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.

翻译：本文开发并验证了一种浸入式近场动力学方法，用于模拟流固耦合框架中超弹性材料的变形、损伤及破坏过程。该方法描述浸没在粘性不可压缩流体中的不可压缩结构，采用欧拉形式表达动量方程与不可压缩约束条件，并以拉格朗日形式描述结构运动及其产生的反作用力。欧拉变量与拉格朗日变量之间的耦合通过狄拉克δ函数核的积分变换实现，这与标准浸入边界方法一致。本方法与常规浸入边界方法的主要区别在于：采用近场动力学而非经典连续介质力学来确定结构力。我们重点研究非普通状态基近场动力学材料描述，该方法可通过本构对应框架利用软材料中已被充分表征的非线性本构模型。通过广泛采用的非线性不可压缩弹性基准问题，我们将本方法的收敛性与精度与传统有限元方法及浸入式有限元方法进行了比较。结果表明，在近场动力学水平尺度参数不同取值且结构自由度相近时，浸入式近场动力学方法可获得相当的计算精度。此外，本方法能够实现网格收敛的数值模拟，可准确描述大变形条件下流体驱动的材料损伤扩展、裂纹萌生与传播及断裂行为。