A finite element model based on mixture theory is presented for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of both infinitesimal and finite deformation. The governing equations are obtained by applying the conservation laws of momentum and mass to each phase and the solid-fluid mixture. A complete formulation based on the motion of the solid and fluid phases is first presented; then approximations are made with respect to the relative acceleration vector to arrive at a so-called u-p formulation, which is subsequently implemented in a finite element model. The variational forms and matrix formulations are presented. The matrix equations are consistently linearized. The Newmark method is chosen as the global solution algorithm for solving the general finite element matrix equations.; In the u-p formulation for the finite deformation analysis, a modified compressible neo-Hookean hyperelastic model with a Kelvin solid viscous enhancement for the solid matrix is implemented as a test function for the nonlinear constitutive model. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. Fluid compressibility is also considered in terms of volumetric logarithmic strain.; Numerical examples in 1-D and 2-D are presented to validate the finite element model. Results of the small and finite deformation analyses are compared at different strain levels. For the 1-D case the numerical simulation was also compared with the analytical solution. These examples demonstrate the significance of large deformation effects on the transient responses of porous structures, as well as the strong convergence profile exhibited by the iterative algorithm.
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机译:提出了一种基于混合理论的有限元模型,用于分析机械现象,其中涉及在无限小变形和有限变形两种状态下从完全饱和的多孔固体基质中动态驱逐流体。通过将动量和质量守恒定律应用于每相和固液混合物,可以得到控制方程。首先介绍了基于固相和液相运动的完整配方。然后相对于相对加速度矢量进行近似计算,得出所谓的 u bold>- p italic>公式,该公式随后在有限元模型中实现。介绍了变体形式和基质配方。矩阵方程始终如一地线性化。选择Newmark方法作为求解一般有限元矩阵方程的整体求解算法。在用于有限变形分析的 u bold>- p italic>公式中,将修改后的可压缩的新霍克超弹性模型(对固体基质采用开尔文固体粘性增强)作为测试功能。用于非线性本构模型。流体流动的本构模型由针对当前配置制定的广义达西定律表示。流体的可压缩性也以体积对数应变的形式考虑。给出了1-D和2-D的数值示例,以验证有限元模型。在不同应变水平下比较了小变形和有限变形分析的结果。对于一维情况,还将数值模拟与解析解进行了比较。这些例子证明了大变形效应对多孔结构瞬态响应的重要性,以及迭代算法表现出的强收敛性。
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