Introduction

With the rapid development of all kinds of transport vehicles, the lives lost and high cost of traffic accidents are of serious concern to modern society. The public is becoming increasingly aware of the safe design of components and systems with the objective of minimizing human suffering as well as the financial burdens on society. At the same time, many other issues in modern engineering, e.g., nuclear plants, offshore structures, and safety gear for humans, also require us to understand the dynamic behavior of structures and materials.

Driven by the needs of engineering, the dynamic response, impact protection, crashworthiness, and energy absorption capacity of various materials and structures have attracted more and more attention from researchers and engineers. As a branch of applied mechanics, impact dynamics aims to reveal the fundamental mechanisms of large dynamic deformation and failure of structures and materials under impact and explosive loading, so as to establish analytical models and effective tools to deal with various complex issues raised from applications.

In the classical theories of elasticity and plasticity, usually only static problems are of concern, in which the external load is assumed to be applied to the material or structure slowly, and the corresponding deformation of the material or structure is also slow. The acceleration of material is very small and thus the inertia force is negligible compared with the applied external load; hence the whole deformation process can be analyzed under an equilibrium state.

However, it is known that the material behavior and structural response under dynamic loading are quite different from those under quasi-static loading. In engineering applications, the external load may be intensive and change rapidly with time, termed intense dynamic loading; consequently, the deformation of material or of a structure has to be quick enough under intense dynamic loading. Some examples are given in the following.

The collision of vehicles. Cars, trains, ships, aircraft, and other vehicles may collide with each other or with surrounding objects during accidents. These accidents will lead to the failure or deformation of the structures as well as personnel casualties, resulting in serious economic losses. As the number of cars has rapidly increased in many countries, car accidents have become the number one cause of death in the world. Collisions between ships and collisions between ships and rocks/bridges all cause huge economic loss as well as environmental pollution. Along with the development of high-speed rail transportation, the safety of occupants is also of greater public concern. It is very dangerous if a bird impinges on the cockpit or engine of an airplane, as the relative velocity between bird and airplane could be high even though the speed of the bird is not great. More and more space debris has been produced as a result of human activities, and the relative velocity of space debris to spacecraft can be as high as 10?km/s, so there would be great damage in the case of a collision.

Damage effects of explosive. Buildings, bridges, pipelines, vehicles, ships, aircrafts, and protective structures could be subjected to intensive explosion loading, due to industrial accident, military action, or terrorist attack. Typically, these structures would be suddenly loaded by a shock wave propagating in the air.

The effects of natural disasters. Natural disasters, such as earthquakes, tsunamis, typhoons, floods and so on will produce intensive dynamic loads to structures, e.g., dams, bridges, and high-rise buildings. These intense dynamic loads are likely to cause damage to the structures.

The strong dynamic loads caused by the local rupture of the storage structures. In nuclear power plants or chemical plants, if there is local damage to a pipeline, the jet of high-pressure liquid that would escape from the broken section exerts a lateral reaction force (the blowdown force) on the broken pipe, causing rapid acceleration and large deformation, termed "pipe whip". After local damage, the consequences from a pressure vessel or a dam could be disastrous.

Load of high-speed forming. During a dynamic metal forming process, such as explosive forming and electromagnetic forming, the work-piece is subjected to intensive dynamic loading and deforms rapidly. Similar situations take place in the process of forging or high-speed stamping.

Impact or collision in daily life and sports. For example, falling objects, falling on the ice, collision between moving people, a football or golf ball hitting the head or body with high speed.

All kinds of the above-mentioned problems encountered in engineering or daily life require the understanding and study of the behavior of the solid materials and structures subjected to intensive dynamic loads. First of all, why is the dynamic behavior of materials and structures usually different from the quasi-static behavior? This is the result of three major attributes in mechanics, as briefly illustrated here.

Stress wave propagation in material and structure. When a dynamic load is applied to the surface of a solid, the stress and generalized deformation will propagate in the form of stress wave. If the disturbance is weak, it is an elastic wave; but if the stress level of wave is higher than the yield strength of the material, it will be plastic wave.

Suppose a solid medium has a characteristic scale of L, and the wave speed of its material is c. It is subjected to an external dynamic loading that has a characteristic time tc, e.g., the time period for the external load to reach its maximum value or time duration of the impulse. If , the stress and deformation distribution in this solid are not uniform; hence, the effect of stress wave propagation must be considered. For example, the characteristic scale of the crust is very large, so the effects of earthquake or underground explosion are mainly presented in the form of stress waves.

In a piling machine or a split Hopkinson pressure bar device (SHPB for short - an important experimental technique in studying the dynamic properties of materials; refer to Chapter 3 for more details), the perturbation is along the longitudinal (large scale) direction of a long bar rather than in the radial (small scale) direction. Hence wave reflection, transmission, and dispersion are important factors that need to be analyzed carefully.

By contrast, some other structural components that are widely used in engineering, such as beams, plates, and shells, are usually subjected to lateral loads along their thickness direction, which is the smallest scale direction of the structure. The elastic wave speed in metals is usually in the order of several kilometers per second (e.g., 5.1?km/s for steel). Therefore, in several micro-seconds all the particles in the thickness direction of the structure will be affected by the external disturbance, and then the entire section of structure will be accelerated and then move together. This global motion of the whole cross-sections of the structure is classified as the elastic-plastic dynamic response of the structure; this is discussed in detail in Part 3 of this book. This subsequent global structural response may last several milliseconds or even several seconds, depending on the type of structure and loading, before the structure reaches its maximum deformation.

Because the effective time of stress wave propagation is usually several orders of magnitude smaller than that of the long-term structural response, the total response of the structure can be divided into two decoupled separate stages. That is, in the analysis of wave propagation, the structure is assumed to remain in its original configuration, which is regarded as the reference frame for geometric relations and equations of motion, while in the analysis of structural response, the early time wave propagation is disregarded and only its global deformation is considered.

Rate-dependency of a material's properties. The material in a solid or structure will deform rapidly under intensive dynamic loading. Depending on the microscopic deformation mechanism, the resistance of material to rapid deformation is generally higher than that to slow deformation, as revealed by numerous experiments on materials. For example, the mechanism of plastic deformation of metals is mainly attributed to the movement of dislocations. The resistance to the dislocation motion will be much higher when the dislocation passes through the metal lattice at a high speed than at a low speed, and this will lead to the higher yield stress and the high flow stress of metals during high-speed deformation.

An important task in the study of dynamic properties of materials is to summarize the effect of strain rate on the stress-strain relationship, based on the experimental data, so as to establish the strain rate-dependent constitutive relation of materials. As the strain history and instantaneous strain rate of the material elements inside a structure vary with position and time, the dynamic constitutive relation has to be simplified to a large extent when it is applied to dynamics analysis of structures.

Inertia effect in structural response. In the analysis of dynamic response of a structure, usually both elastic deformation and plastic deformation exist, and the boundary between elastic-plastic regions changes with time. Therefore, different constitutive relations should be...