Homogenized Yield Surface of an Anisotropic Plate Lattice Metamaterial
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With advancements in additive manufacturing, the fabrication of thin-walled metallic structures has become feasible. This includes plate lattice metamaterials, which can achieve excellent weight-specific mechanical properties. To design and efficiently analyze components composed of such cellular metamaterials, it is necessary to determine their effective mechanical properties. For the transition from micro- to macro-scale, the finite element method (FEM) is particularly suitable. While elastic properties can be homogenized reliably, the treatment of effective plastic properties remains a major challenge and is the focus of current research efforts. This work numerically determines the effective initial yield surface of an anisotropic plate lattice structure, using FEM and periodic boundary conditions, and subsequently describes it using a closed-form, continuously differentiable analytical expression. Because no description of the yield surface in the principal stress space is possible, due to the pronounced effective yield strength anisotropy of the considered structure, a very general weighted-sum function (WS) is used to represent the effective yield surface in the six-dimensional stress space. Finally, the determined yield model is compared with experimental results. The generated model allows for efficient computation of the effective yield surface, and the generality of the used yield function enables its application to a wide range of lattice structures, enhancing the practical utility of the method.
