An artificial damping method for total Lagrangian SPH method with application in biomechanics

Abstract

Introducing artificial damping into the momentum equation to enhance the numerical stability of the smoothed particle hydrodynamics (SPH) method for large strain dynamics has been well established, however, implementing appropriate damping term in the constitutive model as an alternative stabilization strategy in the context of the SPH method is still not investigated. In this paper, we present a simple stabilization procedure by introducing an artificial damping term into the second Piola–Kirchhoff stress to enhance the numerical stability of the SPH method in total Lagrangian formulation. The key idea is to reformulate the constitutive equation by adding a Kelvin–Voigt (KV) type damper with a scaling factor imitating a von Neumann–Richtmyer type artificial viscosity to alleviate the spurious oscillation in the vicinity of sharp spatial gradients. The proposed method is shown to effectively eliminate the appearance of spurious non-physical instabilities and easy to be implemented into the original total Lagrangian SPH formulation. After validating the numerical stability and accuracy of the present method through a set of benchmark tests with very challenging cases, we demonstrate its applications and potentials in the field of biomechanics by simulating the deformation of complex stent structures and the electromechanical excitation–contraction of the realistic left ventricle.