Energy approach to the plasticity of porous materials

Based on the energy criterion recently introduced by Qiu and Weng (1992), the strain potential and yield function of a porous material are derived with nondilute concentration of spherical voids. The derived yield function is expressed in terms of the normalized effective stress and hydrostatic mean stress, as well as the effective secant moduli of the porous material. The theory is suitable for both elastically compressible and incompressible matrix with or without work-hardening. For the special case of elastically rigid, perfectly plastic matrix, it is compared with Gurson's (1977) and Tvergaard's (1981) theories. For an elastically compressible matrix with a perfectly plastic behavior, the yield stress of the porous medium is found to remain constant under pure hydrostatic tension, but show an apparent increase of flow stress under pure shear (or deviatoric loading). The theory is finally applied to predict the tensile and shear stress-strain curves of the porous material with an elastically compressible, work-hardening matrix; the results are found to compare favorably with the finite element calculations.