The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material models, including plasticity, damage, etc., for such materials. However, the prohibitive computational cost arising from the high number of degrees of freedom for engineering structures composed of lattice structures highlights the necessity of homogenization techniques, such as the two-scale computational homogenization method. In the present work, a two-scale homogenization approach with on-the-fly exchange of information is adopted to study the elastoplastic behavior of truss-based lattice structures. The macroscopic homogenized structure is represented by a two-dimensional continuum, while the underlying microscale lattices are modeled as a network of one-dimensional truss elements. This helps to significantly reduce the associated computational cost by reducing the microscopic degrees of freedom. The microscale trusses are assumed to exhibit an elastoplastic material behavior characterized by a combination of nonlinear exponential isotropic hardening and linear kinematic hardening. Through multiple numerical examples, the performance of the adopted homogenization approach is examined by comparing forces and displacements with direct numerical simulations of discrete structures for three types of stretching-dominated lattice topologies, including triangular, X-braced and X-Plus-braced unit cells. Furthermore, the principle of scale separation, which emphasizes the need for an adequate separation between the macroscopic and microscopic characteristic lengths, is investigated.

翻译：金属增材制造技术的革命性进展使得能够生产具有复杂几何特征和高分辨率的合金基点阵结构。这促进了针对此类材料的非线性材料模型（包括塑性、损伤等）的发展。然而，由点阵结构组成的工程结构因其自由度数量庞大而导致的计算成本过高，凸显了均质化技术（如两尺度计算均质化方法）的必要性。在本工作中，采用了一种具有实时信息交换功能的两尺度均质化方法来研究基于桁架的点阵结构的弹塑性行为。宏观均质化结构由二维连续体表示，而底层微观尺度点阵则建模为一维桁架单元网络。这通过减少微观自由度显著降低了相关的计算成本。假设微观尺度桁架表现出弹塑性材料行为，其特征是非线性指数各向同性硬化与线性运动硬化的组合。通过多个数值算例，将所采用的均质化方法得到的力和位移与三种拉伸主导型点阵拓扑（包括三角形、X型支撑和X-Plus型支撑单胞）的离散结构直接数值模拟结果进行比较，从而检验了该方法的性能。此外，还研究了尺度分离原则，该原则强调需要在宏观与微观特征长度之间保持充分的分离。