Linear elastic behavior assumption

This analytical solution review is tractable only for very limited assumptions, such as homogeneity and linearly elastic behavior (not to mention excluding variations that are time- or temperature-dependent). The first deviation that must be examined is the elastic linearity assumption for polishing pads. Polymers, in general, show behavior that lies between that of an elastic solid and a viscous fluid. The term viscoelastic has been applied to this behavior. 

The assumption at the basis of the calculation are the linear-elastic behavior of aU materials, the cross-beam sections remaining plain, and the absence of deformation (perfect bonding) between concrete and steel, and between concrete andFRP. 

Inherent assumption of linear elastic behavior of the parent frame. Except for Lavan and Levy (2005), Lavan et al (2008), Cimellaro et al (2008), and Lavan... 

The purpose of this chapter has been to give a description of some of the most useful contact mechanics expressions as they relate to studies of adhesion. The primary assumption regarding the properties of the materials themselves is that a linear constitutive model is obeyed throughout the strained region, with the possible exception of a relatively small cohesive zone at the contact edge. Many of the results obtained for simple linear elastic behavior are analytic. Linear viscoelasticity can be handled as well, although in this case numerical approaches... 

In this context it has to be pointed out that in the original Dugdale model the material behavior is assumed to be linearly elastic and perfectly plastic the latter assumption leads to a uniform stress distribution in the plastic zone. This may be a simplified situation for many materials to model, however, the material behavior in the crack tip region where high inhomogeneous stresses and strains are acting is a rather complex task if nonlinear, rate-dependent effects in the continuum... 

The preceding equations provided a reasonable foundation for predicting DE behavior. Indeed the assumption that DEs behave electronically as variable parallel plate capacitors still holds however, the assumptions of small strains and linear elasticity limit the accuracy of this simple model. More advanced non-linear models have since been developed employing hyperelasticity models such as the Ogden model [144—147], Yeoh model [147, 148], Mooney-Rivlin model [145-146, 149, 150] and others (Fig. 1.11) [147, 151, 152]. Models taking into account the time-dependent viscoelastic nature of the elastomer films [148, 150, 151], the leakage current through the film [151], as well as mechanical hysteresis [153] have also been developed. 

To specify material properties, anisotropy, and non linear behavior of textile structures have to be considered. These assumptions make the assessments quite complex. However, previous studies showed that the simplifying linear elastic material could lead to reliable results in the modeling of yam pullout [1, 5, 10]. 

The value of is evaluated from the (nonlinear) force-deflection curve of the specimen at the moment of crack propagation and 2T is therefore determined without appeal to either linearity or finite-strain limitations. There is, however, an implicit appeal to elastic behavior, that is, to the assumption that no energy is dissipated in the recovery of strain in the shaded area of Figure 1. Since this is not in general a valid assumption, the fracture parameter 2T contains contributions from energy dissipated remote from the crack itself. A further consequence of this is that 2T may cease to be independent of the specimen configuration (size and shape). This problem is of course present with LEFM also. 

Much of the treatment contained within this volume is limited by the assumptions that the adhesives, and usually the adherends, are linear elastic, homogenous, and isotropic. For bulk adhesives, the assumption of isotropy is usually justified, although instances do arise where preferred orientation of filler particles or crystalline regions can lead to anisotropic behavior. Common adherends such as fiber-reinforced composites, wood, and cold-drawn metals often exhibit anisotropic behavior that can significantly affect Joint behavior. 

For the material models, the following assumptions are made (i) the fibers obey a linear elastic and anisotropic material law, (ii) the matrix follows an isotropic, linear elastic-plastic material law, (iii) the material behavior of the interface elements is described in Section 5.1.2, and (iv) the material model of the anisotropic outer layer is the same as that of the macro-contact model. 

For the calculation of the stress distribution in geometrically complex components, the finite element method, Irequently under the assumption of a linear elastic materials behavior, is widely used. If the results of these finite element calculations are used for a fatigue life analysis, the local strength has to be considered. For the assessment of finite element results, with regard to its fatigue strength, the application of the concept of local stresses offers a solution Local S/N-curves are calculated. 

The basic law of viscosity was formulated before an understanding or acceptance of the atomic and molecular structure of matter although just like Hooke s law for the elastic properties of solids the basic equation can be derived from a simple model, where a flnid is assumed to consist of hypothetical spherical molecules. Also like Hooke s law, this theory predicts linear behavior at low rates of strain and deviations at high strain rates. But we digress. The concept of viscosity was first introduced by Newton, who considered what we now call laminar flow and the frictional forces exerted between layers within a fluid. If we have a fluid placed between a stationary wall and a moving wall and we assume there is no slip at the walls (believe it or not, a very good assumption), then the velocity profile illustrated in Figure... 

Most micromechanical theories treat composites where the thermoelastic properties of the matrix and of each filler particle are assumed to be homogeneous and isotropic within each phase domain. Under this simplifying assumption, the elastic properties of the matrix phase and of the filler particles are each described by two independent quantities, usually the Young s modulus E and Poisson s ratio v. The thermal expansion behavior of each constituent of the composite is described by its linear thermal expansion coefficient (3. It is far more complicated to treat composites where the properties of some of the individual components (such as high-modulus aromatic polyamide fibers) are themselves inhomogeneous and/or anisotropic within the individual phase domains, at a level of theory that accounts for the internal inhomogeneities and/or anisotropies of these phase domains. Consequently, there are very few analytical models that can treat such very complicated but not uncommon systems truly adequately. 

The results of flic interfacial rheological studies on asphaltene adsorption at oil-water interfaces teach us a great deal about the behavior of asphaltenes and their role in emulsion stabili2ation. The conclusions drawn are based largely on the assumption that the rheological properties measured, namely flic elastic film modulus G are directly related to the surface excess concentration of asphaltenes. F. It is understood diat die elastic modulus actually depends on both the surface excess concenlration and the relative conformation (i.e., coimectivity) of the adsorbed asphaltenes. It is further understood that a minimum adsorbed level is required to observe a finite value of G and that the relationship between G and G is not linear. With these caveats in mind, we can conclude die following ... 

The stresses in an adhesive joint depend, once a constitutive model is chosen, on the geometry, boundary conditions, the assumed mechanical properties of the regions involved, and the type and distribution of loads acting on the joint. In practice, most adhesives exhibit, depending on the stress levels, nonlinear-viscoelastic behavior, and the adhetends exhibit elastoplastic behavior. Most theoretical studies conducted to date on the stress analysis of adhesively bonded joints have made simplifying assumptions of linear and elastic and/or viscoelastic behavior in the interest of tracking solutions. 

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