pypd

A simple and performant Python implementation of the bond-based peridynamic model. pypd offers an intuitive class structure with fully interchangeable material models and integration schemes.

Features

• Pure Python: Written entirely in Python, leveraging the power of Numba for optimal performance
• Material Models: Seamlessly switch between various material models including linear, trilinear and nonlinear
• Integration schemes: Fully interchangeable integration schemes
• Examples: Several examples are provided and validated using published experimental data

Usage

Explore examples using pypd in Google Colab

Example description	Notebook
Crack branching in Homalite
Half-notched quasi-brittle beam in three-point bending
Plate with a hole under tension

Getting started

Development version from GitHub:

pip install git+https://github.com/mark-hobbs/pypd.git

or for contributors using Pipenv:

git clone https://github.com/mark-hobbs/pypd.git
cd pypd/
pipenv install --dev
pipenv shell

Usage with uv

Build and install pypd:

uv pip install -e .

Run examples:

uv run -m examples.crack_branching

Dependencies

• NumPy
• Numba
• scikit-learn
• Matplotlib
• tqdm

Development dependencies

• Black
• Ruff
• Jupyter

Examples

Expand for a summary of the examples provided

• Crack branching in notched Homalite sheets
• Plate with a hole in tension
• Three-point bending test of a half-notched concrete beam
• Nuclear graphite ring compression test
• Mixed-mode fracture in concrete

Crack branching

python -m examples.crack_branching

Mixed-mode fracture

python -m examples.mixed_mode_fracture

Example with validation using experimental data.

García-Álvarez, V. O., Gettu, R., and Carol, I. (2012). Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model. Sadhana, 37(1):187–205.

Flexural three-point bending test - half-notched beam

python -m examples.half_notched_beam

Minimal example

✅ TODO

• Write unit tests
• Write documentation
• Publish on PyPI
• Add support for different compute backends:
  • numba-cuda
  • jax
  • warp
• feature/space-filling-curve - sort particles spatially to improve memory access (see this notebook on understanding the Hilbert curve)
• Implement a volume correction scheme to improve spatial integration accuracy
• Bonds are always derivable from Particles. Let Model manage Bonds internally.
• Benchmark GPU kernel performance (roofline model)
• Add additional examples
  • Past, current and future trends and challenges in non-deterministic fracture mechanics: A review
  • A review on phase-field models of brittle fracture and a new fast hybrid formulation

Completed tasks

• feature/animation - add native capabilities to generate animations
• Implement a surface correction scheme to correct the peridynamic surface effect
• Implement different influence functions (constant/triangular/quartic)
• Separate model and simulation logic: simulation.run(model)
• GPU acceleration using numba cuda