A constitutive formulation and numerical procedure to model rate effects on porous materials at finite strains

• A framework to model viscoplastic effects in porous materials is proposed.
• We assume that the overstress function can also depend on the relative density.
• A density evolution effect on viscosity is integrated into the constitutive model.
• Corrections on viscoplastic operators due to density evolution are considered.

A constitutive formulation for viscoplastic porous materials subjected to finite deformations is developed. To account for porosity effects on the viscous response it is proposed an apparent viscosity, that is, it is assumed that the viscosity depends on the relative density evolution. Using an associative Perzyna-type formulation the constitutive equations as well as the density-corrected consistent tangent modulus are obtained from a suitable extension of the elastoplastic porous model. The proposed constitutive formulation is implemented inside the Finite Element Method context and it is numerically assessed by the analysis of some classical examples, as the isostatic compression, simple shear, and die pressing testing. In addition, a more complex simulation is presented. It is shown that in a relaxation test the viscoplastic porous material recovers the rate-independent response as an asymptotic limit only when some conditions are satisfied. Numerical results show that the proposed constitutive formulation is able to capture the rate effects when porous materials are subjected to high deformation speeds. This type of constitutive formulation is convenient for high-velocity metal powder compaction simulation, where rate effects play an important role on the material response and final properties.