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A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning.

Ju Liu1, Alison L Marsden1

  • 1Department of Pediatrics (Cardiology), Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA.

Journal of Computational Physics
|October 10, 2019
PubMed
Summary
This summary is machine-generated.

We present a novel iterative method for hyper-elastodynamics, enhancing computational efficiency. This approach improves solving complex material behavior in simulations.

Keywords:
Anisotropic incompressible hyperelasticityArterial wall modelBlock preconditionerNested iterative methodSaddle-point problemVariational multiscale method

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Area of Science:

  • Computational mechanics
  • Solid mechanics
  • Numerical analysis

Background:

  • Hyper-elastodynamics involves complex material behavior and large deformations.
  • Efficient numerical methods are crucial for simulating these phenomena.
  • Existing methods may face challenges with robustness and computational cost.

Purpose of the Study:

  • To develop a robust and efficient iterative method for solving hyper-elastodynamics problems.
  • To introduce a novel preconditioning technique for improved solver performance.
  • To validate the method's efficacy through representative examples.

Main Methods:

  • A novel continuum formulation for hyper-elastodynamics.
  • Variational multiscale formulation and generalized-α method.
  • Block factorization for decoupling balance laws and linear systems.
  • Nested block preconditioning combining Schur complement and fully coupled approaches.
  • Krylov subspace method integration.

Main Results:

  • Demonstrated robustness of the proposed preconditioning technique compared to SIMPLE and domain decomposition methods.
  • Successful application to compression of an isotropic hyperelastic cube.
  • Effective simulation of a tensile test for an incompressible anisotropic hyperelastic arterial wall model.
  • Examination of robustness with respect to material properties and parallel performance.

Conclusions:

  • The proposed iterative method and preconditioning technique offer a robust and efficient solution for hyper-elastodynamics.
  • The decoupling strategies significantly enhance computational efficiency.
  • The method shows promise for simulating complex biomechanical and material problems.