Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix models”

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.

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

At least 577 records · Page 32

Fully Coupled Micro/Macro Deformation, Damage, and Failure Prediction for SiC/Ti-15-3 Laminates

The deformation, failure, and low cycle fatigue life of SCS-6/Ti-15-3 composites are predicted using a coupled deformation and damage approach in the context of the analytical generalized method of cells (GMC) micromechanics model. The local effects of inelastic deformation, fiber breakage, fiber-matrix interfacial debonding, and fatigue damage are included as sub-models that operate on the micro scale for the individual composite phases. For the laminate analysis, lamination theory is employed as the global or structural scale model, while GMC is embedded to operate on the meso scale to simulate the behavior of the composite material within each laminate layer. While the analysis approach is quite complex and multifaceted, it is shown, through comparison with experimental data, to be quite accurate and realistic while remaining extremely efficient.

Bednarcyk, Brett A.↗

The matrix exponential in transient structural analysis

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Minnetyan, Levon↗

Inelastic response of metal matrix composites under biaxial loading

Theoretical predictions and experimental results were obtained for inelastic response of unidirectional and angle ply composite tubes subjected to axial and torsional loading. The composite material consist of silicon carbide fibers in a titanium alloy matrix. This material is known to be susceptible to fiber matrix interfacial damage. A method to distinguish between matrix yielding and fiber matrix interfacial damage is suggested. Biaxial tests were conducted on the two different layup configurations using an MTS Axial/Torsional load frame with a PC based data acquisition system. The experimentally determined elastic moduli of the SiC/Ti system are compared with those predicted by a micromechanics model. The test results indicate that fiber matrix interfacial damage occurs at relatively low load levels and is a local phenomenon. The micromechanics model used is the method of cells originally proposed by Aboudi. Finite element models using the ABACUS finite element program were used to study end effects and fixture specimen interactions. The results to date have shown good correlation between theory and experiment for response prior to damage initiation.

Lissenden, C. J.↗

A Micromechanics-Based Damage Model for [+/- Theta/90n]s Composite Laminates

A new damage model based on a micromechanical analysis of cracked [+/- Theta/90n]s laminates subjected to multiaxial loads is proposed. The model predicts the onset and accumulation of transverse matrix cracks in uniformly stressed laminates, the effect of matrix cracks on the stiffness of the laminate, as well as the ultimate failure of the laminate. The model also accounts for the effect of the ply thickness on the ply strength. Predictions relating the elastic properties of several laminates and multiaxial loads are presented.

Mayugo, Joan-Andreu↗

A Micromechanics-Based Damage Model for the Strength Prediction of Composite Laminates

A new damage model based on a micromechanical analysis of cracked [+/-0deg/90deg(sub n)]s laminates subjected to multiaxial loads is proposed. The model predicts the onset and accumulation of transverse matrix cracks in uniformly stressed laminates, the effect of matrix cracks on the stiffness of the laminate, as well as the ultimate failure of the laminate. The model also accounts for the effect of the ply thickness on the ply strength. Predictions relating the elastic properties of several laminates and multiaxial loads are presented.

Camanho, Pedro P.↗

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Maghami, Peiman G.↗

Efficient Computation of Closed-loop Frequency Response for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, full-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open and closed loop loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, a speed-up of almost two orders of magnitude was observed while accuracy improved by up to 5 decimal places.

Maghami, Peiman G.↗

Thermohydrodynamic analysis of cryogenic liquid turbulent flow fluid film bearings, phase 2

The Phase 2 (1994) Annual Progress Report presents two major report sections describing the thermal analysis of tilting- and flexure-pad hybrid bearings, and the unsteady flow and transient response of a point mass rotor supported on fluid film bearings. A literature review on the subject of two-phase flow in fluid film bearings and part of the proposed work for 1995 are also included. The programs delivered at the end of 1994 are named hydroflext and hydrotran. Both codes are fully compatible with the hydrosealt (1993) program. The new programs retain the same calculating options of hydrosealt plus the added bearing geometries, and unsteady flow and transient forced response. Refer to the hydroflext & hydrotran User's Manual and Tutorial for basic information on the analysis and instructions to run the programs. The Examples Handbook contains the test bearing cases along with comparisons with experimental data or published analytical values. The following major tasks were completed in 1994 (Phase 2): (1) extension of the thermohydrodynamic analysis and development of computer program hydroflext to model various bearing geometries, namely, tilting-pad hydrodynamic journal bearings, flexure-pad cylindrical bearings (hydrostatic and hydrodynamic), and cylindrical pad bearings with a simple elastic matrix (ideal foil bearings); (2) improved thermal model including radial heat transfer through the bearing stator; (3) calculation of the unsteady bulk-flow field in fluid film bearings and the transient response of a point mass rotor supported on bearings; and (4) a literature review on the subject of two-phase flows and homogeneous-mixture flows in thin-film geometries.

Sanandres, Luis↗

An improved model for the Earth's gravity field

An improved model for the Earth's gravity field, TEG-1, was determined using data sets from fourteen satellites, spanning the inclination ranges from 15 to 115 deg, and global surface gravity anomaly data. The satellite measurements include laser ranging data, Doppler range-rate data, and satellite-to-ocean radar altimeter data measurements, which include the direct height measurement and the differenced measurements at ground track crossings (crossover measurements). Also determined was another gravity field model, TEG-1S, which included all the data sets in TEG-1 with the exception of direct altimeter data. The effort has included an intense scrutiny of the gravity field solution methodology. The estimated parameters included geopotential coefficients complete to degree and order 50 with selected higher order coefficients, ocean and solid Earth tide parameters, Doppler tracking station coordinates and the quasi-stationary sea surface topography. Extensive error analysis and calibration of the formal covariance matrix indicate that the gravity field model is a significant improvement over previous models and can be used for general applications in geodesy.

Tapley, B. D.↗

An Overview of Materials Structures for Extreme Environments Efforts for 2015 SBIR Phases I and II

Technological innovation is the overall focus of NASA's Small Business Innovation Research (SBIR) program. The program invests in the development of innovative concepts and technologies to help NASA's mission directorates address critical research and development needs for Agency projects. This report highlights innovative SBIR 2015 Phase I and II projects that specifically address areas in Materials and Structures for Extreme Environments, one of six core competencies at NASA Glenn Research Center. Each article describes an innovation, defines its technical objective, and highlights NASA applications as well as commercial and industrial applications. Ten technologies are featured: metamaterials-inspired aerospace structures, metallic joining to advanced ceramic composites, multifunctional polyolefin matrix composite structures, integrated reacting fluid dynamics and predictive materials degradation models for propulsion system conditions, lightweight inflatable structural airlock (LISA), copolymer materials for fused deposition modeling 3-D printing of nonstandard plastics, Type II strained layer superlattice materials development for space-based focal plane array applications, hydrogenous polymer-regolith composites for radiation-shielding materials, a ceramic matrix composite environmental barrier coating durability model, and advanced composite truss printing for large solar array structures. This report serves as an opportunity for NASA engineers, researchers, program managers, and other personnel to learn about innovations in this technology area as well as possibilities for collaboration with innovative small businesses that could benefit NASA programs and projects.

integrated reacting fluid dynamics and predictive ↗

Rate dependent stress-strain behavior of advanced polymer matrix composites

The formulation of an elastic/viscoplastic constitutive model which was used to predict the measured behavior of graphite/thermoplastic and graphite/bismaleimide composite materials at elevated temperature is described. The model incorporates the concepts of overstress and effective strain/strain to provide a simple formulation which was able to account for material behavior under monotonic tension or compression loads over a temperature range of 23 to 200 C. Observed behavior such as stress relaxation and steady state creep, in off-axis tension and compression tests, were predicted by the model. Material constants required by the model were extracted from simple off-axis test data.

Gates, Thomas S.↗

CVD silicon carbide monofilament reinforced SrO-Al2O3-2SiO2 (SAS) glass-ceramic composites

Unidirectional CVD SiC fiber-reinforced SrO.Al2O3.2SiO2 (SAS) glass-ceramic matrix composites have been fabricated by hot pressing at various combinations of temperature, pressure and time. Both carbon-rich surface coated SCS-6 and uncoated SCS-0 fibers were used as reinforcements. Almost fully dense composites have been obtained. Monoclinic celsian, SrAl2Si2O8, was the only crystalline phase observed in the matrix from x-ray diffraction. During three point flexure testing of composites, a test span to thickness ratio of approximately 25 or greater was necessary to avoid sample delamination. Strong and tough SCS-6/SAS composites having a first matrix crack stress of approximately 300 MPa and an ultimate bend strength of approximately 825 MPa were fabricated. No chemical reaction between the SCS-6 fibers and the SAS matrix was observed after high temperature processing. The uncoated SCS-0 fiber-reinforced SAS composites showed only limited improvement in strength over SAS monolithic. The SCS-0/SAS composite having a fiber volume fraction of 0.24 and hot pressed at 1400 deg C exhibited a first matrix cracking stress of approximately 231 +/- 20 MPa and ultimate strength of 265 +/- 17 MPa. From fiber push-out tests, the fiber/matrix interfacial debonding strength (tau(sub debond)) and frictional sliding stress (tau(sub friction)) in the SCS-6/SAS system were evaluated to be approximately 6.7 +/- 2.3 MPa and 4.3 +/- 0.6 MPa, respectively, indicating a weak interface. However, for the SCS-0/SAS composite, much higher values of approximately 17.5 +/- 2.7 MPa for tau(sub debond) and 11.3 +/- 1.6 MPa for tau(sub friction) respectively, were observed; some of the fibers were so strongly bonded to the matrix that they could not be pushed out. Examination of fracture surfaces revealed limited short pull-out length of SCS-0 fibers. The applicability of various micromechanical models for predicting the values of first matrix cracking stress and ultimate strength of these composites were examined.

Bansal, Narottam P.↗

P-V-T Properties of Polyimides and Model Imide Compounds

Aromatic polyimides are used as matrix resins in advanced composites, as high strength films, and as high-temperature adhesives, owing in part to their unusual thermal and chemical stability. The polyimides' desirable qualities of very high softening temperatures and negligibly small solubilities in and low permeabilities by most solvents have limited the kinds of fundamental studies that can be performed on these systems. Consequently, relationships between the molecular structure of polyimides and their bulk properties are not as well understood as might be expected given their widespread applications. In particular, the intermolecular forces in polyimides that play a critical role determining their densities, solubilities, viscosities, moduli, glass transitions, etc. are less well characterized for polyimides than for other widely used polymeric materials. The purpose of the present study is to obtain experimental data for establishing parameters that characterize the intermolecular forces in polyimides. We report here our studies on tractable low molecular-weight imides that contain the same structural features that are present in polyimide materials. We have measured equation-of-state properties and dipole moments for a variety of such systems in the liquid state. Both pure compounds and binary mixtures have been studied.

Orwoll, Robert A.↗

Mathematical Model for the Mineralization of Bone

A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

Martin, Bruce↗

Mathematical Model for the Mineralization of Bone

A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

Martin, Bruce↗

Energy absorption mechanisms during crack propagation in metal matrix composites

The stress distributions around individual fibers in a unidirectional boron/aluminum composite material subjected to axial and transverse loadings are being studied utilizing a generalized plane strain finite element analysis. This micromechanics analysis was modified to permit the analysis of longitudinal sections, and also to incorporate crack initiation and propagation. The analysis fully models the elastoplastic response of the aluminum matrix, as well as temperature dependent material properties and thermal stress effects. The micromechanics analysis modifications are described, and numerical results are given for both longitudinal and transverse models loaded into the inelastic range, to first failure. Included are initially cracked fiber models.

Murphy, D. P.↗

A continuum model for damage evolution in laminated composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Lo, D. C.↗

Quasi-Static and Dynamic Analysis of Composite Panels: Challenges in Engineering-Level Commercial Software

In engineering applications, where analysis time and efficiency are essential, analytical models and commercially available finite element (FE) material models are the two mainstream methods used to analyze composite crush scenarios. A reliable numerical model addressing the crushing response of composite materials requires a nonlinear progressive damage analysis which includes appropriate failure mechanisms such as matrix cracking, fragmentation, delamination, and fiber breakage. One might be able to address all these interacting failure responses through implementation/validation of a user defined material model or by utilization of a commercially available model, the latter being the most efficient engineering approach. In this paper, the quasi-static and dynamic crushing response of composite specimens, consisting of a C-channel and a corrugated geometry manufactured with carbon fiber/epoxy matrix fabric, are modeled using the progressive composite damage model within ABAQUS. The novel part of this work, which has not been previously addressed in the literature, is the utilization of a detailed parametric study to optimize composite damage model parameters for a given quasi-static crush simulation in ABAQUS. C-channel experiments were used to calibrate the model and then refine/optimize a set of material parameters that best fit the experimental results. These identical parameters were then used to simulate the crush response of the corrugated channel specimens, thereby making it a pure prediction and not a double recalibration. Next, the dynamic response of both panels were predicted, further confirming the predictive capability of the developed numerical model. The effect of parameter variation on the crush response is fully documented for future use in engineering applications utilizing this specific ABAQUS damage model.

Paria Naghipour↗