Ogden model

The two main types of hyperelastic models are the polynomial model and the Ogden model. In the polynomial model, the strain energy density is given by... 

Fig. 33.3 Fi rst-order Ogden model fitted to experimental data of a IK-MS adhesive system (Terostat MS937) at room temperature.

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. 

Kreutz, T., Steinbugler, M., and Ogden, J., Onboard fuel reformers for fuel cell vehicles Equilibrium, kinetic and system modeling, Proc. 1996 Fuel Cell Seminar, Orlando, FL, 714, 1996. 

Lin, D. Z., Ogden, J., Fan Y. and Sperling, D. (2006). The Hydrogen Infrastructure Transition (HU) Model and its Application in Optimising a 50-Year Hydrogen Infrastructure for Urban Beijing. Research Report UCD-ITS-RR-06-05. Davis Institute of Transportation Studies, University of California. 

Yang, C., Nicholas, M. A. and Ogden, J. (2006). Comparison of idealized and real-world city station sitting models for hydrogen distribution. UCD-ITS-RP-06-09, Institute of Transportation Studies, University of California, Davis. In... 

The SSCHISM hydrogen infrastructure model (Yang and Ogden, 2007a b) designs and costs of an H2 infrastructure to meet a specified market penetration for FCVs. 

Ogden, L.V., Walstra, P., Morris, H.A. 1976. Homogenization-induced clustering of fat globules in cream and model systems. J. Dairy Sci. 59, 1727-1737. 

In electrochemical proton transfer, such as may occur as a primary step in the hydrogen evolution reaction (h.e.r.) or as a secondary, followup step in organic electrode reactions or O2 reduction, the possibility exists that nonclassical transfer of the H particle may occur by quantum-mechanical tunneling. In homogeneous proton transfer reactions, the consequences of this possibility were investigated quantitatively by Bernal and Fowler and Bell, while Bawn and Ogden examined the H/D kinetic isotope effect that would arise, albeit on the basis of a primitive model, in electrochemical proton discharge and transfer in the h.e.r. 

Seto, M., Whitlow, M., McCarrick, M.A., Srinivasan, S., Zhu, Y., Pagila, R., Mintzer, R., Light, D., Johns, A., and Meurer-Ogden, J.A., A model of the acid sphingomyehnase phosphoesterase domain based on its remote structural homolog purple acid phosphatase. Protein Sci, 13 (2004) 3172-3186. 

McCollum DL, Ogden JM. Techno-Economic Models for Carbon Dioxide Compression, Transport, and Storage, UC Davis. 2006. http //pubs.its.ucdavis.edu/dovmload pdf. php id=1047. Accessed May 2007. 

Ogden,. M. (2002). Modeling Infrastructure for a Fossil Hydrogen Energy System with C02 Sequestration. Princeton Environmental Institute. 

Ogden, J. (2005). Overview of Hydrogen System Modeling at ITS-Davis. Sandia National Laboratories. 

In a local detailed analysis, the flexible adhesive is modeled with three-dimensional solid elements to enable the refined capture of any local stress or strain gradients. The adhesive material is described as a rabber-like, nearly incompressible, hyperelastic material characterized by a strain energy function. Using U as the strain energy potential per unit of the reference volume, the form of the Ogden strain energy potential is shown in Eq. (1) jii and u are material parameters which are determined from adhesive material test data. 

The lap shear fatigue test for the joints of the front cab module of the Maglev Transrapid TR08 has been analyzed by a fine detail analysis with 3D solid elements using the real cross-section geometry. The adherend materials are aluminum on one side and GRP on the other see also Section 32.5.1. The PU adhesive Sikaflex -254 Booster is modeled with the Ogden strain energy equation (Eq. (1), with N=2). The computed stiffness correlates well with the test results. The local stress distribution is visualized in Fig. 32.11. 

For flexible (mbbery) adhesives which show Tg far below room temperature, hyperelastic material models are generally used. In the hyperelastic regime, standard solutions are available which use various types of potential functions [7]. The flexible adhesive systems investigated were best fitted by a potential function which is formulated in terms of the principal stretches Aj originally suggested by Ogden [Eq. (1)] [8]. 

Ogden, R.W., 1997. Nonlinear Elastic Deformations, Dover Publications, New York, p. 499. Oppermann, W., Rennar, N., 1987. Model PDMS elastomers. Prog. Coll. Polym. Sci. 75, 49. Osada, Y, Khokhlov, A.R. (Eds.), 2002. Polymer Gels and Networks. Marcel Dekker, New York. Perkins, T.T. et al., 1994a. Relaxation of a single DNA molecule observed by optical microscopy. Science 264, 822-826. 

Johnson, N., Ogden, J. A spatially-explicit optimization model Jot long-term hydrogen pipeline planning. Int. J. Hydrogen Energy 37, 5421-5433 (2012)... 

A natural extension of linear elasticity is hyperelasticity (Ogden 1997). Hyperelasticity is a collective term for a family of models that all have a strain energy density that depends only on tiie currently applied deformation state (and not on the history of deformations). This class of material models is characterized by a nonlinear elastic response, and does not capture yielding, viscoplasticity, or time dependence. Strain energy density is the energy that is stored in the material as it is deformed, and is typically represented either in terms of invariants of the deformation gradient (F) /i, I2, and /, where... 

Uniaxial compression prediction using the Ogden hyperelasticity model. 

Part wall thickness can now be predicted quite accurately with finite element analysis. The physical sheet is replaced with a two-dimensional mesh of triangular elements and nodes, which is then mathematically deformed imder increasing load. When the nodes touch the electronic surface of the mold, they are affixed. Force continues to increase imtil all or most of the elements are rendered immobile. Currently the Ogden power-law model is used as the pol5mier elastic constitutive equation or response to applied load (28). 

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