Constitutive models for metal foams and lattice materials
Dr. V. S. Deshpande
CUED
Over the past few years cellular materials have been produced for a wide range of applications such as the cores of sandwich panels and various automotive parts. The successful implementation of these materials requires the development of design methods based on engineering constitutive laws. Here constitutive models for two classes of cellular solids are presented: metal foams and lattice frame materials.
The yield behaviour of two aluminium alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress and evolve without corner formation. A phenomenological isotropic constitutive model based on a geometrically self-similar yield surface is presented. Good agreement is seen between the experimentally measured stress versus strain responses and the predictions of the model.
Recently a new class of cellular materials with periodic lattice micro-structures has been manufactured. Unlike metal foams, the micro-structure of these materials is such that they deform by cell wall stretching under all loading conditions. Here, theoretical calculations for the elastic and yield behaviour of one such material with a "cubic" micro-structure are presented. A generalisation of Hill's anisotropic yield criteria for metals is proposed as the multi-axial yield function for this "cubic" cellular solid.
