Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids – I: Yield surfaces of representative cells

• FE limit-analyses of ellipsoidal cells containing confocal ellipsoidal voids are performed.
• The results generally agree with Madou and Leblond, 2012a and Madou and Leblond, 2012b's criterion for such cells.
• Slight corners are however observed on the yield surfaces of hollow cylindrical cells.

This work is devoted to some numerical limit-analyses, performed by the finite element method, of elementary cells of arbitrary ellipsoidal shape and containing confocal ellipsoidal voids. The aim is essentially, in the present Part I, to validate an approximate analytic criterion for such cells recently proposed by Madou and Leblond, 2012a and Madou and Leblond, 2012b, and in Part II, to supplement the model by proposing reasonable evolution equations for the length and orientation of the axes of the voids. The results obtained are however not specifically attached to this particular model and could assist in the definition of any similar one for plastic porous materials incorporating void shape effects.The present Part I is devoted to the numerical determination of the yield surfaces corresponding to eight different void geometries (prolate and oblate spheroids, circular and elliptic cylinders, circular and elliptic cracks, two general ellipsoids). The results obtained confirm the general validity of Madou and Leblond, 2012a and Madou and Leblond, 2012b's proposed criterion, although slight corners not accounted for in this criterion are apparent on the numerical yield surfaces of cylindrical cells.