Session: 15-01-01: ASME International Undergraduate Research and Design Exposition

Paper Number: 140278

140278 - A Web-Based Homogenization Engine Based on Microgravity Driven Microstructure Generation for Random Unidirectional Composites 

The continuing expansion of cloud-based computing has produced a rapid increase in the exposure of students at the high school and early university year levels to the development of web-based applications. Concurrently, the relatively recent initiative of undergraduate student exposure to the research environment outside of the traditional NSF-funded REU programs provides opportunities for the integration of web-based applications and specific research topics in support of a Principal Investigator’s effort, while providing training for new generations of STEM leaders in support of the nation’s scientific and technological competitiveness. The work summarized herein leverages the above two trends through exposure of an undergraduate student to fundamental structural mechanics and mechanics of materials concepts in a web-based application, preparing the undergraduate student for successful completion of the required fundamental and advanced mechanics courses in second and third years.

Specifically, this paper describes an Application Programming Interface (API) constructed by a first-year engineering student working under the supervision of a PhD candidate and a faculty member that produces average or homogenized stress-strain curves of unidirectional composites with random microstructures under six fundamental unidirectional loadings. The API integrates two key computational components embedded in Python environment, namely: the homogenization theory known as Finite Volume Direct Averaging Micromechanics (FVDAM) [1] coded in Matlab and connected through the Matlab-engine library, as well as Gravity Driven Microstructure Generation (GDMG) algorithm to generate composite microstructures. To manage server requests, the Flask library was used. To maintain versatility in the API, Python’s lambda functionality was utilized.

The version of FVDAM used in this study employs rectangular unit cell discretization to mimic the composite microstructure through the corresponding material assignment matrix. The material assignment matrix not only defines the composite’s microstructure but is also used in the solution of the unit cell problem for specified unidirectional loading based on the finite volume method. This method provides more efficient solutions to problems with highly heterogeneous domains relative to the popular finite element technique. The key to the automated API execution is the generation of realistic random microstructures accomplished using the GDMG algorithm for a specified fiber content. GDMG mimics the manufacturing process and hence is a more realistic alternative to assigning fiber placement within a unit cell using a random number generator. The user inputs the dimensions of the unit cell that represents the tessellated material in the large, as well as parameters regarding the random distribution of the fibers’ interior and exterior radii, which are each defined individually during runtime. A representative sample of the parameters is generated, along with fiber placement analysis.

There are three main lambda functions employed in the random microstructure generation, namely: the inner radius of the fiber cylinder, the fiber cylinder’s outer radius, and the fiber center’s position vector. The unit cell size and number of fiber cylinders are defined prior to the material matrix generation. Each fiber’s neighbors are analyzed, as well as their angular differentials. Once the parameters for the specified fiber cylinders are established, they are projected onto a material matrix. This material matrix, in addition to the specified material properties, is input into MATLAB through a connecting library. 

The application may be used by scientists and students alike with little knowledge of the underpinning mechanics principles to study the effect of fiber placement randomness, fiber/matrix mechanical properties and content on the overall elastic-plastic response of existing and evolving unidirectional composites and their microstructure-property relationship. In particular, herein we illustrate the extent of scatter in the homogenized stress-strain due to fiber randomness under different loading directions relative to the fiber orientation. The scatter is greatest under transverse normal and shear loading, becomes smaller under out-of-plane shear loading, and practically vanishes under normal loading in the fiber direction, as expected.

 

[1] Bansal, Y. and Pindera, M-J., “Finite-Volume Direct Averaging Micromechanics of Heterogeneous Materials with Elastic-Plastic Phases,” Int. J. Plasticity, Vol. 22, No. 5, 2006, pp. 775-825.

Presenting Author: Samuel Segal University of Virginia

Presenting Author Biography: Mr. Samuel Segal is a second-year civil engineering student at the University of Virginia with a focus on structural engineering. He has a background in generative computation and has developed an algorithm to automatically generate fiber-matrix composite microstructures. He is a current employee at Engineered Materials Concepts LLC, and is working on polishing and applying his program to broader areas of micromechanics.

Authors:

Samuel Segal University of Virginia
Heze Chen University of Virginia
Marek-Jerzy Pindera Engineered Materials Concepts, LLC