Hyperelasticity 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... 

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]. 

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. 

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... 

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. 

Uniaxial compression prediction using the Ogden hyperelasticity model. 

FIGURE 35.9 Comiarison between experimental data (obtained from a uniaxial compression test with an engineering strain rate of -0.05/s) for UHMWPE (GUR 1050, 30kGy TN2) > <1 predictions made using the Ogden hyperelasticity model. 

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