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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Implementation of a Smeared Crack Band Model in a Micromechanics Framework

The smeared crack band theory is implemented within the generalized method of cells and high-fidelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data (where available), and an equivalent finite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single fiber is modeled with generalized method of cells and high-fidelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple fiber repeating unit cell. The generalized method of cells and high-fidelity generalized method of cells models are validated against a very refined finite element model.

Pineda, Evan J.↗
NASA NTRS2002

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

Aboudi, Jacob↗
NASA NTRS2012

Progressive Failure of a Unidirectional Fiber-Reinforced Composite Using the Method of Cells: Discretization Objective Computational Results

The smeared crack band theory is implemented within the generalized method of cells and high-fidelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data (where available), and an equivalent finite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single fiber is modeled with generalized method of cells and high-fidelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple fiber repeating unit cell. The generalized method of cells and high-fidelity generalized method of cells models are validated against a very refined finite element model.

Pineda, Evan J.↗
NASA NTRS2008

Micromechanics-Based Progressive Failure Analysis of Composite Laminates Using Different Constituent Failure Theories

Predicting failure in a composite can be done with ply level mechanisms and/or micro level mechanisms. This paper uses the Generalized Method of Cells and High-Fidelity Generalized Method of Cells micromechanics theories, coupled with classical lamination theory, as implemented within NASA's Micromechanics Analysis Code with Generalized Method of Cells. The code is able to implement different failure theories on the level of both the fiber and the matrix constituents within a laminate. A comparison is made among maximum stress, maximum strain, Tsai-Hill, and Tsai-Wu failure theories. To verify the failure theories the Worldwide Failure Exercise (WWFE) experiments have been used. The WWFE is a comprehensive study that covers a wide range of polymer matrix composite laminates. The numerical results indicate good correlation with the experimental results for most of the composite layups, but also point to the need for more accurate resin damage progression models.

Moncada, Albert M.↗
NASA NTRS2021

Micromechanics-based Modeling of Laminated SiC/SiC Ceramic Matrix Composites

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses.

Ceramic Matrix Composites↗
NASA NTRS2019

A Comparison of Different Modeling Strategies for Predicting Effective Properties of 3D Woven Composites

Three-dimensional (3D) woven composites are an attractive means of achieving superior mechanical performance in aerospace structures. Limited analysis capability currently exists to predict both effective elastic and strength properties for these complex composites. In this study, a comparison of three modeling strategies was performed to assess the ability of the different methods to predict the effective elastic properties of four distinct 3D orthogonal woven composites. Two finite element techniques (in-plane and triply-periodic boundary conditions) and one method of cells technique, the Multiscale Generalized Method of Cells, were considered.

Ricks, Trenton M.↗
NASA NTRS2024

Multiscale Modeling of Thermoplastics Using Atomistic-informed Micromechanics

A multiscale repeating unit cell model of a single spherulite containing four disparate length scales was developed to predict the thermoelastic behavior of semicrystalline thermoplastic materials for composite aerospace applications. The continuum level scales were fully coupled and modeled using the generalized method of cells and the high fidelity generalized method of cells micromechanics theories. Data from molecular dynamics simulations were used as inputs for the amorphous and crystalline constituents in the multiscale continuum models. Effective Young’s modulus, shear modulus, Poisson’s ratio, coefficient of thermal expansion, and thermal conductivity were predicted for polyether ether ketone and polyether ketone ketone, showing good agreement with the available experimental data from the open literature. Moreover, it is shown that predicted properties are fairly insensitive to the fidelity of the micromechanics model used at the highest continuum scale or the assumed shape of the spherulite.

thermoplastics↗
NASA NTRSDate not supplied

Multiscale Modeling of Thermoplastics Using Atomistic-informed Micromechanics

A multiscale model was developed for predicting the thermoelastic behavior of semi-crystalline thermoplastic materials for composite aerospace applications. At the highest scale containing the semi-crystalline spherulite in an amorphous matrix, the generalized method of cells, or high fidelity method of cells, was used to perform the homogenization calculations to obtain the effective properties. Models were developed assuming a cubic, or spherical shape, for the spherulite to understand if the morphology of the spherulite affects the effective thermoelastic properties. The generalized method of cells was used to model at the repeating unit cells at the subscales of the microstructure including the lamellae stacks and granular crystal blocks. The scales are integrated using the multiscale micromechanics method in the NASA Multiscale Analysis Tool. Data from molecular dynamics simulations were used as inputs for the amorphous and crystalline constituents. Convergence studies were performed to determine the best level of discretization for the repeating unit cell at the highest scale. Effective Young’s modulus, shear modulus, Poisson’s ratio, coefficient of thermal expansion, and thermal conductivity were predicted for polyether ether ketone and polyether ketone ketone, and very good agreement between the model utilizing the cubic spherulite and the experimental data, where available, was observed for polyether ketone ketone. Normalization of the data for the bulk polyether ketone ketone, against amorphous data, improved the predictions as compared to experimental data. Overall, the high fidelity method of cells predicted a stiffer response then the generalized method of cells as the crystallinity was increased. The shape of the spherulite had a minimal effect on the predicted bulk properties of the polymers.

thermoplastics↗
NASA NTRS2009

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗
NASA NTRSDate not supplied

Progressive Damage Response of 3D Woven Composites via the Multiscale Recursive Micromechanics Solution with Tailored Fidelity

Progressive failure simulations have been performed for orthogonal 3D woven composites consisting of RTM6 resin matrix and AS4 carbon fibers. The Multiscale Recursive Micromechanics approach has been used, which, while being computationally efficient, captures the primary effects of the microstructure at each considered length scale. This approach also enables use of any micromechanics theory at any length scale, and herein, the fidelity of the chosen theories across the scales has been tailored to strike a balance with computational efficiency. The Mori-Tanaka method is employed at the lowest length scale, the Generalized Method of Cells is used at intermediate scales, and the High-Fidelity Generalized Method of Cells is used at the highest woven composite repeating unit cell scale. Furthermore, two different damage models, also with different levels of fidelity and efficiency, have been used for the resin material at the lowest length scale. Results for the mechanical behavior in response to loading in various directions are compared for the two damage models and with available test data.

3D woven↗
NASA NTRS2006

HFGMC Enhancement of MAC/GMC

Additional information about a mathematical model denoted the high-fidelity generalized method of cells (HFGMC) and implementation of the HFGMC within version 4.0 of the MAC/GMC software has become available. MAC/GMC (Micromechanics Analysis Code With Generalized Method of Cells) was a topic of several prior NASA Tech Briefs articles, version 4.0 having been described in "Comprehensive Micromechanics-Analysis Code - Version 4.0" (LEW-17495-1), NASA Tech Briefs, Vol. 29, No. 9 (September 2005), page 54. MAC/GMC predicts elastic and inelastic thermomechanical responses of composite materials. MAC/GMC utilizes the generalized method of cells (GMC) - a model of micromechanics that predicts macroscopic responses of a composite material as functions of the properties, sizes, shapes, and responses of its constituents (e.g., matrix and fibers). The accuracy of the GMC is limited by neglect of coupling between normal and shear stresses. The HFGMC was developed by combining elements of the GMC and a related model, denoted the higher-order theory for functionally graded materials (HOTFGM), that can account for this coupling. Hence, the HFGMC enables simulation of stress and strain with greater accuracy. Some alterations of the MAC/GMC data structure were necessitated by the greater computational complexity of the HFGMC.

Arnold, Steven M.↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Comparison of Micromechanics Theories for Modeling Discontinuous Long Fiber Reinforced Composites

Two micromechanics theories, the high fidelity generalized method of cells and Carrera Unified Formulation, are used to model a repeating unit cell of a discrete long fiber composite. The models are used to predict the effective properties of a single fiber with varying fiber-to-fiber end gap lengths, as well as the local stresses in the fiber and matrix. Both models produced similar results and demonstrated that they could capture the complex local load transfer due to the shear lag effect.

discrete long fiber composites↗
NASA NTRSDate not supplied

A Convolutional Neural Network for Enhancement of Multi-Scale Localization in Granular Metallic Representative Unit Cells

A convolutional neural network was used to enhance the localization of strain and stress for a generalized method of cells model of a metallic microstructure. Enhanced shear strains, measured in terms of the linear regression coefficients as a function of ground truth strains, were improved from inaccurate and uncorrelated (slope=0.003, Rsq=0.000) to accurate and well correlated (slope=0.890, Rsq=0.882) relative to ground truth (slope=1.0, Rsq=1.0). In applying the convolutional neural network, a convolutional stride of 1.0 (padding=’same’) was only modestly effective while strides of 2 or 3 were more effective yet at higher cost. Additional convolutional layers were generally more expensive than additional dense layers, often with limited benefit. The accuracy of enhanced localized shear strains and stress is expected to yield benefits for damage progression models, especially in the context of hierarchical multi-scale methods where the generalized method of cells is applied at the intermediate scale.

Machine Learning↗
NASA NTRS1999

Micromechanics Analysis Code Post-Processing (MACPOST) User Guide

As advanced composite materials have gained wider usage. the need for analytical models and computer codes to predict the thermomechanical deformation response of these materials has increased significantly. Recently, a micromechanics technique called the generalized method of cells (GMC) has been developed, which has the capability to fulfill this -oal. Tc provide a framework for GMC, the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) has been developed. As MAC/GMC has been updated, significant improvements have been made to the post-processing capabilities of the code. Through the MACPOST program, which operates directly within the MSC/PATRAN graphical pre- and post-processing package, a direct link between the analysis capabilities of MAC/GMC and the post-processing capabilities of MSC/PATRAN has been established. MACPOST has simplified the production, printing. and exportation of results for unit cells analyzed by MAC/GMC. MACPOST allows different micro-level quantities to be plotted quickly and easily in contour plots. In addition, meaningful data for X-Y plots can be examined. MACPOST thus serves as an important analysis and visualization tool for the macro- and micro-level data generated by MAC/GMC. This report serves as the user's manual for the MACPOST program.

Goldberg, Robert K.↗
NASA NTRS2002

MAC/GMC Code Enhanced for Coupled Electromagnetothermoelastic Analysis of Smart Composites

Intelligent materials are those that exhibit coupling between their electromagnetic response and their thermomechanical response. This coupling allows smart materials to react mechanically (e.g., an induced displacement) to applied electrical or magnetic fields (for instance). These materials find many important applications in sensors, actuators, and transducers. Recently interest has arisen in the development of smart composites that are formed via the combination of two or more phases, one or more of which is a smart material. To design with and utilize smart composites, designers need theories that predict the coupled smart behavior of these materials from the electromagnetothermoelastic properties of the individual phases. The micromechanics model known as the generalized method of cells (GMC) has recently been extended to provide this important capability. This coupled electromagnetothermoelastic theory has recently been incorporated within NASA Glenn Research Center's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC). This software package is user friendly and has many additional features that render it useful as a design and analysis tool for composite materials in general, and with its new capabilities, for smart composites as well.

Bednarcyk, Brett A.↗
NASA NTRS2016

Tool for Generation of MAC/GMC Representative Unit Cell for CMC/PMC Analysis

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) 4.0. This tool is especially useful in analyzing ceramic matrix composites (CMCs), where higher fidelity with improved accuracy of local response is needed. The tool, however, can be used for analyzing polymer matrix composites (PMCs) as well. MAC/GMC 4.0 is a composite material and laminate analysis software developed at NASA Glenn Research Center. The software package has been built around the concept of the generalized method of cells (GMC). The computer code is developed with a user friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermomechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that generates a number of different user-defined repeating unit cells (RUCs). In addition, the code has provisions for generation of a MAC/GMC-compatible input text file that can be merged with any MAC/GMC input file tailored to analyze composite materials. Although the primary intention was to address the three different constituents and phases that are usually present in CMCs-namely, fibers, matrix, and interphase-it can be easily modified to address two-phase polymer matrix composite (PMC) materials where an interphase is absent. Currently, the tool capability includes generation of RUCs for square packing, hexagonal packing, and random fiber packing as well as RUCs based on actual composite micrographs. All these options have the fibers modeled as having a circular cross-sectional area. In addition, a simplified version of RUC is provided where the fibers are treated as having a square cross section and are distributed randomly. This RUC facilitates a speedy analysis using the higher fidelity version of GMC known as HFGMC. The first four mentioned options above support uniform subcell discretization. The last one has variable subcell sizes due to the primary intention of keeping the RUC size to a minimum to gain the speed ups using the higher fidelity version of MAC. The code is implemented within the MATLAB (The Mathworks, Inc., Natick, MA) developmental framework; however, a standalone application that does not need a priori MATLAB installation is also created with the aid of the MATLAB compiler.

Materials Engineering↗