A constitutive model for ductile damage evolution

A constitutive model for ductile porous material is formulated within the thermodynamic framework. A yield function based on the lower-bound solution for a cylindrical void model embedded in a plastic matrix is proposed. The new yield function is compared to the classical Gurson yield function using cell model calculations. The results reveal that the proposed yield function agreed well with the plastic region found from the cell model calculations. In addition to the influence of the void-volume ratio, the elastic part of the free energy is dependent on a scalar damage field which allows the elasticity to be influenced by the void-volume fraction. The degradation is controlled by a scalar valued damage field and enters the formulation via the Helmholtz's free energy. This dependence allows the elastic properties to naturally depend upon the damage accumulation. The numerical treatment of the model is derived and the capability of the model is demonstrated via numerical simulation of the necking of an axi-symmetric bar