An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure

TL;DR

This paper introduces an immersed peridynamics method for simulating fluid-structure interactions involving damage and failure in hyperelastic materials, combining Eulerian and Lagrangian formulations for improved accuracy and damage modeling.

Contribution

The paper presents a novel immersed peridynamics approach that integrates nonlinear soft material models into fluid-structure interaction simulations, enabling damage and failure analysis.

Findings

Comparable accuracy to finite element methods for nonlinear elasticity

Capable of simulating crack growth and rupture under large deformations

Achieves grid convergence in damage growth simulations

Abstract

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.