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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Analysis of Curved Sandwich Panels Subjected to Combined Temperature Gradient and Mechanical Loads

The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets and subjected to a temperature gradient through-the-thickness combined with mechanical loadings are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response and its sensitivity to changes in the various panel, effective layer and micromechanical parameters.

Noor, Ahmed K.↗
NASA NTRS1999

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Noor, Ahmed K.↗
NASA NTRS2006

Simulations of Sea-Ice Dynamics Using the Material-Point Method

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

Sulsky, D.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-32167-DND

Fiber Kinking Theory (FKT): Budiansky proposed that kink bands are a result of an initial (infinitely wide) band of misaligned fibers, nonlinear material behavior under shear loading, and accounting for large rotations of the fibers. CompDam is a NASA Langley CDM code that uses the deformation gradient, particular attention paid to kinematics of cracking.

Andrew Bergan↗
NASA NTRS1998

Mechanistic Models of Friction Stir Welding

Friction stir welding is a welding process developed at The Welding Institute (TWI) in England. The method uses very large strain plastic deformation of the material to join two pieces of metal together. The material is deformed using a tool which is forced between the two pieces which rotates causing a bond. Beyond this, very little is actually known although many people working in the field are willing to speculate on the detailed mechanisms involved. Some measurements made using sacrificial thermocouples at the weld joint indicate that the maximum temperature during the weld process is on the order of 370C - well below the melting temperature of the material. However, at this temperature, the material properties are highly temperature dependent, and the yield stress is approximately an order of magnitude less at this temperature than it is at room temperature. As expected, there are many interpretations of the physical mechanisms occurring during the weld process. Although there is very little published concerned with FSW, some of the anecdotal theories will be described. One describes the primary mechanism as frictional heating at the front of the tool caused by slip between the tool and the material. At elevated temperatures, the weld material becomes soft and deforms around the tool but not essentially altered by the tool rotation, similar to an extrusion. As the material meets again at the rear of the tool, the temperatures and pressures are sufficient to cause the material to bond. All other structures seen are secondary and unimportant. Another theory examined last summer at NASA's Marshall Space Flight Center (MSFC) was that there was no slip between the tool and the material resulting in a rotating mass of plastic weld material traveling at a variety of angular velocities - the greatest at the tool surface diminishing to zero at the outer edge of the plastic mass surrounding the tool. This conceptual model was followed by simplified calculations which showed that the balance of moments through the weld plug was not possible under steady state conditions and realistic temperature profiles. This led to some consideration of a quasi-steady oscillating process. Later when force measurements became available some models were modified and new ones were proposed.

Stewart, Michael B.↗
NASA NTRS1995

Load transfer in the stiffener-to-skin joints of a pressurized fuselage

Structural analyses are developed to determine the linear elastic and the geometrically nonlinear elastic response of an internally pressurized, orthogonally stiffened, composite material cylindrical shell. The configuration is a long circular cylindrical shell stiffened on the inside by a regular arrangement of identical stringers and identical rings. Periodicity permits the analysis of a unit cell model consisting of a portion of the shell wall centered over one stringer-ring joint. The stringer-ring-shell joint is modeled in an idealized manner; the stiffeners are mathematically permitted to pass through one another without contact, but do interact indirectly through their mutual contact with the shell at the joint. Discrete beams models of the stiffeners include a stringer with a symmetrical cross section and a ring with either a symmetrical or an asymmetrical open section. Mathematical formulations presented for the linear response include the effect of transverse shear deformations and the effect of warping of the ring's cross section due to torsion. These effects are important when the ring has an asymmetrical cross section because the loss of symmetry in the problem results in torsion and out-of-plane bending of the ring, and a concomitant rotation of the joint at the stiffener intersection about the circumferential axis. Data from a composite material crown panel typical of a large transport fuselage structure are used for two numerical examples. Although the inclusion of geometric nonlinearity reduces the 'pillowing' of the shell, it is found that bending is localized to a narrow region near the stiffener. Including warping deformation of the ring into the analysis changes the sense of the joint rotation. Transverse shear deformation models result in increased joint flexibility.

Johnson, Eric R.↗
NASA NTRS2018

Modeling Fiber Kinking at the Microscale and Mesoscale

A computational micromechanics (CMM) model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking. The CMM model considers an individually discretized three dimensional fiber and surrounding matrix accounting for nonlinearity in the fiber, matrix plasticity, fiber/matrix interface debonding, and geometric nonlinearity. Key parameters of the CMM model were measured through experiments. In particular, a novel experimental technique to characterize the in situ longitudinal compressive strength of carbon fibers through indentation of micropillars is presented. The CDM model is formulated on the basis of Budiansky's fiber kinking theory (FKT) with a constitutive deformation-decomposition approach to alleviate mesh size sensitivity. In contrast to conventional mesoscale CDM models that prescribe a constitutive response directly, the response of the proposed model is an outcome of material nonlinearity and large rotations of the fiber direction following FKT. Comparison of the predictions from the CMM and CDM models shows remarkable correlation in strength, post-peak residual stress, and fiber rotation, with less than 10% difference between the two models in most cases. Additional comparisons are made with several fiber kinking models proposed in the literature to highlight the efficacy of the two models. Finally, the CMM model is exercised in parametric studies to explore opportunities to improve the longitudinal compression strength of a ply through the use of nonconventional microstructures.

Herraez, Miguel↗
NASA NTRS1994

Global, quasi-steady dynamics of the distant solar wind 2: Deformation of the heliospheric current sheet

A three-dimensional (3-D) magnetohydrodynamic (MHD) numerical model is used to trace global deformations of the heliospheric current sheet (HCS) caused by large-scale dynamical interactions associated with corotating solar wind flows. Configurations incorporating the tilted-dipole geometry are investigated out past 30 AU for a variety of dipole tilt angles, alpha. Inclusion of the full, 3-D interplanetary dynamics allows north-south displacements and the east-west warping of the HCS by advective corotational effects to be accurately assessed for the first time. It is found that large-scale spatial correlations between velocity and density imposed at the coronal source (i.e., the geometric arrangement whereby regions of high-speed low-density material lying adjacent to areas of slow, dense flow interact obliquely under the influence of solar rotation) result in a distinctive pattern of deformation of the HCS. For an alpha = 30 deg tilted-dipole example, it is shown that typical zonal variations in radial velocity lead to significant folding of the HCS within about 5 AU of the Sun. By 10 AU, additional sharp bends appear near the latitudinal extremes of the HCS surface, where it is overtaken by shock fronts driven by 3-D corotating interaction regions (CIRs). Moreover, the model suggests that inside about 20 AU, major plasma structures are systematically organized, about the HCS, such that the greatest concentrations of material and magnetic field (the centroids of the 3-D CIR structures) are coincident with the folded crests of the HCS (near heliographic latitudes lambda = +/- alpha). Thus, in these circumstances many of the more interesting dynamical features inconveniently lie well away from the heliographic equator. At larger heliocentric distances, where neighboring CIRs begin to interact strongly, the warping of the HCS abates dramatically and the association between folds in the HCS and major field and density concentrations is weakened and ultimately breaks down. On the basis of the model calculations, quasi-steady deformations and related phenomena should figure prominently in the interplanetary medium, except during those periods when the magnetic dipole and solar spin axes are nearly aligned (alpha is approximately less than 10 deg). Even then, they may be of significance if there are any substantial local warps or kinks in the streamer belt.

Pizzo, V. J.↗
NASA NTRS1979

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Rodal, J. J. A.↗
NASA NTRS2015

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Leone, Frank A., Jr.↗
NASA NTRS1997

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

Deng, Xiaomin↗
NASA NTRS1987

Nonlinear beam kinematics by decomposition of the rotation tensor

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.↗
NASA NTRS1987

Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.↗
NASA NTRS2013

Jet Engine Bird Ingestion Simulations: Comparison of Rotating to Non-Rotating Fan Blades

Bird strike events in commercial airliners are a fairly common occurrence. According to data collected by the US Department of Agriculture, over 80,000 bird strikes were reported in the period 1990-2007 in the US alone [1]. As a result, bird ingestion is an important factor in aero engine design and FAA certification. When it comes to bird impacts on engine fan blades, the FAA requires full-scale bird ingestion tests on an engine running at full speed to pass certification requirements. These rotating tests are complex and very expensive. To reduce development costs associated with new materials for fan blades, it is desirable to develop more cost effective testing procedures than full-scale rotating engine tests for material evaluation. An impact test on a non-rotating single blade that captures most of the salient physics of the rotating test would go a long way towards enabling large numbers of evaluative material screening tests. NASA Glenn Research Center has been working to identify a static blade test procedure that would be effective at reproducing similar results as seen in rotating tests. The current effort compares analytical simulations of a bird strike on various nonrotating blades to a bird strike simulation on a rotating blade as a baseline case. Several different concepts for simulating the rotating loads on a non-rotating blade were analyzed with little success in duplicating the deformation results seen in the rotating case. The rotating blade behaves as if it were stiffer than the non-rotating blade resulting in less plastic deformation from a given bird impact. The key factor limiting the success of the non-rotating blade simulations is thought to be the effect of gyroscopics. Prior to this effort, it was anticipated the difficulty would be in matching the pre-stress in the blade due to centrifugal forces Additional work is needed to verify this assertion, and to determine if a static test procedure can simulate the gyroscopic effects in a suitable manner. This paper describes the various non-rotating concepts analyzed, and demonstrates the effect believed to be gyroscopic in nature on the results.

Howard, Samuel A.↗
NASA NTRS2013

Jet Engine Bird Ingestion Simulations: Comparison of Rotating to Non-Rotating Fan Blades

Bird strike events in commercial airliners are a fairly common occurrence. According to data collected by the US Department of Agriculture, over 80,000 bird strikes were reported in the period 1990 to 2007 in the US alone (Ref. 1). As a result, bird ingestion is an important factor in aero engine design and FAA certification. When it comes to bird impacts on engine fan blades, the FAA requires full-scale bird ingestion tests on an engine running at full speed to pass certification requirements. These rotating tests are complex and very expensive. To reduce development costs associated with new materials for fan blades, it is desirable to develop more cost effective testing procedures than full-scale rotating engine tests for material evaluation. An impact test on a nonrotating single blade that captures most of the salient physics of the rotating test would go a long way towards enabling large numbers of evaluative material screening tests. NASA Glenn Research Center has been working to identify a static blade test procedure that would be effective at reproducing similar results as seen in rotating tests. The current effort compares analytical simulations of a bird strike on various non-rotating blades to a bird strike simulation on a rotating blade as a baseline case. Several different concepts for simulating the rotating loads on a non-rotating blade were analyzed with little success in duplicating the deformation results seen in the rotating case. The rotating blade behaves as if it were stiffer than the non-rotating blade resulting in less plastic deformation from a given bird impact. The key factor limiting the success of the non-rotating blade simulations is thought to be the effect of gyroscopics. Prior to this effort, it was anticipated the difficulty would be in matching the prestress in the blade due to centrifugal forces Additional work is needed to verify this assertion, and to determine if a static test procedure can simulate the gyroscopic effects in a suitable manner. This paper describes the various non-rotating concepts analyzed, and demonstrates the effect believed to be gyroscopic in nature on the results

Howard, Samuel A.↗
NASA NTRS1981

A hybrid state vector approach to aeroelastic analysis with application to composite lifting surfaces

A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.

Lehman, L. L.↗
NASA NTRS1990

Stress field rotation or block rotation: An example from the Lake Mead fault system

The Coulomb criterion, as applied by Anderson (1951), has been widely used as the basis for inferring paleostresses from in situ fault slip data, assuming that faults are optimally oriented relative to the tectonic stress direction. Consequently if stress direction is fixed during deformation so must be the faults. Freund (1974) has shown that faults, when arranged in sets, must generally rotate as they slip. Nur et al., (1986) showed how sufficiently large rotations require the development of new sets of faults which are more favorably oriented to the principal direction of stress. This leads to the appearance of multiple fault sets in which older faults are offset by younger ones, both having the same sense of slip. Consequently correct paleostress analysis must include the possible effect of fault and material rotation, in addition to stress field rotation. The combined effects of stress field rotation and material rotation were investigated in the Lake Meade Fault System (LMFS) especially in the Hoover Dam area. Fault inversion results imply an apparent 60 degrees clockwise (CW) rotation of the stress field since mid-Miocene time. In contrast structural data from the rest of the Great Basin suggest only a 30 degrees CW stress field rotation. By incorporating paleomagnetic and seismic evidence, the 30 degrees discrepancy can be neatly resolved. Based on paleomagnetic declination anomalies, it is inferred that slip on NW trending right lateral faults caused a local 30 degrees counter-clockwise (CCW) rotation of blocks and faults in the Lake Mead area. Consequently the inferred 60 degrees CW rotation of the stress field in the LMFS consists of an actual 30 degrees CW rotation of the stress field (as for the entire Great Basin) plus a local 30 degrees CCW material rotation of the LMFS fault blocks.

Ron, Hagai↗
NASA NTRS1990

Multiple strike slip faults sets: A case study from the Dead Sea transform

In many strike slip tectonic settings, large rotations of crust blocks about vertical axes have been inferred from paleomagnetic data. These blocks are bounded by sets of parallel faults which presumably accommodate the relative motion between the blocks as regional deformation progress. A mechanical model by Nur et al., (1986) suggests that rotations greater than phi sub c equals 25 to 45 degrees must be accommodated by more than one set of faults, with angle phi sub c between their direction; consequently the sum of the angles between sets must be roughly equal to the total tectonic material rotation. To test this model, the authors investigated the fault geometry and field relation of fault sets in the Mt. Hermon area in northern Israel, where paleomagnetic declination implies data 69 degrees plus or minus 13 degrees counter-clockwise block rotation. The statistical and field relation analysis of over 315 faults shows that the faulting is predominantly right lateral strike slip consisting of three distinct sets. The oldest set strikes 253 degrees, the second oldest set strikes 293 degrees and the youngest strikes 339 degrees. This last direction is consistent also with the current north-south direction of the maximum principle stress axis. The angle phi sub c between the first and second sets is 39 degrees and between the second and third sets 46 degrees, in good agreement with the phi sub c angle predicted from mechanical considerations. The sum of the two angles is 85 degrees, in good agreement with the 69 degrees plus or minus 13 degrees CCW paleomagnetically derived rotation. The results suggest specifically that the sequential development of multiple intersecting fault sets is responsible for the faulting in the Mt. Hermon area; and generally that the model of block rotation with multiple faults provides very good simple rules for analyzing very complex fault patterns.

Ron, Hagai↗