Tensor Presentation of Algorithmic Tangent Modulus for Plastic-Damage Models
For a class of plastic-damage models, spectral return-mapping algorithm performed upon the principal effective stresses is efficient, while algorithmic tangent modulus formulated upon the general effective stress components is much simpler. In order to facilitate the transformation between these two sets of stress components in the formulation of algorithmic tangent modulus, a new concept of fictitious stress tensor, which is orthogonally similar to the real stress tensor, is proposed in this paper. The rank four Jacobian tensor of the fictitious effective stress is calculated from spectral decomposition; and a clear tensor formulation of algorithmic tangent modulus is presented.
J. Zhang et al., "Tensor Presentation of Algorithmic Tangent Modulus for Plastic-Damage Models", Applied Mechanics and Materials, Vols. 29-32, pp. 1747-1752, 2010