Title: Homogenization of flow in inflatable periodic structures with nonlinear effects Show Chinese title

Title: 可充气周期结构中考虑非线性效应的流动均质化

Abstract: The paper presents a new type of weakly nonlinear two-scale model of inflatable periodic poroelastic structures saturated by Newtonian fluids. The periodic microstructures incorporate fluid inclusions connected to the fluid channels by admission and ejection valves respected by a 0D model. This induces a nonlinearity in the macroscopic Biot-type model, whereby the Darcy flow model governs the fluid transport due to the channels. Moreover, the fluid channels consist of compartments separated by semipermeable membranes inducing the pressure discontinuity. The homogenized model is derived under the small deformation assumption, however the equilibrium is considered in the Eulerian frame. Deformation-dependent homogenized coefficients of the incremental poroelasticity constitutive law and the permeability are approximated using the sensitivity analysis, to avoid coupled two-scale iterations. Numerical simulations illustrate the inflation process in time. Example of a bi-material cantilever demonstrates the inflation induced bending. The proposed two-scale model is intended to provide a computational tool for designing of porous metamaterials for fluid transport, or shape morphing with various potential applications. Show Chinese abstract

Abstract: 本文提出了一种新型的弱非线性双尺度模型，用于描述由牛顿流体饱和的可膨胀周期性多孔弹性结构。 周期性微观结构包含通过进气和排气阀与流体通道相连的流体夹杂物，这些阀门由0D模型分别描述。 这在宏观的Biot型模型中引入了非线性，其中由于通道的存在，达西流模型控制流体传输。 此外，流体通道由半透膜分隔的腔室组成，从而产生压力不连续性。 均质化模型是在小变形假设下推导的，然而平衡是在欧拉框架中考虑的。 采用敏感性分析近似增量多孔弹性本构定律和渗透率的变形相关均质化系数，以避免耦合的双尺度迭代。 数值模拟展示了随时间变化的膨胀过程。 一种双材料悬臂梁的例子展示了膨胀引起的弯曲。 所提出的双尺度模型旨在为多孔超材料的设计提供计算工具，用于流体传输或形状变换，具有各种潜在应用。