Peridynamics: Meshless method facilitates simulation of fracture in polycrystals

Technical Thrusts

• Quantum Methods - Highly functional codes empowered by basic physics and math theoretical advances.
• Density Functional Theory (DFT)
• Better functionals for improved accuracy.
• Development or extension of efficient, versatile codes (SeqQuest, Picante, RSPt) and parallel eigen-solvers.
• New methods – Finite Element-based DFT implementation, Functionals and codes for Time-dependent and Orbital-free DFT.
• Applications: Electrochemistry; Nanoelectronics; Non-equilibrium Electrons; crystal defect chemistry.
• Investigation of candidate physical systems for qubits.

• Materials Chemistry - Chemistry or reactivity of condensed matter and its effects on the material’s properties and mechanical response.
• LAMMPS – Massively parallel molecular dynamics; full featured, highly versatile.
• GPPT – Genetic programming for automated selection and fitting of classical interatomic potentials.
• SPPARKS - Massively parallel, general purpose kinetic Monte Carlo code.
• Multiscale methods development for rational compound design.
• Applications: Alternate energy and fuel cell concepts; Radiation effects and defect chemistry; High explosives and energetic materials.

• Material Mechanics - Methods to treat the mechanics of highly heterogeneous bodies or other complex geometries (e.g., polycrystals and damaged structures); Shock wave physics.
• Peridynamics – Integral-equation-based meshless continuum mechanics method that provides predictive simulation of damage, fracture, and cracking in an unguided manner.
• XFEM (Extended Finite Element Method) - A effective, new approach for treating complex material geometries.
• Equation of state model development and algorithmic advances.
• Analysis of shock wave effects.

• Multi-scale Materials Simulation R&D – Pursuing the physics to enable well-founded meso-scale simulations and multi-scale couplings.  The key is describing the transition from statistical mechanics to thermodynamics with coarsening length scale in finite systems.
• Coarse-graining via Peridynamics theory.
• Hierarchical multi-scale – Quantum-informed MD; atomistically-informed KMC; Dislocation dynamics; XFEM treatment of heterogeneous continuum.
• Direct coupling – Atom-to-Continuum coupling via meso-scale peridynamics.
• Applications: Rational compound design; electrical device performance; nanoelectronics; electrochemistry.
  

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