Physically motivated invariant formulation for transversely isotropic hyperelasticity

This article discusses an invariant formulation for transversely isotropic hyperelasticity. The work is motivated by the interest of modeling materials such as tendon tissues which may exhibit drastically different characteristics in tensile, shear and volumetric responses. A multiplicative decomposition of the deformation gradient that factors out the dilation and the fiber stretch is proposed. Transversely isotropic strain invariants are constructed on the basis of the multiplicative factors. Within the framework of hyperelasticity theory, these strain invariants generate decoupled stress components in the hydrostatic pressure, the fiber tension and shear terms. An example model is suggested and is assessed against some known features of transversely isotropic solids with strong fibers.