Scale-dependent plasticity potential of porous materials and void growth

In the present paper, a boundary value problem about the macroscopic response and its microscopic mechanism of a representative spherical cell with a spherical microvoid under axisymmetric triaxial tension has been theoretically investigated. To capture the size effects of local plastic deformation in the matrix, the strain gradient constitutive theory including the rotation and the stretch gradients developed by Fleck and Hutchinson [Strain gradient plasticity, in: J.W. Hutchinson, T.Y. Wu (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, 1997, p. 295] is adopted. By means of the principle of minimum plasticity potential and the Lagrange multipliers method, the self-contained displacement field within the matrix has been computationally determined. Based on these, a size-dependent constitutive potential theory for porous material has been developed. The results indicate clearly that the microvoid evolution predicted by the present constitutive model displays very significant dependences on the void size especially when the radius a of microvoids is comparable with the intrinsic characteristic length l of the matrix. And when the void radius a is much lager than l, the present model can retrogress automatically to the Gurson model improved by Wang and Qin [Acta Mech. Solid. Sin. 10 (1989) 127, in Chinese].