An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations

The initial yield surface of 2D lattice materials is investigated under biaxial loading using finite element analyses as well as by analytical means. The sensitivity of initial yield surface to the dominant deformation mode is explored by using both low- and high-connectivity topologies whose dominant deformation mode is either local bending or strut stretching, respectively. The effect of microstructural irregularity on the initial yield surface is also examined for both topologies. A pressure-dependent anisotropic yield criterion, which is based on total elastic strain energy density, is proposed for 2D lattice structures, which can be easily extended for application to 3D cellular solids. Proposed criterion uses elastic constants and yield strengths under uniaxial loading, and does not rely on any arbitrary parameter. The analytical framework developed allows the introduction of new scalar measures of characteristic stresses and strains that are capable of representing the elastic response of anisotropic materials with a single elastic master line under multiaxial loading.