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Fish J.,Columbia University | Filonova V.,Columbia University | Yuan Z.,Multiscale Design Systems, LLC
International Journal for Numerical Methods in Engineering | Year: 2013

We present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables. The method is based on a variant of the transformation field analysis (TFA) where eigenstrains are discretized using C 0 continuous approximation in matrix dominated mode of deformation, hereafter referred to as impotent eigenstrain mode, whereas in multiphase mode of deformation, the eigenstrains are approximated using the usual C -1 approximation. The delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase, both characteristic to averaging methods, are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases. The proposed formulation has been verified against a direct numerical simulation. The method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium. © 2013 John Wiley & Sons, Ltd.


Jiang T.,Multiscale Design Systems, LLC | Shao J.F.,Lille Laboratory of Mechanics
Computers and Geotechnics | Year: 2012

Micromechanical analysis based on the fast Fourier transform (FFT) is presented as applied to the nonlinear behavior of porous geomaterials. In this micromechanical model, a simple classical constitutive model is employed for the solid phase, such that the distinct mechanical properties of porous geomaterials can be subsequently and satisfactorily predicted without the use of additional parameters. Furthermore, the FFT-based model automatically satisfies the periodic boundary condition of the micromechanics scheme. The efficacy of the model is shown by applications to Lixhe chalk and Vosges sandstone. © 2012 Elsevier Ltd.


Fish J.,Columbia University | Filonova V.,Columbia University | Yuan Z.,Multiscale Design Systems, LLC
Computer Methods in Applied Mechanics and Engineering | Year: 2012

We present a new multiscale approach, hereafter referred to as reduced order computational continua (RC 2), that possesses computational efficiency of phenomenological models for heterogeneous media with accuracy inherent to generalized and nonlocal continua models. The RC 2 approach introduces no scale separation, makes no assumption about infinitesimality of the fine-scale structure, does not require higher order continuity, introduces no new degrees-of-freedom, is free of higher order boundary conditions and exploits a pre-computed material database to effectively solve a unit cell (representative volume) problem. It features three building blocks: (i) the nonlocal quadrature scheme, (ii) the coarse-scale stress function and (iii) the residual-free fields. The nonlocal quadrature scheme permits nonlocal interactions to extend over finite neighborhoods and thus introduces nonlocality into the two-scale integrals employed in the multiple-scale asymptotic expansion methods, or alternatively, into the Hill-Mandel macrohomogeneity condition. The coarse-scale stress function, which replaces the classical notion of coarse-scale stress being the average of fine-scale stresses, is constructed to express the governing equations in terms of coarse-scale fields only. Finally, the residual-free fields are constructed to avoid costly discrete equilibrium solution of the unit cell problems, which is known to be the bottleneck of multiscale computations. © 2012 Elsevier B.V..


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase I | Award Amount: 100.00K | Year: 2009

The primary objective of this SBIR is to enhance the multiscale design system (MDS-C product line) with various PMC degradation models and to validate it against selected demonstration problems. MDS-C has been successfully used by our customers, including Rolls-Royce Aerospace (CMC airfoil in JSF), GM, Ford and Chrysler (polymer composites), General Electric (polymer composites), Simulia (ABAQUS), Navy (sandwich structures), and AFRL (concrete).We will utilize both phemenological models of polymer degradation developed by Prof. Ruggles-Wrenn where possible and will simultaneously pursue a mechanistic based approach of Prof. Rajagopal whenever necessary – thereby helping to make the “learning curve” less steep and minimizing the barriers to use. In addition to the formulation and implementation of the degradation mechanisms, Phase I will include additional three tasks: (i) calibration of the MDS-C against test data (in Phase I we will fully rely on the existing experiments conducted by Prof. Ruggles-Wrenn), (ii) development of the initial intuitive, workable, user-friendly GUI, (iii) initial Phase I demonstrations comparing the MDS-C predictions with the experimental data of inelastic deformation behavior of the PMR-15 neat resin subjected to prior aging at 288 °C for 2000 h. Profs. Ruggles-Wrenn and Rajagopal will serve as consultants. BENEFIT: Candidate PMCs that could retain their mechanical properties at elevated temperatures, such as PMR-15, could be utilized in turbine engines, exhaust wash structures and high-speed aircraft skins, where structural components are exposed to harsh service conditions, but their insertion is hindered by their lack of predictability. This lack of predictability has often resulted in overdesign and thus limited their use since the overdesigned component may not yield any design advantages. To address the predictability challenge, an experimentally validated multiscale design system that accounts for phenomena at multiple scales to predict the behavior of PMC components will be developed. Such a design system would be indispensable in systematic exploration of alternative designs at the material and structural scales and it would advance the state-of-the-art in the field far beyond what an equivalent investment in its comprising building blocks, such as materials, mechanics, testing and computations.


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase II | Award Amount: 750.00K | Year: 2011

MDS, LLC in collaboration with Rolls-Royce, Hyper-Therm HTC, AFIT, University of Akron and Columbia University will develop a validated physics-based long-term deformation and life prediction multiscale-multiphysics design system (M2DS) for advanced ceramic matrix composites under aerospace gas turbine engine environmental conditions. Specifically we will develop deterministic and probabilistic coupled thermo-mechano-oxidation models of degradation, mechanistic thermal fatigue model and CMC optimization toolkit that will enable to find the best approaches for protecting against oxidation depending on the application conditions, such as environment, temperature, stresses and required component lives. M2DS will be validated for two material systems, Chemical Vapor Infiltrated CMC and Melt Infiltrated CMC GEN II, by utilizing AFIT/AFRL burner rig to simulate various combustion and mechanical loading conditions. BENEFIT: Currently, there are at least two CMC components planned for eventual introduction into the F136 engine. This process would be accelerated if there were validated structural assurance tools available to the design community. It would also have a huge cost benefit, not only from the improved performance, but also from the reduced development costs. The current approach to structural assurance is to build an extensive data base covering all potential failure modes, very expensive and time consuming, followed by building components and destructively testing them, costing additional resources. Validated life assurance models would remove much of this cost. It would provide the confidence necessary to accelerate the use of CMC components and to gain the experience that would promote their usage. In addition to the application to military craft, there are a significant number of static CMC components planned for civil application, such as advanced friction systems, in the relatively near future. The development of efficient computational tools for sensitivity analysis, error and uncertainty quantification, and the solution of model calibration inverse problems are critically important to design and decision under uncertainty and is therefore a fundamentally important goal across DOD Agencies and civil applications.

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