Advanced constitutive models

In addition to the refined constitutive models adapted for concrete and reinforcing steel, advanced constitutive models are also implemented in the model formulation to define the bond stress vs. slip behavior of the bond slip springs (Fig. 20.6). For deformed (ribbed) reinforcing bars, the bond stress vs. slip model by Harajli (2009) is adopted to represent the splitting-type bond slip behavior expected under inadequate clear cover conditions for unconfined concrete... 

Kalkan E, Kunnath SK (2006) Effects of fling step and forward directivity on seismic response of buildings. Earthq Spectra 22(2) 367-390 King JL, Tucker BE (1984) Observed variations of earthquake motion across a sediment-filled valley. Bull Seismol Soc Am 74(1) 137-151 Kontoe S, Zdravkovic L, Potts DM, Menkiti CO (2011) On the relative merits of simple and advanced constitutive models in dynamic analysis of timnels. Geotechnique 61 815-829... 

Generic material parameters for advanced constitutive models are often not available. Evaluation of material parameters for these models requires significant expertise and detailed site-specific soil properties. 

Given their obvious advantages, the development of advanced constitutive models for UHMWPE and other thermoplastics is an active area of research that is continuously evolving and improving. In the last few years, models... 

This chapter gave an overview of how to simplify complex processes sufficiently to allow the use of analytical models for their analysis and optimization. These models are based on mass, momentum, energy and kinetic balance equations, with simplified constitutive models. At one point, as the complexity and the depth of these models increases by introducing more realistic geometries and conditions, the problems will no longer have an analytical solution, and in many cases become non-linear. This requires the use of numerical techniques which will be covered in the third part of this book, and for the student of polymer processing, perhaps in a more advanced course. 

It must, of course, be clearly understood that e and e are not, like v and a, properties of the fluid involved alone but depend primarily on the turbulence structure at the point under consideration and hence on the mean velocity and temperature at this point and the derivatives of these quantities as well as on the type of flow being considered. The use of e and e does not, in itself, constitute the use of an empirical turbulence model. It is only when attempts are made to describe the variation of 6 and eh through the flow field on the basis of certain usually rather limited experimental measurements that the term eddy viscosity turbulence model is applicable. In fact, even when advanced turbulence models are used, it is often convenient to express the end results in terms of the eddy viscosity and eddy diffusivity. 

Kliippel M, Schramm J (1999) An advanced micromechanical model of hyperelasticity and stress softening of reinforced rubbers. In Dorfmann A, Muhr A (eds) Constitutive models for rubber. A.A. Balkema, Rotterdam... 

Because these developments are focused on intended applications in other fields and not problems of LMFR design there are significant differences in design lives, service conditions, materials, manufacturing practices, etc. The types of structures differ. The impact of these differences on such design information as constitutive models, material failure modes and models, and structural failure modes and consequences are sometimes difficult to assess. However, computer modeling, structural analyses methods, and analytic methods to understand materials behavior have advanced greatly in some of these non nuclear areas. 

Zhang, Q. and Yang, Q.S. (2012) Recent advance on constitutive models of thermal-sensitive shape memory polymers. Journal of Applied Polymer Science, 123, 1502-1508. 

The most advanced material model presently available for UHMWPE is the HM. This model focuses on creating a mathematical representation of the deformation resistance and flow characteristics for conventional and highly crosslinked UHMWPE at the molecular level. The physics of the deformation mechanisms establish the framework and equations necessary to model the behavior on the macroscale. As already mentioned, to use the constitutive model for a given material requires a calibration step where material-specific parameters are determined. A variety of numerical methods may be used to determine the material-specific parameters for a constitutive theory. In the previous section we employed a numerical optimization technique to identify the material parameters for the constitutive theory. 

In summary, there are a number of different constitutive models that can be used to predict different aspects of UHMWPE behavior. The most advanced of the currently available models is the HM, which has been shovm to be able to predict the behavior of both conventional and highly crosslinked UHMWPE used in total joint replacements. The HM is currently limited to isothermal deformation histories, although research is ongoing to enable to arbitrary thermomechanical deformation states. In addition, fatigue, fracture, and wear are targets for current and future studies. 

M. Kluppel and J. Schramm, in An Advanced Micro-Mechanical Model of Hyperelasticity and Stress Softening of Reinforced Rubbers, Proceedings of Constitutive Models for Rubber, Balkema, Rotterdam, 1999. 

This study can be used to predict the rock properties in the EDZ in the tunnel excavation, slope cutting or foundation excavation. It is shown that the deformation and strength parameters are greatly influenced by the confining pressures and plastic strain. More work would be carried out to find the quantitative law among them to advance a suitable constitutive model and strength criterion. 

MSWs are complex mechanical systems and this complexity is compounded when the structures are subjected to transient dynamic loading due to earthquake. Pseudo-static and displacement methods may be sufficient for simple structures, for stable ground conditimis and MSWs in low seismic risk areas, and/or for preliminary design. Otherwise, more sophisticated analyses may be warranted using advanced dynamic finite element model or finite difference computer programs. Today commercially available computer programs offer the user a suite of constitutive models for the component materials and in some cases allow the user to implement their own constitutive models. In order to accurately model the soil in a MSW, it may be necessary to use nonlinear cyclic stress-strain models. The equivalent-linear... 

For accurate assessment of seismic structural collapse, however, there are still challenges that need to be addressed. For example, understanding of nonlinear cyclic component behavior in a condition of oblique bending requires experimental tests and advances in constitutive modeling. Another issue is the quantification of the contribution of nonstructural elements on the seismic collapse capacity. On the other hand, from engineering practice, there is a strong demand on simplified assessment strategies that are simple to apply and at the same time reasonably accurate. 

One of the advantages of these dynamic soil-structure interaction analyses is that the soil layers are modeled to reflect the idealized site stratigraphy each soil layer can be either modeled as a linear elastic material with strain-compatible shear modulus and damping values or characterized via soil constitutive models that represent soil nonlinearity and hysteretic response at small strains. However, the use of the nonlinear constitutive models requires careful selection of input parameters and thus more advanced testing to define those input parameters. The nonlinear behavior and the frequency content of the free-field environment contribute to the stmctural racking behavior. 

With respect to site response analysis, the use of nonlinear time-domain approaches should be encouraged as a viable alternative to the standard linear equivalent method. It can, in fact, better predict soU deformation, degradation of stiffness, and accumulation of excess pore water pressures throughout the shaking. The issue of the accurate predictiOTi of hysteretic damping with advanced soU constitutive models still remains controversial, as these models can significantly... 

The influence of PWP changes during cyclic loading is incorporated in soil constitutive models in two ways (i) semiempirical PWP generation models used in combination with total-stress soil models and (ii) advanced effective-stress models whereby the model formulation is in terms of effective stress, and the PWP change is computed as the change between total stresses (or loads) and effective stresses via the soil constitutive model. 

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