Titlebook: Hyperelasticity Primer; Robert M. Hackett Textbook 2018Latest edition Springer International Publishing AG, part of Springer Nature 2018 1

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Finite Elasticity,troduction of a strain-energy (or stored-energy) function into elasticity is due to George Green (1793–1841) and elastic solids for which such a function is assumed to exist are said to be Green elastic or hyperelastic. Elasticity without an underlying strain-energy function is called Cauchy elastic

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Polar Decomposition,olar decomposition theorem states that any deformation gradient tensor can be multiplicatively decomposed into the product of an orthogonal tensor, known as the rotation tensor, and a symmetric tensor called the right stretch tensor, or into the product of a symmetric tensor called the left stretch

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Strain-Energy Functions,unction of the three invariants of each of the two Cauchy-Green deformation tensors, given in terms of the principal extension ratios, or stretches. A number of different strain-energy formulations exist, having properties and characteristics that make them appropriate for characterizing different h

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Conjugate Pairs,e power spent). Therefore, it is imperative that the stress and strain tensors be conjugate. The notion of conjugation in this context was introduced in the last century. As an example of conjugate pairs, the mechanical work produced by combining second Piola-Kirchhoff stress with Green-Lagrange str