Numerical integration of constitutive models applicable to metal foams.

摘要

Metal foams have unique combinations of physical and mechanical properties and are becoming increasingly popular among researchers and designers. Four elasto-plastic material models for metal foams are studied in detail. All four material models considered are rate independent elastoplastic models with isotropic hardening rules. A return mapping algorithm using the Newton-Raphson closest point projection is discussed for integrating the constitutive equations of the models. A way to do the return mapping along the spectral directions of the stress tensor is described so as to reduce the dimensionality of the problem. An algorithm applicable to all metal foam models, both with associative and non-associative hardening, is presented. A user subroutine is written in FORTRAN for implementing the algorithm. Numerical simulation of the diagonal crushing of metal foam cube is done in FEM program ABAQUS to verify the material model algorithm. The result of the numerical simulation using user defined subroutine, is compared with the result using the inbuilt metal foam model in ABAQUS. The energy absorption capacity of metal foams is demonstrated by comparing the crushing process of a metal foam cube with a solid aluminum cube.