# Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT

## TL;DR

This paper introduces a modular, automatic differentiation-based phase-field modeling approach in the MOOSE framework, enabling rapid, accurate, and flexible development of multiphase models for materials science.

## Contribution

It presents a novel modular free energy approach combined with automatic symbolic differentiation in MOOSE, streamlining the development of complex multiphase-field models.

## Key findings

- Enables dynamic combination of free energy contributions at runtime
- Automates derivative calculations, reducing human error
- Demonstrates efficiency and accuracy in various applications

## Abstract

We present a novel phase-field model development capability in the open source MOOSE finite element framework. This facility is based on the 'modular free energy' approach in which the phase-field equations are implemented in a general form that is logically separated from model-specific data such as the thermodynamic free energy density and mobility functions. Free energy terms contributing to a phase-field model are abstracted into self-contained objects that can be dynamically combined at simulation run time. Combining multiple chemical and mechanical free energy contributions expedites the construction of coupled phase-field, mechanics, and multiphase models. This approach allows computational material scientists to focus on implementing new material models, and to reuse existing solution algorithms and data processing routines. A key new aspect of the rapid phase-field development approach that we discuss in detail is the automatic symbolic differentiation capability. Automatic symbolic differentiation is used to compute derivatives of the free energy density functionals, and removes potential sources of human error while guaranteeing that the nonlinear system Jacobians are accurately approximated. Through just-in-time compilation, we greatly reduce the computational expense of evaluating the differentiated expressions. The new capability is demonstrated for a variety of representative applications.