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A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

机译：统一的连续体和变分多尺度公式，用于流体，固体和流体-结构相互作用

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We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-a method is applied for temporal discretization. A segregated algorithm for the nonlinear solver, based on the original idea introduced in Scovazzi et al. (2016), is carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-alpha method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们使用吉布斯自由能作为热力学势来开发统一的连续谱建模框架。这种框架自然会导致连续体的原始压力变量公式化，在可压缩和不可压缩状态下均表现良好。我们的推导还提供了非线性弹性中自由能的等容-体积加法分解的合理证明。对连续模型进行了变分多尺度分析，为数值离散化奠定了基础。我们首先考虑实例化为超弹性材料的连续体，并针对超弹性动力学问题开发了变分多尺度公式。将通用方法应用于时间离散化。一种基于Scovazzi等人提出的原始思想的非线性求解器的隔离算法。 （2016），经过仔细分析。第二，我们应用新的公式来构造流固耦合问题的新型统一公式。变分多尺度公式用于流体和固体子域中的空间离散化。广义α方法适用于整个连续体，并且在流体和固体子问题中均实现了最佳的高频耗散。在分离算法的基础上，提出了一种新的预测器多校正器算法。在几个基准问题中检查了新配方的功效。结果表明，提出的建模和数值方法构成了一种有前途的技术，可用于生物医学和工程应用，尤其是那些需要不可压缩模型的应用。 （C）2018 Elsevier B.V.保留所有权利。

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