Development of constitutive equations for plastic deformation of a porous material using numerical experiments

New constitutive equations for plastic deformation of a porous material are developed by using numerical experiments. A micro-mechanical unit problem such as growth of an isolated void in incompressible matrix is formulated to represent the instantaneous macroscopic response. The micro-and macro-variables in two different length scales are introduced and connected. The strain hardening, incompressible, viscoplastic behavior of matrix material in a micro-scale is assumed with a state variable model and the unit problems are solved using finite element methods to give a macroscopic compressible plastic response at a material point in a larger length scale. Systematic variations in the macroscopic quantities are obtained by changing the boundary/initial conditions in the unit problems. Such variations provide families of the curves defining the plastic behavior of a porous material and those curves are collapsed into two master curves by scaling procedures. The scaling relations and the forms of those master curves motivate the mathematical structures of the constitutive equations for the plastic behavior of a porous material. Detail comparisons of the proposed constitutive equations to the previous ones are given in terms of shearing viscosity and volumetric viscosity.