# Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations

## TL;DR

This paper introduces a diffuse-interface crystal plasticity model for polycrystals that simplifies boundary conditions into a single boundary-value problem, capturing grain boundary effects through geometrically necessary dislocations.

## Contribution

It develops a novel diffuse-interface model that represents grain boundaries as geometrically necessary dislocations within a unified boundary-value problem framework.

## Key findings

- Constructs a stress-free initial polycrystal with piecewise constant rotation fields.
- Provides a foundation for higher order models with grain boundary energy and evolution.
- Simplifies polycrystal plasticity modeling by unifying boundary conditions.

## Abstract

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-free polycrystal is constructed by imposing F^L to be a piecewise constant rotation field R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.