论文标题
大变形流体饱和多孔结构的均质化
Homogenization of large deforming fluid-saturated porous structures
论文作者
论文摘要
提出了两尺度的计算均质化方法，用于建模局部周期性流体饱和培养基，该培养基受到准负载引起的大变形。周期性异质性与介观量表有关，在介质尺度上，由超弹性骨骼组成的双重多孔培养基和不可压缩的粘性液在渗透性中具有很大的对比度。在与当前变形配置有关的Eulerian框架内，将两尺度均质化方法应用于及时离散的线性化模型，与增量公式相关。为此，使用材料衍生物在对流速度场中分化了在空间构型中表达的平衡方程和质量保护。线性化方程的均匀化过程提供了有效（均质）材料特性，以构成增量的宏观问题。使用有限元方法实现了多尺度问题的耦合算法。提供了孔弹培养基的说明性2D数值模拟，包括简单的验证测试。
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the mesoscopic scale at which a double porous medium constituted by hyperelastic skeleton and an incompressible viscous fluid is featured by large contrasts in the permeability. Within the Eulerian framework related to the current deformed configuration, the two-scale homogenization approach is applied to a linearized model discretized in time, being associated with an incremental formulation. For this, the equilibrium equation and the mass conservation expressed in the spatial configuration are differentiated using the material derivative with respect to a convection velocity field. The homogenization procedure of the linearized equations provides effective (homogenized) material properties are computed to constitute the incremental macroscopic problem. The coupled algorithm for the multiscale problem is implemented using the finite element method. Illustrative 2D numerical simulations of a poroelastic medium are presented including a simple validation test.
