A constitutive model of aluminum foam for crash simulations

Abstract

A new constitutive model for metallic foams is developed to overcome the deficiency of existing models in commercial finite element codes. The proposed constitutive model accounts for volume changes under hydrostatic compression and combines the hydrostatic pressure and von Mises stress into one yield function. The change of the compressibility of the metallic foam is handled in the constitutive model by allowing for shape changes of the yield surface in the hydrostatic pressure-von Mises stress space. The backward Euler method is adopted to integrate the constitutive equations to achieve numerical accuracy and stability. The model is implemented into LS-DYNA as a user-defined subroutine, verified with existing solutions, and validated with foam testing data. The verified and validated model is then utilized in the crushing simulations of foam-filled columns with square and hexagonal cross-sections. Two constitutive models are studied: the first using an exponential function to describe the relationship of plastic Poisson's ratio with respect to true strain and the second using linear interpolation function as an alternative approximation. The new foam model provides satisfactory prediction of crushing forces and deformed shapes compared to experimental results. Additionally, the new foam model was shown to have better numerical stability and accuracy than existing LS-DYNA built-in material models.