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, A hollow sphere as a representative volume element with internal radius a and external radius b. The matrix behavior is viscoplastic and the porosity f = a 3 /b 3 . Molinari and Mercier [26]

, The initial porosity is f 0 =0.01. Two loading rates (?=10MPa/ns, 250MPa/ns) and two strain rate sensitivities (m=0.05, 0.15) are tested for spherical loading. Molinari and Mercier [26], Porosity versus time evolution for both quasi-static and dynamic models

, Homogenous kinematic boundary conditions are applied on the external boundary of the unit cell

R. The and . Gologanu,

, The RVE has a cylindrical shape (height, 2H and diameter, 2L) with a cylindrical void (height, 2h and diameter, 2R) inside, Molinari et al, p.53

, A cylindrical unit cell (length 2l, void radius a, external radius b) is taken as the representative volume element. A cartesian coordinate system is adopted for the derivation of the model with ?l < x 3 < l