limit velocity of the process. Numerical simulations of the penetration process of a blunt solid cylinder into the empty metal columns are performed using the LS-DYNA explicit solver. Different empty columns are used as the targets, and these columns are made from Weldox 460E steel and have different wall thicknesses (6, 7, 8 and 9 mm) and internal column edge lengths (60, 70, 80 and 90 mm). To validate the derived relation for the ballistic limit velocity, the results of the numerical simulations are compared with the corresponding theoretical predictions. Finally, the effects of some geometrical characteristics such as projectile diameter and mass on the perforation process and the ballistic limit velocity are discussed.

This paper studies the effects of polyurethane foam-filler on the axial splitting process of circular composite tubes under the axial quasi-static loading, experimentally. A shear mode of failure in circular composite tubes is initiated by crushing the tube onto a conical die to absorb the energy. The effects of conical die angle, number of fiber fabric layers, resin type and also, diameter and fiber fabric type of the tubes on axial load, energy absorption and specific absorbed energy by the structure are studied. Experimental results show that the polyurethane foam-filler increases energy absorption capability by the tubes. Also, it is found that in the investigated domain, composite tubes with smaller diameters are better energy absorbers, comparing with the composite tubes with larger diameters. Experiments show that foam-filled circular tubes under the axial compression in the splitting process works as good energy dissipater.

A new type of energy absorber called an expansion joint (i.e. a corrugated tube) is examined in this research. Several experiments are performed on three types of thin-walled specimen, namely circular tubes, preformed corrugated tubes and complete corrugated tubes, to investigate the energy absorption of steel specimens under different conditions for quasi-static lateral loading and axial loading. For this purpose, some steel specimens were compressed between two rigid platens in the axial direction, and the other specimens were laterally compressed. The preformed corrugated tubes and the complete corrugated tubes were produced by the hydroforming method. In each geometrical group of specimens, several tubes, which have different wall thicknesses, different inner diameters and different lengths and which are either empty or filled with polyurethane foam, were tested. Experiments show that, for a lateral load, the specific absorbed energies of the complete corrugated tubes are higher than those of the corresponding preformed corrugated tubes and circular tubes with the same characteristics. Tests show that, under lateral loading, a complete corrugated tube with a thicker wall and a smaller diameter is the optimum energy absorber system. Therefore, when a circular tube transforms into the corrugated tube, a better energy absorber system with a higher capability is achieved under lateral loading. Also, experiments show that, under axial loading, simple circular tubes with no forming process have higher specific absorbed energies than corrugated tubes do. Corrugated specimens have more controllable plastic deformation and a more regular deformation mode than simple tubes have. Tests under axial loading illustrate that, when the preformed corrugated tubes are filled with polyurethane foam, the specific absorbed energy increases by up to 74%. A comparison of the results on empty and filled specimens shows that, in some cases, the specific absorbed energies of corrugated tubes under lateral loading are higher than the specific absorbed energies of circular tubes under axial loading. This means that, by shaping the circular tubes into preformed corrugated tubes and complete corrugated tubes via the hydroforming process, a new thin-walled structure with a high specific absorbed energy during the lateral compression process is introduced.

In this article, some theoretical relations are derived to predict instantaneous crushing force and absorbed energy during initial fold formation in polyurethane foam-filled quadrangle tubes under the axial crushing load. Theoretical analysis is performed based on the energy method. In the theoretical analysis, crushing wavelength is considered as a constant parameter through the process and as a function of column geometrical dimensions. In the analytical calculations, interaction effects between the polyurethane foam and inner wall of quadrangle tubes are considered and a formula is presented to predict absorbed energy by the interaction effects. In the experiment part, some foam-filled specimens were prepared and axially crushed to obtain experimental diagram of crushing force versus axial displacement. Comparison of the theoretical predictions of crushing force and absorbed energy with corresponding experimental results showed a good agreement. Also, it was found that theoretical predictions by considering the interaction effects have a better correlation respect to the experiments.

This research involves the experimental study of lateral flattening of tubular structures. Main goals are investigations of the effects of geometrical discontinuities on energy absorption characteristics of these structures and finding new ways for increasing the energy absorption capacities. Three groups of specimens were investigated: square and rectangular aluminum columns, circular brazen tubes and circular composite tubes where some notches of different lengths were created on various positions of them. The specimens were compressed between two rigid plates during a quasi-static process and their energy absorption parameters were calculated using the testing machine’s data. Experimental results show that numbers of notches on walls of the structures may increase or decrease their energy absorption capability, depending on the notches positions. Square columns with notches on up and down sides are cases in which the amounts of energy absorption are more than their corresponding intact specimens. In most of the specimens, notches lengths had reverse relation with their energy absorption. Behaviors of composite tubes under lateral compression loading are more sensitive to the notches lengths than the other specimens. By changing the notches positions on walls of the specimens, the deformation mode and consequently the energy absorption capability can be determined which is the case that is studied in this research.

A new theoretical model of plastic behavior of circular metal tubes during the contraction process as a metal forming and energy absorber processes is presented in this study. Some theoretical relations are developed to predict the axial load versus the axial displacement of the contraction process, based on the theoretical model. Some quasi-static experiments were performed on circular aluminum and brazen tubes to validate the theoretical analysis. In this research, effects of tube radius, contraction ratio, tube wall thickness and angle of conical die on energy absorption characteristics of circular tubes under axial quasi-static loading are investigated by the experimental and theoretical methods. Results show that there is an admissible agreement between the theoretical results and experimental measurements. Experimental results show that there is a steady force during the end zone of the process which is an important factor in viewpoint of the energy absorption. Also, the steady force increases by increment of die semi-angle, tube radius, friction coefficient and the contraction ratio.

This article introduces a new metal forming process for creating a fold with a controllable and certain wavelength into the circular metal tubes during the axial compression. Also, a new analytical model of plastic deformation of the circular metal tubes constrained between two rigid punches subjected to quasi-static axial loading is introduced. Based on the deformation model, some theoretical relations are derived to predict the instantaneous axial load of a complete fold creation into the tubes versus the axial displacement in the elastic and plastic zones. Four different mechanisms of energy absorption are considered in the present theoretical model: two kinds of bending mechanism around circular hinge lines, circumferential expansion and unbending mechanism corresponding to meridian strain. Theoretical prediction shows that the required axial load for creating a complete fold in a constrained metal tube between two rigid punches is dependent on the tube wall thickness, internal radius and initial free length of the tube and also tube material properties. Also, some quasi-static axial compression tests were performed on the circular tubes of brass and aluminum alloys between two rigid punches, and the results were compared with the theoretical predictions that showed a reasonable agreement. Furthermore, the experimental observations show that wavelength of a complete created fold into the circular tubes could be controlled using two rigid dies during the folding process and using the poly(vinyl chloride) Teflon as the filler, instead of the intrinsic wavelength of the tube.

This article performs an experimental analysis on the E-glass/polyester and vinylester composite tubes with circular cross-section subjected to the lateral compression loading during the flattening process in three different filling conditions: empty, polyethylene, and polyurethane Teflon-filled. Energy absorption behavior and failure response of the composite tubes during the lateral compression tests in the quasi-static condition are studied. The effects of Teflon-type, Teflon-filling, Teflon wall thickness and length, tube inner diameter, fiber fabric layer, and tube length are investigated on the crashworthiness parameters of lateral load, total absorbed energy, and specific absorbed energy (SAE) of the circular composite tubes. The experiments introduce the cylindrical polyethylene Teflon with the large wall thickness as the appropriate filler into the composite tubes, but the experimental measurements show that filling the tubes by the polyurethane Teflon-filler has undesirable effects on the mechanical behavior of the flattened specimens. Also, according to the flattening tests, it is found that in the polyethylene Teflon-filled specimens, the tubes with the vinylester resin have the higher SAE, compared with the corresponding specimens with the polyester resin.

In this study, indentation of circular metal tubes during lateral compression process between a V-shape indenter and a rigid platen is investigated by the experimental and theoretical methods. A new analytical model of plastic deformation in the circular metal tubes during the process is introduced and the theoretical analysis is performed based on the energy method and several relations are derived to predict the average lateral load and absorbed energy by the tubes as functions of lateral displacement, geometrical characteristics, and material properties of the tube. Also, to verify the theoretical analysis, some lateral compression tests were performed on circular metal tubes and the results were compared with the corresponding theoretical predictions. The comparison shows a good agreement between the theoretical predictions and experimental results and so, it confirms general form of the present theoretical formula. Also, effects of each geometrical dimension and material properties of the tubes on the average lateral load are investigated using the experimental measurements and the theoretical predictions.

In this article, a new analytical model of plastic deformation during the flattening process on hexagonal metal columns under the lateral loading in the quasi-static condition is presented. Based on the introduced model, some theoretical relations are derived to forecast the average and instantaneous lateral load of the hexagonal column in two different conditions: empty and polyurethane foam-filled. Then, some lateral compression tests were carried out on the empty and foam-filled metal columns and the experimental results were compared with the theoretical predictions by the present formulas that showed an admissible correlation. The theoretical relations estimate variations of the lateral load in terms of lateral displacement. The theoretical analysis shows that the lateral load on the hexagonal column during the flattening process is dependent on the column wall thickness, column length, and material properties of the column and polyurethane foam-filler. Finally, the effects of geometrical characteristics of the hexagonal columns and material properties of the columns and foams on the lateral load are investigated, experimentally.

This article presents a novel method to improve energy absorption performance of thin-walled circular tubes under quasi-static lateral loading through the preforming process. Desirable investigations are carried out by experimental tests and numerical simulations. Firstly, simple circular tubes are shaped into four different types (P1–P4) of preformed specimens, using a semi–cylindrical Teflon die and various blade-shaped indenters with semi–cylindrical nose. Then, the preformed specimens are laterally compressed between two rigid platens to perform flattening tests and their mechanical behaviors are investigated during the lateral flattening experiments, based on viewpoint of energy absorption. Some experiments are carried out and due to the test limitations, numerical simulations are performed, using the ABAQUS/Explicit software. In the following, based on the finite element analysis, various preformed specimens with different geometrical characteristics are simulated to investigate influences of wall thickness, preformed type and internal spanof the specimen cross–section and also, effects of loading direction on energy absorption performance of the preformed specimens. Also, some simple circular tubes are flattened as the benchmark and results of four types of the preformed samples are compared with the corresponding benchmark. The obtained results illustrate that by shaping the simple circular tubes into the preformed specimen, a new hollow prismatic samples are produced that their energy absorption capability is 11.5 times of the corresponding value of the benchmark; consequently, the present article suggest the preformed specimens of various types instead of the corresponding simple circular tubes, as better energy absorber.

This paper presents a theoretical and experimental study on lateral compression of square and rectangular metal columns. Some theoretical relations are derived to predict the absorbed energy, the specific absorbed energy and the instantaneous lateral load during the lateral compression. Analytical relations are obtained in two stages: elastic and plastic parts. In the plastic zone, the total absorbed energy by the column is calculated, based on the energy method. Then, an analytical equation is derived to predict the instantaneous lateral load. In the elastic part, the instantaneous load is obtained by linear behavior assumption. To verify the theoretical formulas, some lateral compression tests were carried out on square and rectangular columns and the experimental results are compared with the theoretical predictions, which shows a good agreement. Also, based on the experiments, effects of geometrical dimensions and material properties of the columns on the energy absorption capability are investigated. The results show that the absorbed energy by a column increases proportional to the column length. Also, columns with the thicker wall have the higher specific absorbed energy and so, rectangular columns with the thicker wall are the better energy absorbers during the flattening process. Also, the absorbed energy increases when the length of the column edge along which the load is applied decreases. Also, it is found that the specific absorbed energy by the aluminum columns is higher than the brazen ones and therefore, flattened columns with the high ratio of the flow stress/density are the better energy absorbers.

This article derives some theoretical relations to predict the instantaneous axial force of the circular metal tubes during the splitting process under the axial compression by the theoretical and experimental methods. A new theoretical model of splitting deformation of the circular tube as a thin-walled structure subjected to the axial loading is introduced and based on the deformation model and using the energy method, some analytical formulas are derived to estimate the instantaneous axial load, maximum splitting load, steady force and curl radius of the tubes. To verify the present theory, some aluminum, mild steel and brazen tubes with the circular cross-section and different geometrical and material characteristics were prepared and axially compressed on conical dies with the different cone angles. Comparison of the theoretical predictions and the experimental measurements shows a good correlation and it affirms verity of the new theoretical deformation model and the present theory. Also, based on the experimental results, the effects of wall thickness and inner radius of the tubes and also, number and length of initial slits and semi-angle of conical die are studied on the axial load and maximum splitting load.

This paper introduces a new theoretical model of plastic deformation during the inversion process on the capped-end frusta using a solid cylindrical punch. Based on the theoretical deformation model, the instantaneous axial load versus the displacement during the inversion process of the capped-end frusta is predicted. In the analytical model, the inversion process is divided into two different stages including plastic deformation of the frusta bottom and inversion of the frusta wall. Also, instantaneous absorbed energy versus the axial displacement and maximum inversion load during the process are estimated using the theoretical model. Some axial inversion experiments were carried out on capped-end conical tubes with different materials and geometrical dimensions to verify the present theory. A good agreement between the theoretical predictions and the experimental results affirms precision and accuracy of the new theoretical model and the analytical formulas.

This paper presents quasi-static crushing performance of empty and polyurethane foam-filled E-glass/vinylester composite tubes with different geometrical characteristics to use in sacrificial cladding structures. Some empty and foam-filled tubes were compressed laterally between two rigid plates. The effects of polyurethane foam-filler on the crushing characteristics and the corresponding energy absorption by the composite tubes are investigated. Composite tubes with three different fiber fabric layers were considered to study the influence of polyurethane foam on the crushing performance. Also, effects of different geometrical characteristics on energy absorption by different tubes are studied. Experimental results show that the presence of polyurethane foam inside the composite tubes suppresses the circumferential delimitation process and fiber fracturing; consequently, it increases the specific absorbed energy by the composite tubes during the flattening process. Also, it is resulted that injection of the polyurethane foam in the tubes causes the more regular deformation mode, comparing with the empty tubes. Finally, experimental results of the present work are compared with some of the previous articles that were investigated the foam-filled composite structures under the different loadings to suggest an optimized energy absorber.

This article derives some theoretical relations to predict diagrams of absorbed energy and axial force versus axial displacement during the folding process in square and rectangular columns. By considering the folding wavelength as a constant parameter during the folds creation and using balance of internal and external energy and minimum principle in plasticity, final relations are calculated. Also, two different relations are introduced to predict the maximum folding force of the empty and polyurethane foam-filled columns with square and rectangular cross sections, by considering the interaction effects between column wall and foam-filler. Furthermore, some experiments were carried out on the empty and foam-filled metal columns and the experimental measurements were compared with predictions of the theoretical formulas that showed good correlation.

This article introduces a new theoretical model of deformation and based on the energy method derives a new theoretical relation to predict the axial load versus the axial displacement during the external inversion process in the circular metal tubes. Several deformation mechanisms are assumed in the theoretical model: bending around circular hinge line, bending in normal to meridian direction and circumferential expansion. A total inversion process in the tubes is divided to three different stages versus the inversion angle, θ: 0 ⩽ θ ⩽ π, π ⩽ θ ⩽ 2π and after θ = 2π. In each stage, the total dissipated energy is calculated by different deformation modes. The different strain components are calculated and based on the principle of energy conservation; some theoretical relations are derived to predict the instantaneous inversion force. Then, some circular brazen tubes are used in the external inversion tests with die radiuses of R = 2.85 mm and 4 mm and diagrams of axial load versus the axial displacement are sketched. Comparison of the theoretical predictions and the experimental results shows a reasonable correlation. The theoretical relations can predict variations of the axial load versus the axial displacement of three considered stages during the whole inversion process with a good agreement. Comparison of the theoretical and experimental curves shows a better correlation in the horizontal part and position of start point of the inversion process with the die radius of R = 4 mm, comparing with the inversion process with the die radius of R = 2.85 mm. Also, the theoretical analysis shows that the absorbed energy and the axial load during the inversion process in the circular tubes depend on the wall thickness and diameter of the tube, tube material type, and the die radius.

In this article, a theoretical relation is derived to predict the folding wavelength in the square and rectangular columns under the axial loading. For this purpose, a new deformation model of the columns during the folding progress is introduced. Based on the energy method, final equation is obtained. The derived relation shows the folding wavelength is dependant on the wall thickness and the edge length of the columns cross section and is independent of the column material. Some static folding tests are performed on the square and rectangular columns. Finally, the predictions of the theoretical formula are compared with the experimental results for which good agreement is observed.

In this article, some theoretical relations are derived to predict the mean folding force, total absorbed energy per unit of tube length and specific absorbed energy per unit of total mass by the polyurethane foam-filled grooved tubes with circular cross section under the axial compression process. During the folding process, a new theoretical model of deformation is introduced for the polyurethane foam-filler. The theoretical analysis is developed on the basis of the energy method. Some foam-filled grooved specimens were prepared and axially compressed to obtain the experimental diagram of the folding force versus the axial displacement. Comparison of the theoretical predictions with the experimental results showed a good agreement. Then, by considering the interaction effect between the polyurethane foam and the inner wall of grooved tubes, a semi-empirical relation was derived. Predictions along with considering the interaction factor obtained from the semi-empirical relation indicate a better correlation with those of the experiments.

This paper investigates the effect of polyurethane foam-filler on the lateral plastic deformation in the circular tubes under radial quasi-static loading, experimentally. For this purpose, the specimens were prepared with five different diameters and thicknesses. For each constant diameter of specimens, several tubes with different lengths were prepared. All geometrical groups of specimens in the lateral compression tests (flattening) were used in empty and polyurethane foam-filled conditions. The effect of length, diameter and wall thickness of tubes on the lateral load, energy absorption and the specific absorbed energy were studied. The experimental results show that the polyurethane foam-filler increase the energy absorption capability of tubes and furthermore the increment of the energy absorption in thinner tubes is more than thicker specimens. Results show that using the polyurethane foam in the circular tubes under the lateral compression works as an excellent filler.

In this paper, the effects of the fillers in the rubber-filled circular tubes are investigated during the inversion process of the tubes under the axial loading, experimentally. For this purpose, a comparison between the experimental results of the empty and rubber filled circular tubes was performed. The inversion tests were carried out on the rubber-filled and empty brazen circular tubes. A pair of die and punch was prepared as the fixtures. All the inversion tests are performed under quasi-static axial loading. The experimental results of the filled tubes show a considerable increase in the energy absorption and the axial force comparing with the empty tubes, during the tube inversion process. The filler material in the circular tubes was supplied from the wastage of the tire producer companies. This is one of the best applications of the tire wastage that has good environmental and economical advantages. The tire wastage filled-tubes are introduced as a good energy absorber that can be used in the energy absorption mechanisms such as automobile bumpers, crashing barriers of roadsides, and aerospace.

This paper presents a theoretical formula to predict the instantaneous folding force of a polyurethane foam-filled square column as a single unit of square honeycombs under axial loading. For this purpose, sum of the dissipated energy rate under folding deformations of the square column and the dissipated energy rate of polyurethane foam compression was equated to the work rate of the external force on the structure. The dissipated energy rate of compression and deformation of polyurethane foam was obtained by presenting a new deformation model and through the reduced volume ratio. The final formula obtained, reasonably predicts the instantaneous folding force of the polyurethane foam-filled square column. Finally, according to the calculated theoretical relation, the instantaneous folding force of the foam-filled square column was sketched versus the axial displacement and compared to the experimental results, which showed a good correlation.

In this paper, a theoretical formula is presented to predict the instantaneous folding force of the first fold creation in square and rectangular columns under axial loading. The rectangular column is a small and single model of honeycombs with square or rectangular cells. Calculations are based on the analysis of the Basic Folding Mechanism (BFM). For this purpose, sum of the dissipated energy rate under bending around horizontal and inclined hinge lines and the dissipated energy rate under extensional deformations was equal to the work rate of the external force on the structure. The final formula obtained in this research, reasonably predicts the instantaneous folding force of single-cell square and rectangular honeycombs instead of the average value. Finally, according to the calculated theoretical relation, the instantaneous folding force of the first fold creation in a square column was sketched versus folding distance and compared to the experimental results, which showed a good correlation.

This article calculates a theoretical formula to predict the instantaneous folding force of the first fold creation in a single cell hexagonal honeycomb under axial loading. For this purpose, the sum of dissipated energy rate under bending around horizontal and inclined hinge lines and that under extensional deformations was equated to the work rate of the external force on the column. The final formula reasonably predicts the instantaneous folding force of the first fold of the thin-walled hexagonal columns during the folding progress. Finally, according to the calculated theoretical relation, the instantaneous folding force of the hexagonal column versus the axial displacement was sketched, and the comparison to the experimental results showed a good correlation.