Mechanics of materials model

From the standpoint of the continuum simulation of processes in the mechanics of materials, modeling ultimately boils down to the solution of boundary value problems. What this means in particular is the search for solutions of the equations of continuum dynamics in conjunction with some constitutive model and boundary conditions of relevance to the problem at hand. In this section after setting down some of the key theoretical tools used in continuum modeling, we set ourselves the task of striking a balance between the analytic and numerical tools that have been set forth for solving boundary value problems. In particular, we will examine Green function techniques in the setting of linear elasticity as well as the use of the finite element method as the basis for numerical solutions. 

The mechanics of materials model uses simple analytical equations to arrive at effective properties of a composite, using simplifying assumptions about the stress and strain distribution in a repre-... 

In this context Morais [27] derived a closed-form equation for the transverse modulus using a relatively simple mechanics-of-materials model. The method employed is a sophistication of the technique presented in Section 11.4.2. The formula obtained for the transverse modulus is given by... 

Loret, B. and Simoes, F.S. (2003) Articular cartilage with intra- and extrafibrillar waters.A chemo-mechanical model. Mechanics of Materials, to appear... 

The model system comprising the reaction sequence from initial 0-atom attack to steady-state erosion of a hydrocarbon surface can serve as a benchmark for fundamental atom-surface interactions at hyperthermal collision energies and for etching mechanisms of materials. Within this model system, there is still much to learn. It is likely that when a hyperthermal oxygen atom strikes a saturated hydrocarbon surface, it will either abstract a hydrogen atom or it will scatter inelastically. The subsequent reaction sequence becomes murky. Very little is known about the mechanisms of oxidation, surface roughening, or material loss. In fact, even the sticking... 

Reuter K, Stampfl C, SchefHer M (2005), Ab Initio Atomistic Thermodynamics and Statistical Mechanics of Surface Properties and Functions. In Yip S (ed.). Handbook of Materials Modeling. Part A Methods Springer, Berlin... 

One of the key linkages between continuum and microscopic descriptions of interfaces is the notion of an interfacial energy. Though the use of such energies is by now entirely routine, nevertheless, this exemplifies the type of information passage that is one of the hallmarks of multiscale modeling. Note that from the perspective of the continuum mechanics of materials with interfaces, the total energy is often written in the form... 

If the mechanism of material transport in sintering is grain boundary diffusion, the viscosity can be expressed as a function of the temperature and the grain size. From a model for boundary diffusion controlled creep proposed by Coble [7] and the temperature dependence of diffusion coefficients, we obtain... 

I. Basak, A. Ghosh Mechanism of material removal in electrochemical discharge machining a theoretical model and experimental verification. Journal of Materials Processing Technology 71 (1997), p. 350. 

The method developed in this book is also used to provide input parameters for composite models which can be used to predict the thermoelastic and transport properties of multiphase materials. The prediction of the morphologies and properties of such materials is a very active area of research at the frontiers of materials modeling. The prediction of morphology will be discussed in Chapter 19, with emphasis on the rapidly improving advanced methods to predict thermodynamic equilibrium phase diagrams (such as self-consistent mean field theory) and to predict the dynamic pathway by which the morphology evolves (such as mesoscale simulation methods). Chapter 20 will focus on both analytical (closed-form) equations and numerical simulation methods to predict the thermoelastic properties, mechanical properties under large deformation, and transport properties of multiphase polymeric systems. 

Kletschkowski, T., Schomburg, U., and Bertram, A., Endochronic Viscoplastic Material Model for Filled VTTE, Mechanics of Materials, 34 795-808 (2002)... 

J.W. Ju, Y. Zhang Axisymmetric thermomechanical constitutive and damage modeling for airfield concrete pavement under transient high temperature. Mechanics of Materials 29 (1998) 307-323. 

Chapter 3 deals with in depth discussion on basic mechanism of material removal for EMM. Moreover, equivalent electrical circuit, material removal rate (MRR) model, formulation of MRR based on equivalent electrical circuit model as well as comparison of basic model and electrical circuit model of... 

Boyce, M.C., Parks, D.M., and Argon, A.S. (1988) Large inelastic deformation of glassy polymers, Part I Rate-dependent constitutive model. Mechanics of Materials, 7, 15-33. 

Dupaix, R.B. and Boyce, M.C. (2007) Constitutive modeling of the finite strain behavior of amorphous polymers in and above the glass transition. Mechanics of Materials, 39, 39-52. 

Hutchinson, J.W. and Jensen, H.M. (1990) Models of fiber debonding and pullout in brittle composites with friction. Mechanics of Materials, 9, 139-163. 

Farinholt, K. and Leo, D. (2004). Modeling of electromechanical charge sensing in ionic polymer transducers. Mechanics of Materials 36, pp. 421-433. 

The major difficulty in using computational models is the development of material models, which require a complete set of material parameters in constitutive and failure models information (Anderson and Bodner, 1988). Furthermore, a ntrmerical method based on continuum mechanics encounters a fundamental difficrrlty when material failttre is involved, as such numerical methods, for example FE and finite differences (FD), are incapable of deahng with a large ntrmber of discontinrrities. 

Sierka M, Sauer J (2005) Hybrid quantum mechanics/molecular mechanics methods and their application. In Yip S (ed) The handbook of materials modeling. Part A. Methods. Springer, Dordrecht, pp 241-258... 

The mechanism of material removal in abrasive machining of brittle ceramics has been well documented by Evans and Marshall who developed the lateral-crack chipping model. They demonstrated that material removal rate, AT caused by a passage of each grinding particle is related to the peak normal penetration forces, Fn, Vicker s hardness and fracture resistance as follows, ... 

In Chap. 5 we have discussed the flow-induced fiber orientation. In this Chapter we will begin with a particular aspect of material modeling, namely, the modeling of mechanical and thermal properties of the short-fiber composites from the given properties of the individual components and the fiber orientation distributions. A correct evaluation of material properties is a prerequisite for shrinkage and warpage modeling. 

Paley M. and Aboudi J. (1992) Micromechanical analysis of composites by the generalized cells model. Mechanics of Materials, 14(2), 127-139. 

The mechanics of materials approach is the simplest and least useful. It assumes that each phase is subjected either to the same strain (the Voigt model Equation 9.4) or the same stress (the Reuss model Equation 9.5). This yields the relationships ... 

C. Li, T.W. Chou, Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach. Mechanics of Materials, 36, 1047-1055, (2004). 

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