Multi-Scale Analysis of Composite Materials Using Calculix and the Method of Cells: An Open Source Implementation

Date of Award


Degree Name

Master of Science in Engineering


Mechanical and Aerospace Engineering

First Advisor

Dr. Peter A. Gustafson

Second Advisor

Dr. Muralidhar Ghantasala

Third Advisor

Dr. William Liou

Access Setting

Masters Thesis-Abstract Only

Restricted to Campus until



A unified analysis framework is presented that makes available multiscale analysis of composite structures using the open-source FEA solver package CalculiX CrunchiX (CCX). At the center of this framework is the coupling and use of the Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) library from NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), coupled with CCX to allow multiscale analysis. This implementation allows performing nonlinear micromechanics simulation, using the Generalized Method of Cells (GMC), at each integration point of the FEA model and receive homogenized material response provided at each increment of the simulation. This framework follows the execution principle of FEAMAC with Abaqus, which is the initial implementation of this framework using the commercial FEA package Abaqus/Standard. The evaluation method for the proposed framework is to compare three validated examples, purely structural problems (i.e., no thermal), from the distribution of FEAMAC. The error between the methods was calculated for each model and material orientation, using the reference values from FEAMAC with Abaqus documentation. The reported values were taken at their relative extrema over the range of respective unit of measure for the particular problem. The most significant error reported was in a composite beam four-point bend test specimen with less than 1 % difference. These results show that the proposed coupling can be used with appropriate care for multiscale FEA simulations of composite materials. This work represents the first step to support the use and growth of the audience who can utilize multiscale analysis for composite materials and structures using the low-cost efficient tools such as MAC/GMC code and the open-source FEA package CCX.

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