Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids – II: Evolution of the length and orientation of the void axes

• Evolution equations for the internal parameters of Madou and Leblond (2012)'s model are defined.
• Use is made of “elastic” equations proposed by Ponte-Castaneda and coworkers.
• Heuristic correction factors determined numerically are introduced into these equations.

In Part I, Madou and Leblond, 2012a and Madou and Leblond, 2012b's criterion for plastic porous materials containing arbitrary ellipsoidal voids was validated by comparing its predictions with the results of some numerical limit-analyses of elementary cells containing such voids. In the present Part II, our aim is now to complete the model by proposing reasonable evolution equations for the length and orientation of the axes of the voids. Again, however, the equations proposed are not attached to this specific model and could be used in conjunction with any similar criterion accounting for void shape effects.In the definition of the evolution equations looked for, a central role is played by “elastic” expressions for the strain and rotation rates of the voids proposed by Ponte-Castaneda and Zaidman (1994) and Kailasam and Ponte-Castaneda (1998) from homogenization theory. The importance of plastic effects however makes it necessary to modify these expressions; this is done heuristically by introducing stress-dependent correction factors determined numerically in a number of reference cases and suitably interpolated between these cases.