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1、CHAPTER 1 INSTRODUCTION11. INTRODUCTION1.1. Elasticity and plasticityEssential properties of deformable bodies subjected to external force or other external action are elastic and plastic behavior. As discussed in the discipline of mechanics of materials, that is, if the external forces producing de
2、formation do not exceed a certain limit, that is so called yield criteria, the deformation disappears with the removal of the forces, then we consider this properties as elasticity. Otherwise, the deformation do not disappeared after removal of the forces, then we consider the property as plasticity
3、. Another main difference between perfect elasticity and plasticity, in mathematical view, is a linear problem and a nonlinear problem, respectively. The atom forces in the material internal structure determine the mechanism of this two kind deformation. In fact, the internal structure of solid mate
4、rials is always stable, on the basis of balance forces between atoms in solids. The suction force makes the atoms tend to close up to each other, and the repulsion force makes the atoms maintain some reasonable distance. In normal cases, these two forces are in Equilibrium State. Atomic structure wi
5、ll not be considered here. It will be interested in the macroscopically response only. When a solid body is subject to external loading, there are two different responses: elastic response and plastic response. Elastic deformation is a simple case easy to be understood. Plastic deformation is a more
6、 complex case. Figure 1.1 show the typical curve for a simple tension specimen of metal. The initial elastic region generally appears as a straight line OA, where A defines the limit of proportionality. On further straining, the relation between stress and strain is no longer linear but the material
7、 is still elastic, and upon release of the load, the specimen reverts to its original length. The maximum stress point B at which the load can be applied without causing any permanent deformation Fig.1.1 Stress-strain diagram for an annealed cast-steel specimen.CHAPTER 1 INSTRODUCTION2(a) (b)(c) (d)
8、Fig. 1.2 Stress-strain diagrams: (a) ductile metal, (b) cast iron and glass, (c) typical concrete or rock,(d) soils, triaxial compression. (Experimental data taken from reference 15.)defines the elastic limit. The point B is also called the yield point, for it marks the initiation of plastic or irre
9、versible deformation. Usually, there is very little difference between the proportional limit, A, and the elastic limit, B. The behavior in the flat region BC is generally referer to as plastic flow. After C the material is exhibited strain hardening or also known as work hardening. Over some point
10、D the material may be exhibit strain softening, as shown in figure 1.1. Now, consider the unloading from some point E beyond the yield point. The behavior is as indicated in figure 1.1. That is, when the stress is reduced, the strain decreases along an almost elastic unloading line OA .So we say tha
11、t the unloading obey the elastic rule. Fig. 1.2 is the typical graph of stresses versus relative elongation (compression) for four kinds of materials.CHAPTER 1 INSTRODUCTION31.2. Basic hypothesisThe subject of theory of elasticity and plasticity is concerned with the deformation and motion of elasti
12、c-plastic bodies or structures under the action of applied load or other disturbances. The general assumptions employed in the study of theory of elasticity and plasticity are the same as those used in the mechanics of continuous medium. Therefore, throughout this book, we have: (a), continuum hypot
13、hesis, we shell suppose that the macroscopic behavior of the solid bodies is the same as if they were perfectly continuous in structure; and physical quantities such as the mass and momentum associated with the matter contained within a given small volume will be regarded as being spread uniformly a
14、nd without any caves, cracks and discontinuous.(b), Uniform hypothesis and isotropic hypothesis, that is, the materials of elastic-plastic body is homogeneous and uniformly distributed over its volume so that the smallest element cut from the body possesses the same specific physical properties as t
15、he body. The elastic properties are the same in all directions. (c), small deformation hypothesis, in this book, we discuss small deformation only.1.3. Historical remarks Before the engineering design of structures, one must not only know the internal force field acting on the structural material an
16、d but also know the material response. It means that we need give an analysis of the stresses, deformation and displacement of structural elements. Therefore we have to know the constitutive relation of materials. Seeking some methods to solve these problems, many researchers have continually studied for over 2000 years. The pioneering works of theory of elastici
