A non-ordinary state-based Godunov-peridynamics formulation for strong shocks in solids

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Abstract

The theory and meshfree implementation of peridynamics has been proposed to model problems involving transient strong discontinuities such as dynamic fracture and fragment-impact problems. For effective application of numerical methods to these events, essential shock physics and Gibbs instability should be addressed. The Godunov scheme for shock treatment has been shown to be an effective approach for tackling these two issues but has not been considered yet for peridynamics. This work introduces a physics-based shock modeling formulation for non-ordinary state-based peridynamics, in which the Godunov scheme is introduced by embedding the Riemann solution into the force state, resulting in a shock formulation free of tuneable parameters. Several benchmark problems are solved to demonstrate the effectiveness of the proposed formulation for modeling problems involving shocks in solids.

Original languageEnglish (US)
JournalComputational Particle Mechanics
DOIs
StatePublished - Jan 1 2019

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Shock
Shock problems
Physics
Formulation
Godunov Scheme
Numerical methods
Dynamic Fracture
Strong Discontinuity
Riemann Solution
Meshfree
Modeling
Fragment
Numerical Methods
Benchmark
Demonstrate
Model

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Civil and Structural Engineering
  • Numerical Analysis
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes
  • Computational Mathematics

Cite this

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abstract = "The theory and meshfree implementation of peridynamics has been proposed to model problems involving transient strong discontinuities such as dynamic fracture and fragment-impact problems. For effective application of numerical methods to these events, essential shock physics and Gibbs instability should be addressed. The Godunov scheme for shock treatment has been shown to be an effective approach for tackling these two issues but has not been considered yet for peridynamics. This work introduces a physics-based shock modeling formulation for non-ordinary state-based peridynamics, in which the Godunov scheme is introduced by embedding the Riemann solution into the force state, resulting in a shock formulation free of tuneable parameters. Several benchmark problems are solved to demonstrate the effectiveness of the proposed formulation for modeling problems involving shocks in solids.",
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AB - The theory and meshfree implementation of peridynamics has been proposed to model problems involving transient strong discontinuities such as dynamic fracture and fragment-impact problems. For effective application of numerical methods to these events, essential shock physics and Gibbs instability should be addressed. The Godunov scheme for shock treatment has been shown to be an effective approach for tackling these two issues but has not been considered yet for peridynamics. This work introduces a physics-based shock modeling formulation for non-ordinary state-based peridynamics, in which the Godunov scheme is introduced by embedding the Riemann solution into the force state, resulting in a shock formulation free of tuneable parameters. Several benchmark problems are solved to demonstrate the effectiveness of the proposed formulation for modeling problems involving shocks in solids.

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