Response of material

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

Machine components ate commonly subjected to loads, and hence stresses, which vary over time. The response of materials to such loading is usually examined by a fatigue test. The cylinder, loaded elastically to a level below that for plastic deformation, is rotated. Thus the axial stress at all locations on the surface alternates between a maximum tensile value and a maximum compressive value. The cylinder is rotated until fracture occurs, or until a large number of cycles is attained, eg, lO. The test is then repeated at a different maximum stress level. The results ate presented as a plot of maximum stress, C, versus number of cycles to fracture. For many steels, there is a maximum stress level below which fracture does not occur called the... 

Rheology is the science of the deformation and flow of matter. It is concerned with the response of materials to appHed stress. That response may be irreversible viscous flow, reversible elastic deformation, or a combination of the two. Control of rheology is essential for the manufacture and handling of numerous materials and products, eg, foods, cosmetics, mbber, plastics, paints, inks, and drilling muds. Before control can be achieved, there must be an understanding of rheology and an ability to measure rheological properties. 

Fowles, G.R. (1972), Experimental Technique and Instrumentation, in Dynamic Response of Materials to Intense Impulsive Loading (edited by P.C. Chou and A.K. Hopkins), pp. 405-480. 

In this section, we discuss the role of numerical simulations in studying the response of materials and structures to large deformation or shock loading. The methods we consider here are based on solving discrete approximations to the continuum equations of mass, momentum, and energy balance. Such computational techniques have found widespread use for research and engineering applications in government, industry, and academia. 

The chapter on equation-of-state properties provides the basic approaches used for describing the high-pressure shock-compression response of materials. These theories provide the basis for separating the elastic compression components from the thermal contributions in shock compression, which is necessary for comparing shock-compression results with those obtained from other techniques such as isothermal compression. A basic understanding of the simple theories of shock compression, such as the Mie-Gruneisen equation of state, are prerequisite to understanding more advanced theories that will be discussed in subsequent volumes. 

Finally, several chapters are provided which summarize the applications of shock-compression techniques to the study of material properties, and which illustrate the multidisciplinary nature of shock-wave applications. These applications include the inelastic response of materials, usually resulting from the extreme impact loads produced by colliding bodies, but also resulting from intense radiation loading. 

Dremin, A.N. and Breusov, O.N., Processes Occurring in Solids Under the Action of Powerful Shock Waves, Russian Chem. Rev. 37 (5), 392-402 (1968). Gilman, J.J., Dislocation Dynamics and the Response of Materials to Impact, Appl. Meek Rev. 21 (8), 767-783 (1968). 

Oscarson, J.H. and Graff, K.F., Summary Report on Spall Fracture and Dynamic Response of Materials, Battelle Memorial Institute Report No. BAT-197A-4-3, Columbus, OH, 37 pp., March 1968. 

Swift, H.F., Preonas, D.D., Dueweke, P.W., and Bertke, R.S., Response of Materials to Impulsive Loading, Air Force Materials Laboratory Technical Report No. AFML-TR-70-135, Wright-Paterson AFB, OH, 76 pp.. May 1970. 

As these problems were encountered in the past, it became evident that we did not have at hand the physical or mathematical description of the behavior of materials necessary to produce realistic solutions. Thus, during the past half century, there has been considerable effort expended toward the generation of both experimental data on the static and dynamic mechanical response of materials (steel, plastic, etc.) as well as the formulation of realistic constitutive theories (Appendix A PLASTICS DESIGN TOOLBOX). 

The designer must be aware that as the degree of anisotropy increases, the number of constants or moduli required to describe the material increases with isotropic construction one could use the usual independent constants to describe the mechanical response of materials, namely, Young s modulus and Poisson s ratio (Chapter 2). With no prior experience or available data for a particular product design, uncertainty of material properties along with questionable applicability of the simple analysis techniques generally used require end use testing of molded products before final approval of its performance is determined. 

It is useful to get preliminary learning on the mechanical properties of materials under simple static tension. Members of engineering structures are often subjected to steady axial loads in tension. Moreover, the response of materials subjected to other types of loading also can often be explained or predicted on the basis of knowledge of their behaviour under simple tension. In addition, such behaviour is usually quite easy to study experimentally. 

To understand the response of materials upon light irradiation, we describe the macroscopic polarization P as a function of the electric field E as ... 

The study of chiral materials with nonlinear optical properties might lead to new insights to design completely new materials for applications in the field of nonlinear optics and photonics. For example, we showed that chiral supramolecular organization can significantly enhance the second-order nonlinear optical response of materials and that magnetic contributions to the nonlinearity can further optimize the second-order nonlinearity. Again, a clear relationship between molecular structure, chirality, and nonlinearity is needed to fully exploit the properties of chiral materials in nonlinear optics. 

Most characterisation of non-linear responses of materials with De < 1 have concerned the application of a shear rate and the shear stress has been monitored. The ratio at any particular rate has defined the apparent viscosity. When these values are plotted against one another we produce flow curves. The reason for the popularity of this approach is partly historic and is related to the type of characterisation tool that was available when rheology was developing as a subject. As a consequence there are many expressions relating shear stress, viscosity and shear rate. There is also a plethora of interpretations for meaning behind the parameters in the modelling equations. There are a number that are commonly used as phenomenological descriptions of the flow behaviour. 

Material response is typically studied using either direct (constant) applied voltage (DC) or alternating applied voltage (AC). The AC response as a function of frequency is characteristic of a material. In the future, such electric spectra may be used as a product identification tool, much like IR spectroscopy. Factors such as current strength, duration of measurement, specimen shape, temperature, and applied pressure affect the electric responses of materials. The response may be delayed because of a number of factors including the interaction between polymer chains, the presence within the chain of specific molecular groupings, and effects related to interactions in the specific atoms themselves. A number of properties, such as relaxation time, power loss, dissipation factor, and power factor are measures of this lag. The movement of dipoles (related to the dipole polarization (P) within a polymer can be divided into two types an orientation polarization (P ) and a dislocation or induced polarization. 

Abstract Optical techniques for three-dimensional micro- and nanostructuring of transparent and photo-sensitive materials are reviewed with emphasis on methods of manipulation of the optical field, such as beam focusing, the use of ultrashort pulses, and plasmonic and near-field effects. The linear and nonlinear optical response of materials to classical optical fields as well as exploitation of the advantages of quantum lithography are discussed. 

The nonlinear response of material to optical excitation is the main requirement for formation of 3D patterns by photopolymerization. The appU-cation potential of such patterns in microphotonic, photonic crystal, MEMS, and microlluidic appUcations is described in our contributions to [58]. 

RHEOLOGY. The study of the response of materials to an applied force. Rheology deals with the deformation and flow of matter. 

In the above consideration of the elastic response of materials it has been asssumed that the stress is a linear function of the strain only. In practice this is not true and the stress... 

Besides deformation, fracture is the other response of materials to a stress. Fracture is the stress-induced breakup of a material. Two types of fracture are commonly defined. A brittle fracture is breakup which occurs abruptly without localized reduction in area. A ductile fracture is the failure of the material which is preceded by appreciable plastic deformation and localized reduction in area (necked region). The brittle fracture and ductile fracture are schematically illustrated in Fig. 1.10. 

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