A study on buckling of thin conical frusta under axial loads

Experiments were performed wherein conical frusta of aluminium of thicknesses between 0.7 and 1.62 mm and semi-apical angles range of 16–29° were axially compressed in a universal testing machine. The load–deformation curves and deformed shapes of specimens were recorded. These deformed in axisymmetric concertina mode and non-symmetric diamond modes.A three dimensional numerical simulation was carried out for all samples tested under quasi-static loading using ANSYS^®. Various stages of collapse of the shell, including non-symmetrical lobe formation were simulated for the first time, and material, geometric and contact non-linearities were incorporated. The plastic region of the material curve was assumed to be piecewise linear. Tensile tests were performed on standard samples to obtain stress–strain curves. Results thus obtained compared well with the experiments.Based on the formation of rolling and stationary plastic hinges an analysis was also carried out to study the behaviour of shells under axial compression and results were compared with experimental and numerical results.     

Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression

In the present study, crashworthiness characteristics of thin-walled steel tubes containing annular grooves are studied. For this purpose, the grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are controlling the buckling mode and predicting energy absorption capacity of the tubes. To do so, circumferential grooves are cut alternately inside and outside of the tubes at predetermined intervals. Quasi-static axial crushing tests are performed and the load-displacement curves are studied. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. It is found a good agreement between the theoretical results and experimental findings. The results indicate that the load-displacement curve and energy absorbed by the axial crushing of tubes could be controlled by the introduction of grooves with different distances. Also, grooves can stabilize the deformation behavior and thus, the proposed method could be a good candidate as a controllable energy absorption element.     

Inward inversion of capped-end frusta as impact energy absorbers

Results of an experimental investigation on the quasi-static axial inward inversion of right circular frusta are given. Effects of wall thickness, frustum angle and material on inversion were studied by quasi-static as well as drop hammer dynamic tests. Finite element (FE) modeling and analysis of the deformation modes are presented. The results of the experimental and the FE analyses are discussed. A good agreement is reported between the force histories predicted by the FE study and the experimental results.     

Study of the behaviour of schist grains under crushing

Schist is abundant in the Kabylia region of Algeria and hence its use for civil engineering applications, particularly in pavements, is desirable. The paper reports a study on three of the more common schists to determine the characteristics controlling the mechanical behaviour of these materials. The geological and engineering properties of the schists are described and it is concluded that anisotropy is a more important influence than the mineralogy. Of the three schists studied, the harder minerals present in the mottled schist make this the most applicable for use in pavements.      

Mathematical modeling of axial crushing of cylindrical tubes

Different aspects of mathematical modeling for the axial crushing of cylindrical tubes with straight fold have been discussed. The variation of circumferential strain during the formation of a fold has been taken into account. The present paper tries to answer questions such as (a) how great is the inside and outside folding, and (b) how the crushing load varies. In the present paper, the influence of the consideration of the conservation of mass on the mathematical formulation has been studied. The results of average and varying circumferential strain have also been compared.     

Quasi-static axial and lateral crushing of radial corrugated composite tubes

This paper presents the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tube. Experimental investigations were carried out on three geometrical different types of composite tubes subjected to axial and lateral compressive loadings. On the addition to a radial corrugated composite tube, cylindrical composite tube, and corrugated surrounded by cylindrical tube were fabricated and tested under the same condition in order to know the effect of corrugation geometry. The results showed that the loading carrying capability is significantly influenced by corrugation geometry in axial crushing. However, no affect of corrugation geometry was observed for lateral crushing. Load–displacement curve was plotted for all conducted tests, thus clear comparison between different specimen's geometry was achieved. It is also found that radial corrugation could significantly applicable as a stable and effective energy absorber.     

Influence of end constraints on the collapse of axially impacted frusta

The energy absorption performance of right circular frusta subjected to dynamic axial load is studied and compared with the results of quasi-static tests. Frusta of different geometric ratios and end constraints were axially crushed using a drop hammer at initial velocities in the range of 2–5 m s. The effect of heat treatment on the collapse behaviour and energy absorption is also investigated. The experimental observations indicate that the effects of end constraints and heat treatment on energy absorption were qualitatively similar to those observed under quasi-static testing. Due to inertia effects, the absolute values of the energy absorbed by similar frusta were higher under dynamic loads than under quasi-static loads. It has been established that constraining the frusta enhances their energy absorption capacity under static and dynamic loading particularly at the top (smaller diameter). The optimum geometric parameters for maximum energy absorption performance are identified when residual stresses and strain hardening characteristics, arising from spinning the frusta, were removed.     

Curved fold model analysis for axi-symmetric axial crushing of tubes

In the present paper, a plastic curved fold model with partly inside and partly outside folding and variable straight length has been developed. The variation of circumferential strain with change in the hinge angle during the formation of a fold has been taken into account. The size of fold and proportions of inside and outside fold lengths have been determined by minimizing the average crushing load. The mean, as well as the variation of crushing load, have been computed. Most of the earlier straight as well as curved fold models can be easily derived from the present model. The maximum hinge angle and the final radius of curvature of fold have been determined mathematically. The validation with experiments provides reasonably good agreement. The results are of great help in understanding the phenomenon of actual fold formation.     

Crashworthiness investigation of kagome honeycomb sandwich cylindrical column under axial crushing loads

For the classic thin-walled energy absorber, the energy dissipation during a collision is concentrated over relatively narrow zones. This means that a great deal of materials of the columns do not participate in the plastic deformation or not enter into the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, a new type of kagome honeycomb sandwich bitubal circular column is presented in this paper. This innovative impact energy absorber is made of two circular aluminum tubes filled with core shaped as a large-cell kagome lattice. The interaction effect, deformation mode and energy absorption characteristics of the composite structure are investigated numerically. Observing the collapsing process, it is found that the kagome lattices buckle first, which triggers the outer and inner skin tubes to fold locally. This behavior increases the plastic deformation areas. Moreover, the presence of the outer and inner tubes strengthens the buckling capacity of kagome cell. Furthermore, the folded tube walls intrude into the gap of the honeycomb cell, which further retards the collapse of the honeycomb cell. So the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. In addition, the effects of geometrical parameters of the kagome honeycomb on the structural crashworthiness are studied. It is found that the cell wall thickness and cell distribution (cell number in the circumferential direction) have distinct effects on the specific energy absorption. Besides, we also studied the foam-filled column with the same foam density as the kagome honeycomb and compared it with the kagome sandwich structure. It is found that the kagome sandwich column has higher mean crash force and better energy absorption characteristics.     

Comparisons of honeycomb sandwich and foam-filled cylindrical columns under axial crushing loads

For the conventional thin-walled energy absorber, the energy dissipation during a collision is concentrated in relatively narrow zones. This means that a great deal of material does not participate in the plastic deformation or enter the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, the authors presented a new type of honeycomb sandwich circular column. This innovative energy absorber is a composite structure composed of two circular aluminum tubes filled with core shaped as a large-cell honeycomb lattice. In this paper, six different honeycomb sandwich circular columns were investigated numerically. Comparisons of the interaction effect between tubes and filler, the deformation modes and the energy absorption abilities of these columns were conducted. The results were as following. The kagome sandwich column had the best energy absorption capability, followed by the columns sandwiched with triangle, hexagon lattices. In addition, foam-filled columns with different adhesive conditions were also simulated and compared with the honeycomb sandwich columns. It was found that increasing the adhesive strength improved the energy absorption and changed the deformation mode of the foam-filled columns. Furthermore, comparison showed that the honeycomb sandwich columns had higher specific energy absorption capability than the foam-filled tubes except for the strong bonded case. The kagome sandwich column performed best in crashworthiness, followed by triangle sandwich column.     

Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes

A comprehensive experimental and numerical study of the crash behavior of circular aluminum tubes undergoing axial compressive loading is performed. Non-linear finite element analyses are carried out to simulate quasi-static and dynamic test conditions. The numerical predicted crushing force and fold formation are found to be in good agreement with the experimental results. A summary of available analytical solutions is presented in order to estimate the mean crushing load and establish a comparison between these analytical loads and the experimental one. Some observations are made on the influence of geometrical imperfections and material strain rate effect.     

An analytical model for axial crushing of a thin-walled cylindrical shell with a hollow foam core

A thin-walled tube filled with light-weighted foam has wide engineering applications because of its excellent energy absorption capacity. When the structure is axially crushed, the interaction between the tube and foam core plays an important role in its energy absorption performance. Previous theoretical studies so far have largely been concerned with fully in-filled tubes. In this paper, a theoretical model is proposed to predict the axi-symmetric crushing behaviour of such structures but with a partial infill. Using a modified model for shell and considering the volume reduction for the foam core, the mean crushing force is predicted by the energy balance. The proposed formula agrees well with previous results reported in literature. A parametric study is carried out to examine the contribution of foam core plateau stress (σ_f), amount of filling and shell's radius-to-thickness ratio (R/h) on the axial crushing behaviour of the structure. This study can give valuable design guidelines in using thin-walled structures as an energy absorber.     

A numerical study of the influence of bump type triggers on the axial crushing of top hat thin-walled sections

This paper deals with the issue of a trigger design and its performance. In this respect, a numerical investigation is carried out to study the effects of the geometrical features of a bump type trigger on the crush behavior of an energy absorbing member subjected to axial impact loading. The member was constructed by joining a top hat profile with a flat lid. The trigger was considered to be a bump with a semi-circular cross section on the hat profile. The finite element solver, LS-DYNA was used in all crush simulations. As a result, the introduction of the trigger was found to be effective on the peak crush force and the energy absorption capability of the member under axial impact loading. It was also shown that the crush response could be controlled by varying the location and the geometry of the trigger.     

Experiments and theory on deck and girder crushing

This paper is concerned with theoretical and experimental analysis of deep plastic collapse of a deck or deep girder subjected to an in-plane, concentrated load. A theory is derived which is valid until initiation of fracture in the structure. The presented experimental results show load–deflection curves and modes of deformation for decks, stringer decks and deep thin-walled beams subjected to central or excentric point loads between transverse frames. Based on theory and experiments, various modelling aspects of the local/global failure of the beams are discussed. The agreement between the theoretical closed form solutions and the experimental results is good.     

Optimization of thin conical frusta for impact energy absorption

Experimental and numerical investigations were carried out to optimize thin-walled conical shells for their use in design for energy absorption. Geometrical parameters, such as bottom diameter, height, and semi-apical angle were considered to obtain the design space. The numerical analysis and impact experiments were designed using design of experiments (DOE). A three-level, second-order Box–Bhenken technique was used to select the design points from the design space. Various set of numerical simulations were carried out using LS-DYNA. To investigate the influence of flow stress of the material on the energy absorption, numerical simulations were carried out using frusta made of aluminium, zinc, and mild steel. From the numerical results, mathematical models were created using response surface methodology (RSM). With the help of impact experiments carried out on specimens made of zinc on a drop mass test rig, a mathematical model has been developed using RSM. The mathematical models developed using experimental data and the numerical data were used as objective functions for optimization of the design. The non-dominated sorting genetic algorithm code NSGA II was used to optimize the design. The mathematical models were also used to predict the energy absorbed and deformation. The influence of various design parameters on energy absorption has been analysed and is discussed.     

Axial crushing of flattened expanded metal tubes

This paper presents an investigation on the structural behavior of flattened expanded metal tubes subjected to axial crushing. At first, the study is carried out experimentally to investigate the effect of the angle formed between the expanded metal cell and the applied load. Secondly, the results are compared with experimental results for standard expanded metal sheets. Thereafter, numerical analyses are conducted by means of nonlinear finite element models, to investigate the enhancement in the energy absorption characteristics due to flattening of the expanded metal. Both results, experimental and numerical show a significant increase in energy absorbing capacity and mean force for the flattened tubes.     

考虑颗粒破碎效应的粒状材料本构研究：进展及发展

颗粒破碎会引起材料的压缩性变大及强度软化,因此颗粒破碎对粒状材料力学特性影响的研究非常重要。首先从试验研究方面着手,总结了颗粒破碎的描述方法、不同加载条件下（一维及等向压缩、三轴剪切、扭剪及单剪）应力应变的颗粒破碎效应;接着总结了考虑颗粒破碎效应的粒状材料力学本构模拟方法,即一维及等向压缩模型、三维剪切模型及基于离散元法的微观土力学模型。最后,通过大量试验结果分析并结合笔者近年来的研究成果,指出可破碎颗粒材料在应力应变过程中的颗粒级配变化可由修正相对破碎指数来表示,可通过塑性功来确定,且塑性功确定法的优越性还体现在循环加载下的累积破碎评价;然后再通过修正相对破碎指数,来确定临界状态线的位置,进而可通过当前状态与临界状态线的相对位置来评价颗粒破碎对颗粒材料力学特性的影响。所提出的以修正相对破碎指数为关键变量的本构方程可直接应用于考虑颗粒破碎效应的粒状材料静动力本构模型的开发。     

Cross-section crushing behaviour of hat-sections (Part II: Analytical modelling)

Hat-sections are often used to experimentally investigate building sheeting subject to a concentrated load and bending. In car doors, hat-sections are used for side-impact protection. For building sheeting, two types of crushing (by moving yield lines) exist. This article shows that cross-section behaviour can partly be used to explain total section behaviour. This is shown by finite element models of a very small strip dx of the hat-section. The quality of the finite element models for describing moving yield lines is verified.     

破碎处理对陶粒及其混凝土性能的影响

采用对比试验的方法研究了破碎处理对页岩陶粒及陶粒混凝土性能的影响,结果表明:通过破碎处理的方式可有效地改善陶粒的级配、减小颗粒粒径、提高筒压强度和堆积密度;使用破碎陶粒配制混凝土可显著提高混凝土的抗压强度,增强抗离析能力,改善工作性能,但对混凝土的热工性能有一定程度的不利影响。     

Axisymmetric particle-element coupled method for deformation problems of geomaterial

Although grid-based particle methods are widely used for engineering deformation problems, due to their robustness in large deformation analyses, the computational cost of these methods is quite high compared with mesh-based methods. In 3D problems, the computational cost becomes even higher, whereas some mechanical systems can be regarded as axisymmetric, allowing them to be modeled as two-dimensional axisymmetric entities, resulting in a reduced computation cost. In order to decrease the computational cost further, arbitrary spatial discretization has been introduced to reduce the degrees of freedom in the system. The Particle-Element Coupled Method (PEM), the coupled method of the Material Point Method (MPM) and the Arbitrary Particle Domain Interpolation (APDI) method, enables a system to be discretized in arbitrary spatial resolutions. In this paper, PEM is extended to axisymmetric problems, whose formulation and applicability to geomaterial deformation are presented. Firstly, the axisymmetric MPM simulation of a granular column collapse experiment and its efficiency in computation are reported. Secondly, in the simulation of footing penetration, it is shown that the axisymmetric MPM and the axisymmetric PEM can be used to analyze large deformations that cannot be analyzed by mesh-based methods, such as the Finite Difference Method (FDM). The axisymmetric PEM yields equivalent average pressure–displacement relationships and shear strain distributions, realizing a reduction in the computation cost by half as much.