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Welcome to **PhaseFieldX** :footcite:t:`code_phasefieldx`. The documentation for the Phase-Field simulation code based on FEniCSx!

Introduction
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The **PhaseFieldX** :footcite:t:`code_phasefieldx` project is designed to simulate and analyze material behavior using phase-field models, which provide a continuous approximation of interfaces, phase boundaries, and discontinuities such as cracks. Leveraging the robust capabilities of *FEniCSx* :footcite:t:`code_BarattaEtal2023`, a renowned finite element framework for solving partial differential equations, this project facilitates efficient and precise numerical simulations. It supports a wide range of applications, including phase-field fracture, solidification, and other complex material phenomena, making it an invaluable resource for researchers and engineers in materials science.


Purpose
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The **PhaseFieldX** :footcite:t:`code_phasefieldx` project aims to advance phase-field modeling through open-source contributions. By leveraging the powerful *FEniCSx* framework, our goal is to enhance and broaden the application of phase-field simulations across various domains of materials science and engineering. We strive to make these advanced simulation techniques more accessible, enabling researchers and engineers to conduct more accurate and comprehensive scientific investigations. Through collaborative efforts, our mission is to deepen understanding, foster innovation, and contribute to the broader scientific community’s pursuit of knowledge in complex material behaviors.

Key Features
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- **Phase-Field Method:** The code employs the phase-field method, a versatile mathematical framework for modeling phenomena such as fracture, phase transitions, and pattern formation as diffuse processes. It enables the simulation of complex behaviors and multiple interacting phenomena within a unified framework.

- **FEniCSx Integration:** Integrated with FEniCSx, a powerful finite element framework, the code provides robust capabilities for solving partial differential equations governing phase-field simulations. This integration ensures efficient computation and adaptive mesh refinement, enhancing simulation accuracy and scalability.
  
- **User-Friendly Interface:** Designed with usability in mind, the code features an intuitive interface for defining material properties, boundary conditions, and simulation parameters. This interface caters to both novice users and experienced researchers, facilitating straightforward setup and execution of simulations.

- **Advanced Visualization:** The code includes advanced visualization tools to depict simulation results effectively. These tools enable comprehensive analysis of crack propagation, stress distributions, and other key quantities, supporting insightful interpretations and comparisons across simulations.


Getting Started
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Whether you are new to phase-field fracture simulations or an experienced researcher, this documentation will guide you through the process of setting up, running, and analyzing simulations using our Phase-Field Fracture code. From installation instructions to detailed usage examples, you'll find comprehensive resources to embark on your phase-field simulation journey.


Contributions and Feedback
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We welcome contributions and feedback from the community to enhance the code's functionality, reliability, and user experience.To get started, please review our `Contributing Guidelines <https://phasefieldx.readthedocs.io/en/latest/extras/DeveloperNotes/main.html>`_ to share your insights and collaborate with fellow developers.

Thank you for choosing our Phase-Field Fracture simulation code. We trust this tool will prove invaluable in advancing your understanding of fracture mechanics and its practical applications.

If you use **PhaseFieldX** :footcite:t:`code_phasefieldx` in your scientific research, please consider citing our work to support its development and increase its scientific visibility.

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.. toctree::

   getting-started/index
   theory/index
   api/index
   auto_examples/index
   extras/index
