An efficient three-dimensional (3D) multiscale method has been introduced to simulate the geometrically nonlinear behaviors of the plant inspired smart cellular structures. In this method, the scale gap between the geometrical information of motor cells in the small-scale and mechanical behaviors of the cellular structures at the macroscale is bridged through a multiscale framework named multiscale finite element method. The heterogeneous information of the microstructure is then equivalent to the macroscopic coarse elements through the multiscale base functions about the displacements for the solid matrix as well as the fluid pressure. Combined with the “element-independent” corotational algorithm, both the tangent stiffness matrix of the coarse grid elements and their nodal forces can be directly deduced, which will be utilized to decompose the geometrically nonlinear motions of equivalent coarse grid elements at the macroscale level. Consequently, the initial geometrically nonlinear behaviors of the 3D fluidic cellular structures could be simulated by the iteration procedures on the coarse-grid meshes, which will greatly reduce the computation time and memory cost. At the same time, the mechanical responses of the motor cells in the microscale could be easily computed from the obtained macroscopic solutions by the downscaling technique of the multiscale method. To verify the proposed nonlinear multiscale method, some numerical examples are presented. The results demonstrated that the developed nonlinear multiscale formulation for the 3D problems could provide high precision solutions as well as acceptable numerical efficiencies.

一种有效的三维（3D）多尺度方法已被引入，以模拟植物启发的智能细胞结构的几何非线性行为。在这种方法中，通过称为多尺度有限元方法的多尺度框架弥合了小规模运动细胞的几何信息与宏观结构的力学行为之间的尺度差距。然后，通过多尺度基函数，关于固体基质的位移以及流体压力，微观结构的异质信息就相当于宏观的粗糙元素。结合“独立于元素”的校正算法，可以直接推导出粗网格单元的切线刚度矩阵及其节点力，它将用于在宏观尺度上分解等效粗网格元素的几何非线性运动。因此，可以通过在粗网格网格上的迭代过程来模拟3D蜂窝结构的初始几何非线性行为，这将大大减少计算时间和存储成本。同时，通过多尺度方法的降尺度技术，可以很容易地从获得的宏观解中计算出微观尺度上运动细胞的机械响应。为了验证所提出的非线性多尺度方法，给出了一些数值例子。结果表明，针对3D问题开发的非线性多尺度公式可以提供高精度解决方案以及可接受的数值效率。