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Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites

The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.

Finite element analysis↗
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 NTRS1993

Plate tectonics and crustal deformation around the Japanese Islands

We analyze over a century of geodetic data to study crustal deformation and plate motion around the Japanese Islands, using the block-fault model for crustal deformation developed by Matsu'ura et al. (1986). We model the area including the Japanese Islands with 19 crustal blocks and 104 faults based on the distribution of active faults and seismicity. Geodetic data are used to obtain block motions and average slip rates of faults. This geodetic model predicts that the Pacific plate moves N deg 69 +/- 2 deg W at about 80 +/- 3 mm/yr relative to the Eurasian plate which is much lower than that predicted in geologic models. Substantial aseismic slip occurs on the subduction boundaries. The block containing the Izu Peninsula may be separated from the rigid part of the Philippine Sea plate. The faults on the coast of Japan Sea and the western part of the Median Tectonic Line have slip rates exceeding 4 mm/yr, while the Fossa Magna does not play an important role in the tectonics of the central Japan. The geodetic model requires the division of northeastern Japan, contrary to the hypothesis that northeastern Japan is a part of the North American plate. Owing to rapid convergence, the seismic risk in the Nankai trough may be larger than that of the Tokai gap.

Hashimoto, Manabu↗
NASA NTRS1990

Factors controlling the location of compressional deformation of oceanic lithosphere in the Central Indian Ocean

One- and two-dimensional models for the deformation by horizontal compression of an elastic plate containing a preexisting deflection were developed and analyzed in order to explain why the compressionally deformed oceanic lithosphere in the Central Indian-Ocean basin is not located where maximum levels of compressive stress in the Indo-Australian plate were predicted by Cloetingh and Wortel (1985, 1986). It is concluded from the results that the location of the deformed region is controlled by an earlier lithospheric deformation that is attributed to the emplacement of the Afanazy-Nikitin seamount group in Late Cretaceous or early Tertiary time.

Karner, Garry D.↗
NASA NTRS1997

A Viscoplastic Constitutive Theory for Monolithic Ceramic Materials

With increasing use of ceramic materials in high temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior. This paper, which is the first of two in a series, will focus on inelastic deformation behavior associated with these service conditions by providing an overview of a viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (e.g., creep, stress relaxation, etc.) in monolithic structural ceramics. Early work in the field of metal plasticity indicated that inelastic deformations are essentially unaffected by hydrostatic stress. This is not the case, however, for ceramic-based material systems, unless the ceramic is fully dense. The theory presented here allows for fully dense material behavior as a limiting case. In addition, ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperature. When subjected to elevated service temperatures, ceramic materials exhibit complex thermomechanical behavior that is inherently time-dependent, and hereditary in the sense that current behavior depends not only on current conditions, but also on thermo-mechanical history. The objective of this work is to present the formulation of a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the overview contained in this paper focuses on the multiaxial derivation of the constitutive model, and examines the scalar threshold function and its attending geometrical implications.

Janosik, Lesley A.↗
NASA NTRS1975

The effect of adhesive layer elasticity on the fracture mechanics of a blister test specimen

An analytical model of a blister type specimen for evaluating adhesive bond strength was developed. Plate theory with shear deformation was used to model the deformation of the plate, and elastic deformation of the adhesive layer is taken into account. It is shown that the inclusion of the elastic deformation of the adhesive layer can have a significant influence in the energy balance calculations of fracture mechanics.

Updike, D. P.↗
NASA NTRS1988

Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io

The deformation of Io, the tidal dissipation rate, and its interior spatial distribution are investigated by means of numerical simulations based on (1) a three-layer model (with dissipation in the mantle) or (2) a four-layer model (with dissipation in the asthenosphere). The mathematical derivation of the models is outlined; the selection of the input-parameter values is explained; the results are presented in extensive graphs and contour maps; and the constraints imposed on the models by observational data on the hot-spot distribution, tidal deformation, and gravity field are discussed in detail. It is found that both dissipation mechanisms may play a role on Io: model (2) is better able to explain the concentration of hot spots near the equator, while the presence of a large hot spot near the south pole (if confirmed by observations) would favor model (1).

Segatz, M.↗
NASA NTRS2005

Satellite Geodetic Constraints On Earthquake Processes: Implications of the 1999 Turkish Earthquakes for Fault Mechanics and Seismic Hazards on the San Andreas Fault

Our principal activities during the initial phase of this project include: 1) Continued monitoring of postseismic deformation for the 1999 Izmit and Duzce, Turkey earthquakes from repeated GPS survey measurements and expansion of the Marmara Continuous GPS Network (MAGNET), 2) Establishing three North Anatolian fault crossing profiles (10 sitedprofile) at locations that experienced major surface-fault earthquakes at different times in the past to examine strain accumulation as a function of time in the earthquake cycle (2004), 3) Repeat observations of selected sites in the fault-crossing profiles (2005), 4) Repeat surveys of the Marmara GPS network to continue to monitor postseismic deformation, 5) Refining block models for the Marmara Sea seismic gap area to better understand earthquake hazards in the Greater Istanbul area, 6) Continuing development of models for afterslip and distributed viscoelastic deformation for the earthquake cycle. We are keeping close contact with MIT colleagues (Brad Hager, and Eric Hetland) who are developing models for S. California and for the earthquake cycle in general (Hetland, 2006). In addition, our Turkish partners at the Marmara Research Center have undertaken repeat, micro-gravity measurements at the MAGNET sites and have provided us estimates of gravity change during the period 2003 - 2005.

Reilinger, Robert↗
NASA NTRS1990

Finite-element models of continental extension

Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.

Lynch, H. David↗
NASA NTRS1996

A General Interface Method for Aeroelastic Analysis of Aircraft

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Tzong, T.↗
NASA NTRS2000

Aeroelastic Deformation Measurements of Flap, Gap, and Overhang on a Semispan Model

Single-camera, single-view videogrammetry has been used to determine static aeroelastic deformation of a slotted flap configuration on a semispan model at the National Transonic Facility (NTF). Deformation was determined by comparing wind-off to wind-on spatial data from targets placed on the main element, shroud, and flap of the model. Digitized video images from a camera were recorded and processed to automatically determine target image plane locations that were then corrected for sensor, lens, and frame grabber spatial errors. The videogrammetric technique has been established at NASA facilities as the technique of choice when high-volume static aeroelastic data with minimum impact on data taking is required. The primary measurement at the NTF with this technique in the past has been the measurement of static aeroelastic wing twist on full span models. The first results using the videogrammetric technique for the measurement of component deformation during semispan testing at the NTF are presented.

Burner, A. W.↗
NASA NTRS2003

Modeling of High-Strain-Rate Deformation, Fracture, and Impact Behavior of Advanced Gas Turbine Engine Materials at Low and Elevated Temperatures

Gamma titanium aluminides have received considerable attention over the last decade. These alloys are known to have low density, good high temperature strength retention, and good oxidation and corrosion resistance. However, poor ductility and low fracture toughness have been the key limiting factors in the full utilization of these alloys. More recently, Gamma-met PX has been developed by GKSS, Germany. These alloys have been observed to have superior strengths at elevated temperatures and quasi-static deformation rates and good oxidation resistance at elevated temperatures when compared with other gamma titanium aluminides. The present paper discusses results of a study to understand dynamic response of gamma-met PX in uniaxial compression. The experiments were conducted by using a modified split Hopkinson pressure bar between room temperature and 900 C and strain rates of up to 3500 per second. The Gamma met PX alloy showed superior strength when compared to nickel based superalloys and other gamma titanium aluminides at all test temperatures. It also showed strain and strain-rate hardening at all levels of strain rates and temperatures and without yield anomaly up to 900 C. After approximately 600 C, thermal softening is observed at all strain rates with the rate of thermal softening increasing dramatically between 800 and 900 C. However, these flow stress levels are comparatively higher in Gamma met PX than those observed for other TiAl alloys.

Shazly, Mostafa↗
NASA NTRS2020

Shape Estimation for Elongated Deformable Object using B-spline Chained Multiple Random Matrices Model

In this paper, a B-spline chained multiple random matrix models (RMMs) representation is proposed to model geometric characteristics of an elongated deformable object. The hyper degrees of freedom structure of the elongated deformable object make its shape estimation challenging. Based on the likelihood function of the proposed B-spline chained multiple RMMs, an expectation-maximization (EM) method is derived to estimate the shape of the elongated deformable object. A split and merge method based on the Euclidean minimum spanning tree (EMST) is proposed to provide initialization for the EM algorithm. The proposed algorithm is evaluated for the shape estimation of the elongated deformable objects in scenarios, such as the static rope with various configurations (including configurations with intersection), the continuous manipulation of a rope and a plastic tube, and the assembly of two plastic tubes. The execution time is computed and the accuracy of the shape estimation results is evaluated based on the comparisons between the estimated width values and its ground-truth, and the intersection over union (IoU) metric.

Gang Yao↗
NASA NTRS1992

Modeling and analysis methodology for aeroelastically tailored chordwise deformable wings

Structural concepts have been created which produce chordwise camber deformation that results in enhanced lift. A wing box can be tailored to utilize each of these with composites. In attempting to optimize the aerodynamic benefits, we have found there are two optimal designs that are of interest. There is a weight optimum which corresponds to the maximum lift per unit structural weight. There is also a lift optimum that corresponds to maximum absolute lift. New structural models, the basic deformation mechanisms that are utilized and typical analytical results are presented. It appears that lift enhancements of sufficient magnitude can be produced to render this type of wing tailoring of practical interest. Experiments and finite element correlations are performed which confirm the validity of the theoretical models utilized.

Rehfield, Lawrence W.↗
NASA NTRS1994

Patterns of brittle deformation under extension on Venus

The development of fractures at regular length scales is a widespread feature of Venusian tectonics. Models of lithospheric deformation under extension based on non-Newtonian viscous flow and brittle-plastic flow develop localized failure at preferred wavelengths that depend on lithospheric thickness and stratification. The characteristic wavelengths seen in rift zones and tessera can therefore provide constraints on crustal and thermal structure. Analytic solutions were obtained for growth rates in infinitesimal perturbations imposed on a one-dimensional, layered rheology. Brittle layers were approximated by perfectly-plastic, uniform strength, overlying ductile layers exhibiting thermally-activated power-law creep. This study investigates the formation of faults under finite amounts of extension, employing a finite-element approach. Our model incorporates non-linear viscous rheology and a Coulomb failure envelope. An initial perturbation in crustal thickness gives rise to necking instabilities. A small amount of velocity weakening serves to localize deformation into planar regions of high strain rate. Such planes are analogous to normal faults seen in terrestrial rift zones. These 'faults' evolve to low angle under finite extension. Fault spacing, orientation and location, and the depth to the brittle-ductile transition, depend in a complex way on lateral variations in crustal thickness. In general, we find that multiple wavelengths of deformation can arise from the interaction of crustal and mantle lithosphere.

Neumann, G. A.↗
NASA NTRS1978

Postseismic surface deformations due to lithospheric and asthenospheric viscoelasticity

A model is proposed for post seismic surface deformations attributing them to lithospheric and asthenospheric viscoelasticity. The model predicts that the deformations due to lithospheric viscoelasticity depend on the ratio of the effective shear modulus acting long after the lithospheric viscoelastic relaxation to that acting immediately following the earthquake. While such deformations are generally smaller than those associated with asthenospheric viscoelasticity, they occur on a shorter time scale and may be in opposite direction to both the motion occurring at the time of the earthquake and that occurring as the asthenospheric relaxation occurs.

Cohen, S. C.↗
NASA NTRS1986

Evidence of ongoing crustal deformation related to magmatic activity near Socorro, New Mexico

Leveling measurements conducted in 1980-1981 by the National Geodetic Survey in the Socorro area of the Rio Grande rift are analyzed. Crustal uplift related to magma inflation in the midcrustal magma body is detected; an uplift of 0.18 cm/yr is measured for the time between 1951-1980. The survey data of 1911 and 1959 are compared to the present data and good correlation is observed. The systematic leveling errors including height-dependence and refraction errors are studied. The 30-km-wide subsidence in the area is examined. The spatial correlation between seismic activity, the Socorro magma body, and crustal deformation in Socorro is investigated. The crustal movement from magma reservior activities is modeled using the formulations of Dieterich and Decker (1975). The modeling of the deformation reveals that the movement in the Socorro area is associated with the 19-km deep Socorro magma body.

Larsen, S.↗
NASA NTRS1988

Geodetic evidence of the seismic potential at Parkfield, California

The average rates of line-length change and the rates of the shallow fault slip observed near Parkfield, California, were used to estimate the slip rate at depth on the San Andreas fault (SAF), using the Matsu'ura et al. (1986) procedure to model the aseismic deformation as a perturbation to steady block motion across the SAF. Five different models were tested against the data, with one model, featuring a nearly monotonic transition from creeping behavior on the northwest to locked behavior on the southeast, found to fit the data acceptably well. It is shown that stored elastic energy southeast of Parkfield could produce an earthquake of magnitude up to 8.0, that would have displacement and rupture length similar to historic earthquakes of the same size.

Sung, Li-Yu↗