oa Homogeneous Deformation Of Internally Balanced Compressible Hyperelastic Materials

It is common nowadays to implement principles of continuum mechanics to describe the behavior of advance engineering materials. Continuum mechanics take into account the mapping of material pointsXdescribed in reference (undeformed) configuration into x described in current (deformed) configuration due to action of physical factors e.g. force or heat. The gradient of this mapping is denoted by F. It is common to model the behavior of the material in terms of stored energy function that for hyperelastic material expressed in terms of F; W(F). In practice, material behavior may consist of elastic response combined with some other type of nonelastic response such as plastic flow or biological growth. Therefore, it is common to decompose the deformation gradient at each material point such as F = F^ . F* (1) where F^ is elastic response and it is determined by the rules of variational calculus. The nonelastic response F is subjected to some kind of time dependent evolution law. Pence et al. (2013) have introduced a radically new way of viewing material using this concept. Actually, they consider the case where arguments of variational calculus apply to both factors and can be used to determine the decomposition itself. Preliminary indications is that this will offer great benefit in the modeling of complex material especially as regards to the development of singular surfaces that can be interpreted as locations of concentrated microstructural rearrangement. The extension of this internally balanced material models to include compressible hyperelasticity is investigated Hadoush et al. (2013). In this work the homogeneous deformation; dilatation, uniaxial and simple shear are examined for the two special cases of Blatz-Ko material model. It is found that the new theory retrieves conventional hyperelasticity for certain limiting cases.