Kim Keon Ho, Bhalla Amneet P S, Griffith Boyce E
Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA.
Department of Mechanical Engineering, San Diego State University, San Diego, CA, USA.
J Comput Phys. 2023 Nov 15;493. doi: 10.1016/j.jcp.2023.112466. Epub 2023 Sep 1.
This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary methods. The major difference between our approach and conventional immersed boundary methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well-characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations.
本文开发并基准测试了一种浸入式围道动力学方法，用于在流固耦合框架内模拟超弹性材料的变形、损伤和失效。浸入式围道动力学方法描述了一种浸没在粘性不可压缩流体中的不可压缩结构。它以欧拉形式表达动量方程和不可压缩性约束，并以拉格朗日形式描述结构运动和合力。与标准浸入边界方法一样，通过狄拉克δ函数核的积分变换实现欧拉变量和拉格朗日变量之间的耦合。我们的方法与传统浸入边界方法的主要区别在于，我们使用围道动力学而不是经典连续介质力学来确定结构力。我们专注于基于非普通状态的围道动力学材料描述，这使我们能够使用本构对应框架，该框架可以利用特征明确的软材料非线性本构模型。使用广泛使用的非线性不可压缩弹性基准问题，将我们方法的收敛性和准确性与传统方法和浸入式有限元方法进行了比较。我们证明，对于围道动力学视界大小的几种选择，浸入式围道动力学方法在结构自由度数量相似的情况下产生了相当的精度。我们还证明，该方法可以生成流体驱动的材料损伤增长、裂纹形成和扩展以及大变形下破裂的网格收敛模拟。
