ECCOMAS 2024

A First-Order Conservation Law Framework for Fast Dynamic Brittle Fracture: Smoothed Particle Hydrodynamics Method

  • Refachinho de Campos, Paulo (Independent Researcher)
  • Hean Lee, Chun (University of Glasgow)
  • Gil, Antonio (Swansea University)
  • Bonet, Javier (CIMNE)

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This work presents the extension of the Updated Reference Lagrangian Smoothed Particle Hydrodynamics (SPH) algorithm introduced in [1-2] to the context of dynamic brittle fracture. The key feature of this formulation is the multiplicative decomposition of the deformation tensor into an internal state variable and an incremental deformation. This is achieved by considering that the original configuration deforms into the current configuration through a series of intermediate configurations. Taking advantage of this formalism, an entropy-stable upwiding stabilisation method derived by means of Rankine Hugoniot jump conditions is utilised. To understand the dynamics of fracture in linear elastic materials, it is beneficial to consider that a portion of the pre-fracture strain energy is converted into both kinetic and fracture energies. However, in scenarios dominated by significant inertial effects, one might be tempted to assume that the fraction of energy allocated to creating new fracture surfaces is significantly less than that converted into kinetic energy. This perspective suggests that, during the fracturing event, strain potential energy can be completely transformed into kinetic energy. With this hypothesis, we develop a set of expressions that describe the changes in velocity and the deformation gradient occurring post-fracture. The effects of energy dissipation associated with fracture energy are accounted by a cohesive force model. From the numerical standpoint, a continuous crack is represented as a set of contiguous fractured particles. Upon reaching a failure criterion, each fractured particle is split into two child particles. Finally, to demonstrate the applicability of the methodology, preliminary results are presented for classic 2D dynamic fracture benchmarks. [1] Refachinho de Campos, P. R., Gil, A. J., Hean Lee, C., Giacomini, M., Bonet, J. A New Updated Reference Lagrangian Smooth Particle Hydrodynamics algorithm for isothermal elasticity and elasto-plasticity. Comput. Methods Appl. Mech. Engrg. (2022) 392:114680. [2] Refachinho de Campos, P. R. A New Updated Reference Lagrangian Smooth Particle Hydrodynamics framework for large strain solid dynamics and its extension to dynamic fracture. PhD Thesis. Swansea University. (2023)