Hyperelastic component

Karamanou et al. [65] have performed finite element analyses to large strains to simulate the thermoforming process, in which thin sheets of polymer are inflated using gas pressure. They adopted a model comprising hyperelastic components and a linear viscous element. Applying a thin shell analysis enabled them to produce realistic predictions of the inflating membrane. 

Hyperelastic models within finite element codes should be used carefully when a component experiences multiaxial stresses. 

All of these material models are so-called hyperelasticity models. The stress in the material is clearly a function of the elongation, i.e., each defined deformation state in a structural material component has exactly one correlative load application state [12]. 

In the paper, a theory for mechanical and diffiisional processes in hyperelastic materials was formulated in terms of the global stress tensor and chemical potentials. The approach described in was used as the basic principle and was generalized to the case of a multi-component mixture. An important feature of the work is that, owing to the structure of constitutive equations, the general model can be used without difficulty to describe specific systems. 

Swieszkowski et al. studied the use of PVA-C as cartilage replacement for the shoulder joint. PVA-C was used as the articular layer of the glenoid component. The mechanical effects of using this material in the glenoid component were evaluated and a model of the cryogel as a hyperelastic material was developed to allow design modifications to limit contact stress [96]. 

When it is assumed, as is usually done, that the stiffiiess and compliance tensors are additionally symmetric with respect to their diagonals, the total number of independent components is reduced from 36 to 21 (so-called Green elasticity or hyperelasticity, in contrast to the so-called Cauchy elasticity, where this is not the case). Thus in the most general case of well-defined anisotropy (triclinic monociystals) the (6 x 6) stiffness or compliance matrices or, alternatively, the fourth-order stiffness or compliance tensors, have 36 elastic constants or coefficients, respectively, 21 of which can be assumed to be independent, cf. [Pabst Gregorova 2003a]. For reasons of convenience we confine ourselves to the stiffiiess matrices in the sequel. It is understood, however, that completely analogous relations and symmetry considerations are valid in the case of the compliance matrices. 

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