Numerical determination of initial and subsequent yield surfaces of open-celled model foams

In the present work, the overall yield behaviour of a three-dimensional model foam is investigated by microstructural modeling and numerical homogenisation. The analyses are performed on an elasto-plastic lattice of tetrakaidecahedral cells which provides a surrogate model for metallic foams with open cells. For the determination of the macroscopic yield surfaces in strain space as well as in stress space, a strain-energy based homogenisation scheme is applied to a representative volume element. This scheme is derived directly from the Hill principle and thus assures the physical consistency with mechanically defined effective properties in a natural manner. By tracing the evolution of the overall yield surface, the different hardening mechanisms are addressed. It is found that for complex load histories the yield surfaces are not only shifted but may also change their shape and size considerably.