FEpX { Finite Element Polycrystals
Theory, Finite Element Formulation, Numerical Implementation
and Illustrative Examples
Paul R. Dawson and Donald E. Boyce
Deformation Process Laboratory
Sibley School of Mechanical and Aerospace Engineering
Cornell University
April 14, 2015
1.1 Purpose
The purpose of this article is to lay out a complete system of equations for modeling the anisotropic,
elasto-viscoplastic response of polycrystalline solids comprised of aggregates of grains and to summarize
a nite element formulation that may be employed to compute the motion and stress in polycrystals
governed by the system of equations under imposed loadings. The governing equations together with
associated solution methodologies dene a modeling framework, referred to as FEpX, that is focused
at a physical length scale of an ensemble of grains. There is an associated nite element code, also
named FEpX, that follows the framework. A major motivation for archiving this article is to provide
a thorough and accessible reference that researchers who utilize the code can readily cite. However,
the article stands independently in providing a complete summary of a crystal-scale model for the
elasto-viscoplastic response of polycrystalline aggregates and a nite element formulation that enables
solving the model equations over motions that entail large deformations.
The content provided here regarding the governing equations and nite element framework draws
primarily from the following published articles: [1, 2, 3, 4]. The present article is not intended to serve
as a primer for computational crystal plasticity, so background knowledge of solid mechanics, including
crystal plasticity, and nonlinear nite element methods is assumed. Rather, it strives to encapsulate
the full set of equations, assumptions, and solution approximations necessary to document simulation
results with sucient detail to facilitate those results being reproduced by others.
1.2 Scope
The scope of this article is limited to the theory and methods that dene the FEpX framework, plus
a general overview of the data
ow within the framework and the interfaces with tools to instantiate
virtual polycrystals and to visualize simulation results. Consequently, there are sections of the article
devoted to these topics, as listed in the Table of Contents. Also provided are representative examples to
illustrate application of the derivative nite element code to modeling of single and dual phase metallic
alloys. No detailed information is included on the specic formatting used for problem denition, code
execution, or exported simulation results. That information is contained in separate documentation
associated with the code itself.
1.3 Complementary modeling tools
The role of FEpX in the modeling of polycrystals is to solve the boundary
http://arxiv.org/pdf/1504.03296v1.pdf
Theory, Finite Element Formulation, Numerical Implementation
and Illustrative Examples
Paul R. Dawson and Donald E. Boyce
Deformation Process Laboratory
Sibley School of Mechanical and Aerospace Engineering
Cornell University
April 14, 2015
1.1 Purpose
The purpose of this article is to lay out a complete system of equations for modeling the anisotropic,
elasto-viscoplastic response of polycrystalline solids comprised of aggregates of grains and to summarize
a nite element formulation that may be employed to compute the motion and stress in polycrystals
governed by the system of equations under imposed loadings. The governing equations together with
associated solution methodologies dene a modeling framework, referred to as FEpX, that is focused
at a physical length scale of an ensemble of grains. There is an associated nite element code, also
named FEpX, that follows the framework. A major motivation for archiving this article is to provide
a thorough and accessible reference that researchers who utilize the code can readily cite. However,
the article stands independently in providing a complete summary of a crystal-scale model for the
elasto-viscoplastic response of polycrystalline aggregates and a nite element formulation that enables
solving the model equations over motions that entail large deformations.
The content provided here regarding the governing equations and nite element framework draws
primarily from the following published articles: [1, 2, 3, 4]. The present article is not intended to serve
as a primer for computational crystal plasticity, so background knowledge of solid mechanics, including
crystal plasticity, and nonlinear nite element methods is assumed. Rather, it strives to encapsulate
the full set of equations, assumptions, and solution approximations necessary to document simulation
results with sucient detail to facilitate those results being reproduced by others.
1.2 Scope
The scope of this article is limited to the theory and methods that dene the FEpX framework, plus
a general overview of the data
ow within the framework and the interfaces with tools to instantiate
virtual polycrystals and to visualize simulation results. Consequently, there are sections of the article
devoted to these topics, as listed in the Table of Contents. Also provided are representative examples to
illustrate application of the derivative nite element code to modeling of single and dual phase metallic
alloys. No detailed information is included on the specic formatting used for problem denition, code
execution, or exported simulation results. That information is contained in separate documentation
associated with the code itself.
1.3 Complementary modeling tools
The role of FEpX in the modeling of polycrystals is to solve the boundary
http://arxiv.org/pdf/1504.03296v1.pdf
