论文标题
参考配置中非线性固体力学的晶格玻尔兹曼方法
A Lattice Boltzmann Method for nonlinear solid mechanics in the reference configuration
论文作者
论文摘要
通过足够良好的离散化，晶格Boltzmann方法（LBM）模仿了某些类型的平衡定律的二阶曲柄 - 尼科尔森方案（Farag等人[2021]）。这允许显式，高度可行的LBM有效地求解固体力学的基本方程：质量的保护，线性动量的平衡和组成关系。 迄今为止，所有用于实体模拟的LBM算法 - 参见例如Murthy等。 [2017]，Escande等。 [2020]，Schlüter等。 [2021] - 仅限于小应变案例。此外，在电流（Eulerian）构型中对LBM的典型解释不容易被大型菌株扩展，因为较大的拓扑变化使边界条件的处理复杂化。 在本出版物中，我们提出了一种大变形晶格玻尔兹曼方法，用于几何和组成型非线性固体力学。为了促进多功能边界建模，该算法在参考（Lagrangian）配置中定义。
With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to efficiently solve the fundamental equations of solid mechanics: the conservation of mass, the balance of linear momentum, and constitutive relations. To date, all LBM algorithms for solid simulation - see e.g. Murthy et al. [2017], Escande et al. [2020], Schlüter et al. [2021] - have been limited to the small strain case. Furthermore, the typical interpretation of the LBM in the current (Eulerian) configuration is not easily extensible to large strains, as large topological changes complicate the treatment of boundary conditions. In this publication, we propose a large deformation Lattice Boltzmann Method for geometrically and constitutively nonlinear solid mechanics. To facilitate versatile boundary modelling, the algorithm is defined in the reference (Lagrangian) configuration.
