On the Construction of Constitutive Relations in Hyperelasticity

Luoyi Tao, Rajagopal R Kumbakonam


The notion of abstract bodies and their configurations in a three-dimensional Euclidean space as used in rational continuum mechanics is examined with a view towards assessing how well it reflects physicalperspective, by considering the traditional formulation of constitutiverelations between the stress and the deformation gradient for homogeneous compressible hyperelastic materials. It is found that the notion of deformation gradient tensor that is currently used needs to be modified, the notion of material symmetry should be introduced in a different manner, and the traditional formulation needs to be recast and extended.

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