A complete set of independent and physically meaningful invariants in the mechanics of solids reinforced by two families of fibres

It has recently been shown [2,3] that only seven of the classical deformation invariants employed in hyperelasticity of solids reinforced by two families of unidirectional fibres are independent. This short communication demonstrates a manner in which such a set of seven invariants is conveniently identified without much deviation from well-known features that characterise their classical counterparts. It also shows that, unlike several of their classical counterparts, these newly identified invariants have all their own physical meaning. This new development is immediate applicable on mass-growth problems of tissue that preserve fibre direction [1] and, notably, on problems involving mass-growth of a circular tube reinforced by two families of helices wound symmetrically around the tube in opposite directions.