Tubes are widely used structural components across various industries, including construction, transportation, space, and aerospace sectors. Energy absorption is a key performance indicator of tubes under axial crushing which is used to evaluate their ability to dissipate energy and protect the main structure and, in many cases, passengers. In this note, two dimensionless performance indicators for the crashworthiness of tubes, i.e., the energy-absorbing effectiveness factor (EAEF) and the effectiveness of energy absorption (EEA), are articulated and compared with some available experimental data.

Metal foams are extensively utilized in engineering due to their excellent energy-absorption capacity. The plateau stress and the densification strain of foams are the two key parameters for the energy absorbing capacity, which are conventionally gained by drawing data from the foams’ stress-strain curves, while they have been found to vary with the foam’s initial density and crushing speed. However, traditional force measurement methods require additional sensors that are often impractical in real applications. In our previous study (Hu et al., 2019), quasi-static experiments on open-celled metal foams demonstrated that instantaneous density—rather than initial density—governs the current stress, enlightening an innovative way to understand the foams’ mechanical behaviors. Under high-speed dynamic crushing, the shock-wave propagation dominates the deformation process with both stress and deformation distributed nonuniformly within the foam. In this study, based on the images obtained from numerical simulations and/or experiments, we examine whether the nonuniform stress distribution is correlated with the nonuniform deformation of the crushed foam by the relation between the current stress and the instantaneous density, which can be regarded as an inherent property of the foam as revealed in our previous study. Then we will show that both experiments and numerical simulations verified this hypothesis. According to the local density variation, the deformed foam is divided into three zones: densified zone, transition zone, and undeformed zone. Plateau stress at the impact-end and the support-end can be evaluated by the density of transition and undeformed zone, respectively, while the densification strain can be evaluated by the average density of the deformed zones (including densified and transition zones) during crushing. The evaluated results agree closely with experimental and numerical data, demonstrating that the dynamic mechanical properties of metal foams can be accurately evaluated using image-based density analysis, reducing reliance on direct force measurements.

An analytical model is developed to describe the dynamic response of a long beam made of a perfectly plastic material and resting on a Winkler-type elastic foundation. A localized rectangular pressure pulse is applied causing large deflections requiring the consideration of the interaction between the bending moment and membrane force in the beam. The previously developed Membrane Factor Method (MFM) is employed in analyzing the response of beams made of a strain-rate insensitive material while a modified membrane factor is introduced to consider the effects of the strain rate material sensitivity. The saturated phenomenon in the beam-foundation system is addressed when the influences of the beam and foundation stiffness characteristics on the saturated response of beams of a rectangular cross-section is examined. The various dependencies predicted by the analytical model and related to the saturated beam response are verified by numerical simulations.

Engineering structures can suffer severe local structural damage when subjected to extreme dynamic pulse loadings such as slamming impact. However, there is paucity of information on how the loading pulses affect the large plastic deformations. This paper presents information on an experimental investigation into the dynamic pressure pulse generated by slamming and the plastic response of metal plate. In our experiments, plates made of aluminum and steel alloy, were dropped from various heights ranging from 0.1 m to 1.3 m, onto the calm water in a tank. Based on the experimental results, the effects of structural material and water impact velocity on the slamming pressures pulse are investigated in detail. The results indicate that not only the peak pressure but also the pressure pulse duration play important roles in governing the dynamic response of the impacted structures. It is shown that the maximum strain and deflection at the plate center increase almost linearly with the drop height of the drop model. In view of the lack of previous experimental evidence for the saturation phenomenon of structures under slamming, we compared the dynamic response at the center of the plate with the experimentally measured slamming pressure under various drop heights, so that we have evidently verified the saturation phenomenon of flat plates for the first time under slamming in drop tests. It is also revealed that the dynamic response of the flat plates under slamming becomes more prone to the saturation phenomenon with the increase of drop height.

Nowadays, the need for protective devices at man–machine interfaces is increasing in the fields of traffic, sports, construction, and military, etc. Dynamic pressure sensing technology with wide measuring range, high sensitivity, softness, and fast response is crucial for evaluation and optimization of the personal protective equipment under impact scenarios. However, current sensors hardly possess all the aforesaid required characteristics. For the first time, this article reports the evaluation and application of an innovative soft pressure sensor with modulus of 2 MPa, maximum pressure of 8 MPa, and over 500‐Hz frequency. A theoretical model, taking strain rate into consideration, is established to characterize the dynamic sensing behavior. A sensing network in the form of smart clothing is developed and used in a sled crash test, which is a standard approach to evaluate the safety of automobiles in collisions. The pressure distribution over the dummy's surface during the crash is acquired in real‐time, and compared with numerical simulations. This study is important to the study of occupant injury and crashworthiness design for vehicles, and it will benefit the automotive industry. With the built‐in sensing network, the smart clothing has promising applications in the pressure mapping of 3D flexible man–machine interface under impact scenarios.

Metamaterials whose properties are inaccessible with conventional materials offer powerful tools for unprecedentedly manipulating physical signals. However, an effective design strategy of metamaterials still remains a challenge for changing the compression or tension characters of stress waves during forward propagation. Here, we introduce a class of spring-linkage–based metamaterials exhibiting mere tension output at the distal end, no matter that the input is an axial impact, a sudden tension, or even alternating tension-compression. The metamaterials can turn compressive waves into pure tension and filter them out from the tension-compression mixed ones while allowing tensile signal stably propagating in soliton form. This is achieved by combining nonuniform and nonlinear properties of the proposed cells. In particular, these extraordinary functions of the metamaterial can be turned on or off and adjusted by tuning a key switch cell; thus, it is anticipated to serve as a start for more complex manipulation and utilization of mechanical signals.

The impulse saturation of ship structures subjected to pressure pulse in blast and slamming has been taken into account recently in terms of the development of mechanical principles and phenomena. This article reviews the recent studies of the saturated impulse for ship structures under pressure pulse loading, including the modal approximation technique, the effect of transient response phase, membrane factor method, and so on. A newly proposed tool by combined membrane factor method (MFM) and saturation analysis (SA), which considers the transient response phase and exact yield condition, can provide more accurate predictions. In addition, based on the Youngdahl Equivalent Method (Y-EM) and Saturated Equivalent Method (S-EM) proposed earlier, a more effective and wide applicable method, named Progressive Equivalent Method (P-EM), is proposed. These studies have demonstrated that for long-duration pulse loaded structures, saturation analysis and pulse-equivalent method would be a superior option in structural design for performance improvement.

This chapter starts with the establishment of the fundamental equations of plates. Based on those fundamental equations and relevant boundary conditions, the limit analysis of axisymmetric bending of circular plates is conducted, particularly resulting in the limit loads of circular plates with simply supported and clamped boundary conditions. For noncircular plates, the procedure to obtain kinematically admissible solutions is illustrated, which provides the upper bound of related limit loads. When plates undergo large deformation, their load-carrying capacity is also analytically investigated, by using the Calladine method and membrane factor method, respectively. Finally, an example related to stamping of circular plates is presented in the context of large deflection analysis.

One of the main differences between the theory of elasticity and the theory of plasticity is in the relationship between stress and strain. The stress–strain relationship of the theory of elasticity is described by the generalized Hooke law, which readers are familiar with. In this chapter, we first summarize the features of the elastic constitutive relations, and then discuss the plastic constitutive relation based on Drucker's postulate, as well as the loading and unloading criteria. The emphasis is put on the widely applied incremental theory (flow theory), in which stress is related to increments of strain, while the deformation theory and the constitutive relation in rock-soil mechanics are also briefly illustrated.

Inspired by the microstructures of the bamboo culm wall, we propose a topological tubular honeycomb with structural hierarchy and subsequently demonstrate the outstanding energy absorption capabilities through experiments and numerical modeling. A theoretical model is developed and demonstrated to capture the fundamental structure-performance characteristics of the topology and structural hierarchy in bamboo-inspired tubular honeycombs. The energy absorption capacities of tubular honeycombs with different topological parameters and hierarchical orders are accurately predicted. Results reveal that the governing laws of the structural hierarchy, topological parameters, and their coupling effects on the energy performance of tubular honeycombs. Mechanism maps are also presented to offer insights for designing the next-generation energy absorbers and novel hierarchical/topological structures for energy absorption and impact resistance.

The determination of limit load (limit force or limit bending moment) for statically determinate beams has been illustrated in Chapter 6. In this chapter, the calculation procedure of limit load of statically indeterminate structures will be elaborated on. First, collapse mechanisms including plastic hinges and bound theorems in limit analysis of beams and frames are illustrated. Then, the kinematical method and statical method are presented with illustrative examples. Finally, the limit curve and its applications are demonstrated.

To demonstrate the influence of material plasticity on structural behavior, a statically indeterminate three-bar truss is studied in this chapter. By analyzing the plastic performance of the three-bar truss made of elastic, perfectly plastic material or linear hardening elastic-plastic material, the basic characteristics of structural plasticity are explored. The influence of large deformation on the load-carrying capacity of the truss structure and the effect of loading path on the stress and strain of the truss are described. Finally, the yield curve and limit curve on a load plane are introduced.

A solid body will deform under an external load. When the external load exceeds a limit, even after the load is removed, the deformation will not be completely recovered. This permanent deformation is known as plastic deformation. This chapter introduces the basic plastic properties of metallic materials, based on the stress–strain curves obtained from unidirectional tension/compression tests. The microscale structure of metallic materials and the physical mechanism of plastic deformation are briefly illustrated to facilitate the understanding of the experimental observations of metallic materials. Plastic instability during uniaxial tension is briefly discussed also. In accordance with the simplified assumptions on the plastic behavior of materials, a few idealized models for the stress–strain relationship are described.

In this article, the properties and applications of electro-rheological fluids in shock absorbers are systematically summarized. First, the rheological properties of ER fluids are briefly reviewed and mainly represented by Bingham-plastic model. Then, different characterization methods for their flow properties, such as yield stress, post-yield viscosity and response time, are described, showing that the capillary rheometer is more suitable for high strain-rate. Further, typical designs and the corresponding characteristics of the ER fluid shock absorbers in three different working modes, i.e., flow mode, shear mode and squeeze flow mode, are illustrated with the focus on the impact force and controllability index. Finally, some issues for the real applications are discussed, such as the modeling of dynamic response, controllability, durability and so on.

In the classical Alexander model for a rigid, perfectly plastic circular tube under axial progressive crushing, an expression for the average crushing force over one complete folding cycle was given in terms of the folding length while the value of the folding length was determined by minimising the average force. This approach is often misunderstood as a correct upper-bound method and has been widely used for analysing large plastic deformation of structures. In this paper, it is highlighted that Alexander approach is strictly not an upper-bound analysis and alternative analyses are presented. A new initial collapse mechanism involving folding both inwards and outwards of the tube wall is proposed for an upper-bound analysis, which leads to the determination of the folding characteristics such as the folding length. Subsequently, a repeatable mechanism is idealised for the periodic folding process. The upper-bound analysis is performed by minimizing the instant force required for maintaining the folding process, which is equivalent to adopting the energy balance for the incremental plastic deformation rather than the total deformation of one complete folding cycle. Instead of merely obtaining the average force as Alexander did, the present theoretical analysis gives a complete force-displacement curve as well as plastic folding length, etc., which agrees well with the existing knowledge. Furthermore, an equilibrium approach is presented involving detail stress state for a deforming configuration of the tube. The lower-bound results re-produce the variation of the force as obtained from the upper-bound analysis when the folding configurations are the same as those in the assumed collapse mechanisms. The present study conceptually reconciles the upper-bound and low-bound theories in structural plasticity for large deformation analysis.

今年是王仁先生百年诞辰,也是他逝世20周年.抚今忆昔,我同王仁先生的许多同事、学生和朋友一样,深深地缅怀先生的谆谆教导和深厚情谊. 我特别要怀念的是,在我学术人生中的几个重要关头,都是王仁先生伸出他温厚的手,给予关怀和扶助.

A corrugated sandwich panel consists of two face-sheets and a corrugated core, which is made of sheets that are folded into a corrugated shape. In this paper, the mechanical response of aluminium corrugated sandwich panels subjected to longitudinal loading along its middle line is investigated experimentally, numerically, and theoretically. A parametric study is conducted using ABAQUS/Explicit to examine the effects of geometric configurations (i.e., corrugation angle, core height, and core web thickness) on the deformation mode, peak force, and specific energy absorption (SEA) of panels. Two major deformation modes (Mode I and Mode II) are observed. The sandwich panels that deformed in Mode I has higher peak force and energy absorption ability. When the density of core remains the same, the energy dissipated by sandwich panels can be tailored by varying the geometry of the core. Thicker core webs result in greater energy absorption. Based on the experimental and simulation observations, a theoretical analysis using energy method is carried out to predict the crushing force of panels during large deformation.