A New Perspective on the Mathematical Modeling of Highly Nonlinear Anisotropic Plastic Flows in a Heterogeneous Solid
A new mathematical formulation is presented for describing the three-dimensional anisotropic plastic flow behavior of a heterogeneous polycrystalline solid. By using three principal stresses, three loading orientation angles, and a generally non-quadratic, real-valued stress exponent, a mathematical theory of anisotropic plasticity is formulated as two coupled orthogonal series expansions in both the 3D principal stress space (the p–plane) and the 3D loading orientation space. A geometrical interpretation of the new mathematical representation of anisotropic plasticity is offered. Specific examples are given to illustrate the application of the proposed theory for modeling the plastic anisotropy of orthotropic polycrystalline sheets under uniaxial and biaxial tension.
C. Esling, M. Humbert, R.A. Schwarzer and F. Wagner
W. Tong "A New Perspective on the Mathematical Modeling of Highly Nonlinear Anisotropic Plastic Flows in a Heterogeneous Solid ", Solid State Phenomena, Vol. 105, pp. 271-276, 2005