Finite element analysis on yield surface evolution of cellular materials

Abstract

The yield surface is the boundary of elastic region in the theory of plasticity, therefore the area and the shape of the yield surface can represent the capability of cellular materials in the stress space. The yield point and the yield surface of one kind of 2D cellular materials, hexagonal honeycombs, is investigated in this study via the finite element analysis with a representative block approach. All components of requisites to computationally investigate yield surface evolution of 2D cellular materials are prepared. A proper determination of yield point for the honeycombs is proposed for the detection of initial and subsequent yield surfaces in the axial-shear stress space and the yield point determination is validated by the comparison between experimental result and finite element analysis. Taking into account a wide range of relative density for honeycombs, the mesh size as well as the pattern and the size of the representative block in finite element is investigated and selected based on the analysis of the mesh convergence analysis, the boundary effect, and the size effect. After probing paths and preloading paths are designed, the initial and subsequent yield surfaces of the honeycombs with different relative density are detected and the influence of relative density on the yield surface evolution is investigated. The investigation shows a shear preloading path followed by an axial preloading path strengthens the capability of honeycombs and the honeycomb with lower relative density may exhibit different behavior of yield surface evolution than those with higher relative density. Further, phenomena of cellular materials including the Bauschinger effect and the hardening behavior (isotropic, kinematic, rotation, distortional) are observed from the yield surface evolution of honeycombs.