Physically based strain invariant set for materials exhibiting transversely isotropic behavior

A novel set of 5 strain invariants for materials exhibiting transversely is otropic behavior with respect to a reference configuration is developed thr ough analysis of physical attributes of deformation. Experimental advantage for hyperelastic materials is demonstrated by showing that common tests ca n directly determine terms in W, the strain energy per unit reference volum e. An analysis of symmetry allows the general form of PY to be refined a pr iori. Moreover, this kinematics framework is potentially useful for solving inverse problems since the 5 response terms in the Cauchy stress t are mos tly orthogonal (9 of the 10 mutual inner products vanish). For small deform ation they are fully orthogonal tall 10 inner products vanish). A response term in t consists of an invariant response function multiplied by its asso ciated kinematic tensor. (C) 2001 Elsevier Science Ltd. All rights reserved .