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This paper develops and benchmarks an immersed peridynamics method tosimulate the deformation, damage, and failure of hyperelastic materials withina fluid-structure interaction framework. The immersed peridynamics methoddescribes an incompressible structure immersed in a viscous incompressiblefluid. It expresses the momentum equation and incompressibility constraint inEulerian form, and it describes the structural motion and resultant forces inLagrangian form. Coupling between Eulerian and Lagrangian variables is achievedby integral transforms with Dirac delta function kernels, as in standardimmersed boundary methods. The major difference between our approach andconventional immersed boundary methods is that we use peridynamics, instead ofclassical continuum mechanics, to determine the structural forces. We focus onnon-ordinary state-based peridynamic material descriptions that allow us to usea constitutive correspondence framework that can leverage well characterizednonlinear constitutive models of soft materials. The convergence and accuracyof our approach are compared to both conventional and immersed finite elementmethods using widely used benchmark problems of nonlinear incompressibleelasticity. We demonstrate that the immersed peridynamics method yieldscomparable accuracy with similar numbers of structural degrees of freedom forseveral choices of the size of the peridynamic horizon. We also demonstratethat the method can generate grid-converged simulations of fluid-drivenmaterial damage growth, crack formation and propagation, and rupture underlarge deformations.

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