SEARCH · Engineering Papers

Results for “generalized multiscale finite element method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗

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 NTRS2019

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results and Analysis: Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally-cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using Matlab® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

NASA NTRS2019

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results & Analysis - Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using MatlabÂ® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

DOE OSTI2021

Learning constitutive relations using symmetric positive definite neural networks

In this work, we present a new neural-network architecture, called the Cholesky-factored symmetric positive definite neural network (SPD-NN), for modeling constitutive relations in computational mechanics. Instead of directly predicting the stress of the material, the SPD-NN trains a neural network to predict the Cholesky factor of the tangent stiffness matrix, based on which the stress is calculated in incremental form. As a result of this special structure, SPD-NN weakly imposes convexity on the strain energy function, satisfies the second order work criterion (Hill's criterion) and time consistency for path-dependent materials, and therefore improves numerical stability, especially when the SPD-NN is used in finite element simulations. Depending on the types of available data, we propose two training methods, namely direct training for strain and stress pairs and indirect training for loads and displacement pairs. We demonstrate the effectiveness of SPD-NN on hyperelastic, elasto-plastic, and multiscale fiber-reinforced plate problems from solid mechanics. The generality and robustness of SPD-NN make it a promising tool for a wide range of constitutive modeling applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 NTRS2012

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

Pineda, Evan J.↗

DOE OSTI2021

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

Motivated by recent advances in manufacturing, the design of materials is the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for the mesoscale-level design of particulate composites for an optimal macroscale-level response. The method relies on a custom shape optimization scheme to find the extrema of a nonlinear cost function subject to a set of constraints. Three key “modules” constitute the method: multiscale modeling, sensitivity analysis, and optimization. Multiscale modeling relies on a classical homogenization method and a nonlinear NURBS-based generalized finite element scheme to efficiently and accurately compute the structural response of particulate composites using a nonconformal discretization. A three-parameter isotropic damage law is used to model microstructure-level failure. An analytical sensitivity method is developed to compute the derivatives of the cost/constraint functions with respect to the design variables that control the microstructure's geometry. The derivation uncovers subtle but essential new terms contributing to the sensitivity of finite element shape functions and their spatial derivatives. Several structural problems are solved to demonstrate the applicability, performance, and accuracy of the method for the design of particulate composites with a desired macroscopic nonlinear stress-strain response.

42 ENGINEERING↗

NASA NTRS2017

Comparison of Multiscale Method of Cells-Based Models for Predicting Elastic Properties of Filament Wound C/C-SiC

Three different multiscale models, based on the method of cells (generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent multiscale modeling of all phases using the generalized method of cells, synergistic (two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical (one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC. Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute.

multiscale modeling↗

DOE OSTI2023

A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2016

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

composite structures↗

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 NTRS2019

Integration of MAC/GMC into CalculiX, an Open Source Finite Element Code

An 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 of the Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) library from NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) to allow micromechanics analysis. The results show that the proposed coupling can be used with appropriate care for multiscale FEA simulations of composite materials. The largest error reported in this validation was in a four-point bend test specimen with an error of less than 1% difference in the maximum deflection of the beam.

Yapor Genao, Francisco A.↗

NASA NTRS2013

On Multiscale Modeling: Preserving Energy Dissipation Across the Scales with Consistent Handshaking Methods

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity at both scales, the energy density and the energy release rate must be preserved identically across the two scales. This requires a consistent characteristic length or localization limiter. The effects of scaling (or not scaling) the dimensions of the microscale repeating unit cell (RUC), according to the macroscale element size, in a multiscale analysis was investigated using two examples. Additionally, the ramifications of the macroscale element shape, compared to the RUC, was studied.

Pineda, Evan J.↗

NASA NTRSDate not supplied

A Convolutional Neural Network for Multiscale Modeling of Composite Materials

An artificial convolutional neural network was created to efficiently mimic a micromechanics model, the High Fidelity Generalized Method of Cells, for use in multi-scale structural finite element analysis. The network was found to quickly and accurately replicate the stiffness predicted by the micromechanics model using a 2D image of an idealized representative volume element of a fiber/matrix microstructure. The long-term goal of this work is to efficiently apply multi-scale methods for predicting the damage progression of a composite structure.

Composites↗

NASA NTRS2006

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗

NASA NTRS2007

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗