Session: 13-06-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures I

Paper Number: 161880

Response of Complex Microstructure Composites via an Integrated API Based on Finite-Volume Homogenization 

The recent advances in the manufacturing of composite materials have produced a paradigm shift in the ability to produce materials with complex microstructures that target specific applications. Composite materials with hybrid fibers whose diameters may be varied are realizable nowadays with ordered or disordered microstructures. The different microstructural arrangements affect not only the elastic response defined by the homogenized moduli but also the response in the elastic-plastic region. Both regions are important in defining optimal performance for the intended application. Because of the complexity of the boundary-value problem for the response of a composite material with complex microstructure informed by the intended application, the design of optimal microstructures is conducted using numerical simulation techniques. The finite-element method has emerged as the dominant approach in the analysis of complex microstructure material response. However, the construction of representative volume elements for finite-element analysis is not straightforward, and the usage of this method requires specialized computational training which materials scientists and others often lack.

To make the analysis of complex microstructure materials accessible to the materials/mechanics community at large involved in the design and fabrication of new generations of materials, an Application Programming Interface (API) was constructed that produces homogenized stress-strain response of composite materials 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) coded in Matlab and connected through the Matlab-engine library, as well as Gravity Driven Microstructure Generation (GDMG) algorithm that generates complex composite microstructures [1]. The GDMG algorithm mimics composite microstructures 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. Through an extended Graphical User Interface, the user inputs the dimensions of the unit cell representative of the material at large, as well as parameters regarding the distribution of reinforcing fibers (or porosities), their diameter statistics and elastic properties.

The API may be used by scientists and students alike with little knowledge of the underpinning mechanics to study the effects of ordered/disordered fiber placement, fiber/matrix mechanical properties and content on the overall elastic-plastic response of existing and evolving unidirectional composites and their microstructure-property relationship. Herein we focus on the response of Hashin-type Composite Cylinder Assemblage architectures to study the convergence of both elastic moduli and elastic-plastic response to transversely isotropic behavior under different loading directions as a function of the number of different-diameter fibers at fixed fiber volume fractions. A preliminary study was conducted on ten sets of microstructures containing increasing number of fibers ranging from 5 to 50 with variable diameters at the fixed fiber content of 0.40. Five different realizations were generated for each set of microstructures with fixed number of fibers, and loading was limited to the elastic range. Convergence to transverse isotropy with increasing number of fibers was assessed by the differences in the transverse homogenized moduli E₂₂ and E₃₃, axial shear moduli G₁₂ and G₁₃, axial Poisson’s ratios v₁₂ and v₁₃, and satisfaction of the relationship G₂₃=E₂₂/[2(1+v₂₃)]. While the transverse Young’s moduli, and axial shear moduli and Poisson’s ratios converged to transversely isotropic behavior with microstructures containing 10-15 fibers in a representative volume element, up to 50 fibers were required for the transverse shear modulus G₂₃ that satisfied the relationship G₂₃=E₂₂/[2(1+v₂₃)].

The developed API enables rapid generation of the homogenized response of complex microstructure composites both in the elastic and plastic regions, and its correlation with microstructural statistics, that will be reported in our full contribution.

[1] S. Segal , H. Chen and M-J Pindera (2025). An integrated homogenization engine based on microgravity driven microstructure generation for random unidirectional composites. J. Mater. Ed.

Presenting Author: Samuel Segal University of Virginia

Presenting Author Biography: Mr. Samuel Segal is a third-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