ON THE TANGENT MODULUS TENSOR IN HYPERELASTICITY

The tangent modulus tensor, denoted as D, plays a central role in nonl inear finite element simulation of elastomeric components such as seal s. It is derived from the strain energy function w for isotropic elast omers. Using Kronecker product notation, a compact expression for D ha s been derived in Nicholson [1] and Nicholson and Lin [2] for invarian t-based strain energy functions such as the Mooney-Rivlin model. In th e current investigation, a corresponding expression is derived for str etch ratio-based strain energy functions such as the Ogden model. Comp ressible, incompressible and near-incompressible elastomers are addres sed. The derived expressions are considerably more elaborate than thei r counterparts for invariant based models. As illustration, D is evalu ated and presented for the torsion of a natural rubber shaft described by a three term Ogden model, using coefficients reported by Treloar.