Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theorectically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.