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NASA NTRS1983

Constitutive Models Based on Compressible Plastic Flows

The need for describing materials under time or cycle dependent loading conditions has been emphasized in recent years by several investigators. In response to the need, various constitutive models describing the nonlinear behavior of materials under creep, fatigue, or other complex loading conditions were developed. The developed models for describing the fully dense (non-porous) materials were mostly based on uncoupled plasticity theory. The improved characterization of materials provides a better understanding of the structual response under complex loading conditions. The pesent studies demonstrate that the rate or time dependency of the response of a porous aggregate can be incorporated into the nonlinear constitutive behavior of a porous solid by appropriately modeling the incompressible matrix behavior. It is also sown that the yield function which wads determined by a continuum mechanics approach must be verified by appropriate experiments on void containing sintered materials in order to obtain meaningful numbers for the constants that appear in the yield function.

Rajendran, A. M.↗

NASA NTRS1986

Ultrasonic nondestructive materials characterization

A brief review of ultrasonic wave propagation in solid materials is presented with consideration of the altered behavior in anisotropic and nonlinear elastic materials in comparison with isotropic and linear elastic materials. Some experimental results are described in which ultrasonic velocity and attenuation measurements give insight into materials microstructure and associated mechanical properties. Recent developments with laser beam non-contact generation and detection of ultrasound are presented. The results of several years of experimental measurements using high-power ultrasound are discussed, which provide substantial evidence of the inability of presently accepted theories to fully explain the interaction of ultrasound with solid materials. Finally, a special synchrotron X-ray topographic system is described which affords the possibility of observing direct interaction of ultrasonic waves with the microstructural features of real crystalline solid materials for the first time.

Green, R. E., Jr.↗

NASA NTRS2013

Applications of Automation Methods for Nonlinear Fracture Test Analysis

Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

Allen, Phillip A.↗

NASA NTRS1989

Generic element processor (application to nonlinear analysis)

The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.

Stanley, Gary↗

NASA NTRS1995

Buckling and postbuckling of composite panels with cutouts subjected to combined edge shear and temperature change

The results of a detailed study of the buckling and postbuckling responses of composite panels with central circular cutouts are presented. The panels are subjected to combined edge shear and temperature change. The panels are discretized by using a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the panel. The fundamental unknowns consist of the average mechanical strains through the thickness and the displacement components. The effects of geometric nonlinearities and laminated anisotropic material behavior are included. The stability boundary, postbuckling response and the hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the panel stiffnesses, and the material properties of both the individual layers and the constituents (fibers and matrix). Numerical results are presented for composite panels with central circular cutouts subjected to combined edge shear and temperature change, showing the effects of variations in the hole diameter, laminate stacking sequence and fiber orientation, on the stability boundary and postbuckling response and their sensitivity to changes in the various panel parameters.

Noor, Ahmed K.↗

NASA NTRS1993

Femtosecond pulses generated from a synchronously pumped chromium-doped forsterite laser

Kerr lens mode-locking (KLM) has become a standard method to produce femtosecond pulses from tunable solid state lasers. High power inside the laser resonator propagating through the laser-medium with nonlinear index of refraction, coupled with the stability conditions of the laser modes in the resonator, result in a passive amplitude modulation which explains the mechanism for pulse shortening. Recently, chromium doped forsterite was shown to exhibit similar pulse behavior. A successful attempt to generate femtosecond pulses from a synchronously pumped chromium-doped forsterite laser with intracavity dispersion compensation is reported. Stable, transform limited pulses with duration of 105 fs were routinely generated, tunable between 1240 to 1270 nm.

Seas, A.↗

NASA NTRS1986

The role of damage-softened material behavior in the fracture of composites and adhesives

Failure mechanisms of materials under very high strains experienced at and ahead of the crack tip such as formation, growth, and interaction of microvoids in ductile materials, microcracks in brittle solids or crazes in polymers and adhesives are represented by one-dimensional, nonlinear stress-strain relations possessing different ways by which the material loses capacity to carry load up to fracture or total separation. A double cantilever beam (DCB) type specimen is considered. The nonlinear material is confined to a thin strip between the two elastic beams loaded by a wedge. The problem is first modeled as a beam on a nonlinear foundation. The pertinent equation is solved numerically as a two-point boundary value problem for both the stationary and the quasi-stationay propagating crack. A finite element model is then used to model the problem in more detail in order to assess the adequacy of the beam model for the reduction of experimental data to determine in-situ properties of the thin interlayer.

Ungsuwarungsri, T.↗

NASA NTRS2017

Order-Reduced Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique for accurately simulating nonlinear composite material behavior. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for a more accurate determination of the subcell stressstrain fields at the cost of some computational efficiency. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents was reduced in size through the use of a Petrov-Galerkin-based Proper Orthogonal Decomposition order-reduction scheme. A number of cases were presented that address the computational feasibility of using order-reduction techniques to solve solid mechanics problems involving complex microstructures.

order-reduction↗

NASA NTRS2002

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Freed, Alan D.↗

NASA NTRS1998

Protein Crystallization: Specific Phenomena and General Insights on Crystallization Kinetics

Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.

Rosenberger, F.↗

NASA NTRS1983

Advances and trends in structural and solid mechanics; Proceedings of the Symposium, Washington, DC, October 4-7, 1982

The mechanics of materials and material characterization are considered, taking into account micromechanics, the behavior of steel structures at elevated temperatures, and an anisotropic plasticity model for inelastic multiaxial cyclic deformation. Other topics explored are related to advances and trends in finite element technology, classical analytical techniques and their computer implementation, interactive computing and computational strategies for nonlinear problems, advances and trends in numerical analysis, database management systems and CAD/CAM, space structures and vehicle crashworthiness, beams, plates and fibrous composite structures, design-oriented analysis, artificial intelligence and optimization, contact problems, random waves, and lifetime prediction. Earthquake-resistant structures and other advanced structural applications are also discussed, giving attention to cumulative damage in steel structures subjected to earthquake ground motions, and a mixed domain analysis of nuclear containment structures using impulse functions.

Noor, A. K.↗

NASA NTRS1983

Generation of sound in turbulent shear flows

An alternative to the Lighthill acoustic analogy for jet noise is discussed. It involves calculating the unsteady flow that produces the sound along with its resulting sound field starting from a prescribed upstream state that, ideally, is specified just ahead of the region where the sound generation takes place. Sound generation by turbulence interacting with solid obstacles is considered. It is shown that the process can be described by linear theory. Sound generated by turbulence interacting with itself is discussed. The processes are nonlinear and the theory is incomplete. Theories of sound generation are compared with experiment and the inadequacies of each are indicated. Additional mechanisms that appear at supersonic speeds are discussed.

Goldstein, M. E.↗

NASA NTRS1989

Calculating Dynamic Shear Moduli Of Polymers

Improved nonlinear mathematical model developed to fit experimental data on relaxation of stresses in viscoelastic materials. Developed specifically to study shear moduli of rubbery solid rocket propellants, also used to characterize polymers in general, other viscoelastic materials, and composites of viscoelastic materials. Facilitates and improves accuracy of analysis and numerical simulation of mechanical behavior of structural components (for example, tires) made of such materials.

Moore, Carleton J.↗

NASA NTRS1979

User's guide: SPAR processor MN analysis of inelastic three-dimensional solids, part 2

A user's guide to the processor MN is presented. The processor MN is used to analyze systems in which some or all of the three dimensional elements have nonlinear stress-strain relations. Representations of nonlinear material behavior implemented into the system are provided including Von Mises yield criterion, the Prandtl-Reuss flow rule, and the mechanical sublayer method. The primary data sets used to represent the state of the system are presented.

Whetstone, W. D.↗

NASA NTRS1983

Micromechanically Based Constitutive Relations for Polycrystalline Solids

A basic method to estimate the overall mechanical response of solids which contain periodically distributed defects is presented. The method estimates the shape and growth pattern of voids periodically distributed over the grain boundaries in a viscous matrix. The relaxed moduli are obtained for a polycrytalline solid that undergoes relaxation by grain boundary sliding which accounts for the interaction effects. The overall inelastic nonlinear response at elevated temperatures in terms of a model which considers nonlinear power law creep within the grains, and linear viscous flow in the grain boundaries is discussed.

Nemat-Nasser, S.↗

NASA NTRS1990

A database for solid-state laser, optical, and nonlinear materials

The database contains the physical properties of laser, optical, and nonlinear materials used by the laser models of a laser-modeling software system. The database is subdivided into two parts: spectra and tabulated data. The spectra are ASCII files of laser-material's absorption and emission spectra, and laser-diode's emission spectra. The tabulated data contains physical properties of laser, optical, and nonlinear materials, including crystalline, thermal, and mechanical properties. A menu-driven interface allows the execution from a personal directory where the user can store files containing input parameters for a specific model or the results of model's calculations.

Cross, P. L.↗

NASA NTRS1985

The effects of strain heating in lithospheric stretching models

The deformation by stretching of a continental type lithosphere has been formulated so that the problem can be solved by a continuum mechanical approach. The deformation, stress state, and temperature distribution are constrained to satisfy the physical laws of conservation of mass, energy, momentum, and an experimentally defined rheological response. The conservation of energy equation including a term of strain energy dissipation is given. The continental lithosphere is assumed to have the rheology of an isotropic, incompressible, nonlinear viscous, two layered solid.

Stanton, M.↗

NASA NTRS2003

A Model for the Oxidation of C/SiC Composite Structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Sullivan, Roy M.↗