Application of finite anisotropic elasticity to the behavior of natural rubbers
Anisotropic strain energy function describing mechanical behavior of rubber
RUBBER↗
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Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing
Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.
Stein, M.↗
On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry.
Bounds for plane strain bulk modulus and shear moduli of multiphase fiber reinforced materials of arbitrary transverse phase geometry
BULK MODULUS↗
Strain Center For Analysis Of Forces
Concept of strain center introduced to facilitate analysis of forces resulting from eccentric load after elastic limit exceeded. After yielding, forces perpendicular to radii from strain center. Concept useful where loads known and directions of forces being analyzed, such as limiting frictional force between wheel and ground.
Bickler, Donald B.↗
Mode I fracture behavior of nonlinear materials
A finite element analysis is presented for the Mode I fracture behavior of cracked plates (stationary crack) made of different nonlinear materials (elastoplastic or elastic locking). The assumed stress-strain behavior of the nonlinear materials was piecewise linear. For each given 'stationary' crack size, the corresponding critical remote tensile stress was calculated based on the maximum crack-tip stress failure criterion. It was found that in the log-log plots of the critical remote stress versus critical crack length, the fracture data of the piecewise linear materials obey a 'stepwise-linear-inverse-square-root' fracture law. It is also shown how the fracture data of the piecewise linear materials can be fitted by proper piecewise graphical shifting of the classical 'inverse-square-root' fracture curve for the linearly elastic materials.
Ko, W. L.↗
A three dimensional photoelasto-plastic stress analysis method.
Photoelastoplastic method using creep and stress characteristics of epoxy resins under thermal cycle, discussing stress-strain behavior
ELASTIC PROPERTY↗
Plate and butt-weld stresses beyond elastic limit, material and structural modeling
Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.
Verderaime, V.↗
Vascular mechanics of the coronary artery
This paper describes our research into the vascular mechanics of the coronary artery and plaque. The three sections describe the determination of arterial mechanical properties using intravascular ultrasound (IVUS), a constitutive relation for the arterial wall, and finite element method (FEM) models of the arterial wall and atheroma. METHODS: Inflation testing of porcine left anterior descending coronary arteries was conducted. The changes in the vessel geometry were monitored using IVUS, and intracoronary pressure was recorded using a pressure transducer. The creep and quasistatic stress/strain responses were determined. A Standard Linear Solid (SLS) was modified to reproduce the non-linear elastic behavior of the arterial wall. This Standard Non-linear Solid (SNS) was implemented into an axisymetric thick-walled cylinder numerical model. Finite element analysis models were created for five age groups and four levels of stenosis using the Pathobiological Determinants of Atherosclerosis Youth (PDAY) database. RESULTS: The arteries exhibited non-linear elastic behavior. The total tissue creep strain was epsilon creep = 0.082 +/- 0.018 mm/mm. The numerical model could reproduce both the non-linearity of the porcine data and time dependent behavior of the arterial wall found in the literature with a correlation coefficient of 0.985. Increasing age had a strong positive correlation with the shoulder stress level, (r = 0.95). The 30% stenosis had the highest shoulder stress due to the combination of a fully formed lipid pool and a thin cap. CONCLUSIONS: Studying the solid mechanics of the arterial wall and the atheroma provide important insights into the mechanisms involved in plaque rupture.
NASA Program Biomedical Research and Countermeasur↗
Characterization of Composite Fan Case Resins
The majority of commercial turbine engines that power today s aircraft use a large fan driven by the engine core to generate thrust which dramatically increases the engine s efficiency. However, if one of these fan blades fails during flight, it becomes high energy shrapnel, potentially impacting the engine or puncturing the aircraft itself and thus risking the lives of passengers. To solve this problem, the fan case must be capable of containing a fan blade should it break off during flight. Currently, all commercial fan cases are made of either just a thick metal barrier or a thinner metal wall surrounded by Kevlar-an ultra strong fiber that elastically catches the blade. My summer 2004 project was to characterize the resins for a composite fan case that will be lighter and more efficient than the current metal. The composite fan case is created by braiding carbon fibers and injecting a polymer resin into the braid. The resin holds the fibers together, so at first using the strongest polymer appears to logically lead to the strongest fan case. Unfortunately, the stronger polymers are too viscous when melted. This makes the manufacturing process more difficult because the polymer does not flow as freely through the braid, and the final product is less dense. With all of this in mind, it is important to remember that the strength of the polymer is still imperative; the case must still contain blades with high impact energy. The research identified which polymer had the right balance of properties, including ease of fabrication, toughness, and ability to transfer the load to the carbon fibers. Resin deformation was studied to better understand the composite response during high speed impact. My role in this research was the testing of polymers using dynamic mechanical analysis and tensile, compression, and torsion testing. Dynamic mechanical analysis examines the response of materials under cyclic loading. Two techniques were used for dynamic mechanical analysis. The ARES Instrument analyzed the material through torsion. The second machine, TA Instruments apparatus, applied a bending force to the specimen. These experiments were used to explore the effects of temperature and strain rate on the stiffness and strength of the resins. The two different types of loading allowed us to verify our results. An axial-torsional load frame, manufactured by MTS Systems, Inc., was used to conduct the tensile, compression, and torsional testing. These tests were used to determine the stress-strain curves for the resins. The elastic and plastic deformation data was provided to another team member for characterization of high fidelity material property predictions. This information was useful in having a better understanding of the polymers so that the fan cases could be as sturdy as possible. Deformation studies are the foundation for the computational modeling that provides the structural design of a composite engine case as well as detailed analysis of the blade impact event.
Dvoracek, Charlene M.↗
A simplified method for elastic-plastic-creep structural analysis
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
Kaufman, A.↗
A simplified method for elastic-plastic-creep structural analysis
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
Kaufman, A.↗
Plane elastic waves of finite amplitude - Hadamard materials and harmonic materials.
Plane elastic waves of finite amplitude in Hadamard materials and harmonic materials
STRESS-STRAIN DISTRIBUTION↗
Tailoring Elastic Properties of Silica Aerogels Cross-Linked with Polystyrene
The effect of incorporating an organic linking group, 1,6-bis(trimethoxysilyl)hexane (BTMSH), into the underlying silica structure of a styrene cross-linked silica aerogel is examined. Vinyltrimethoxysilane (VTMS) is used to provide a reactive site on the silica backbone for styrene polymerization. Replacement of up to 88 mol 1 of the silicon from tetramethoxyorthosilicate with silicon derived from BTMSH and VTMS during the making of silica gels improves the elastic behavior in some formulations of the crosslinked aerogels, as evidenced by measurement of the recovered length after compression of samples to 251 strain. This is especially true for some higher density formulations, which recover nearly 100% of their length after compression to 251 strain twice. The compressive modulus of the more elastic monoliths ranged from 0.2 to 3 MPa. Although some of these monoliths had greatly reduced surface areas, changing the solvent used to produce the gels from methanol to ethanol increased the surface area in one instance from 6 to 220 sq m2/g with little affect on the modulus, elastic recovery, porosity, or density.
Nguyen, Baochau N.↗
Elastic plate spallation
The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.
Oline, L.↗
On composites with periodic structure
The overall moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions or voids, and hence can be computed once and for all for given geometries. For solids with periodic structures these infinite series play exactly the same role as does Eshelby's tensor for a single inclusion or void in an unbounded elastic medium. For spherical and circular-cylindrical geometries, the required infinite series are calculated and the results are tabulated. These are then used to estimate the overall elastic moduli when either the overall strains or the overall stresses are prescribed, obtaining the same results. These results are compared with other estimates and with experimental data. It is found that the model of composites with periodic structure yields estimates in excellent agreement with the experimental observations.
Nemat-Nasser, S.↗
High temperature low-cycle fatigue mechanisms in single crystals of nickel-based superalloy Mar-M 200
Twenty three high temperature low-cycle fatigue tests were conducted on single crystals of the nickel-based superalloy Mar-M 200. Tests were conducted at 760 and 870 C. SEM fractography and transmission electron microscopy were used to determine mechanisms responsible for the observed orientation dependent fatigue behavior. It has been concluded that the plastic characteristics of the alloy lead to orientation-dependent strain hardening and fatigue lives at 760 C. At 870 C, the elastic characteristics of the alloy dominated the behavior, even though the plastic strain ranges were about the same as they were at 760 C. This led to orientation-dependent fatigue lives, but the trends were not the same as they were at 760 C.
Milligan, W. W.↗
Burner liner thermal/structural load modelling
The objective of this program is to develop a thermal data transfer computer program module for the burner liner thermal structural load modeling program. This will be accomplished by (1) reviewing existing methodologies for thermal data transfer and selecting three heat transfer codes for application in this program; (2) evaluating the selected codes to establish criteria for developing a computer program module to transfer thermal data from the heat transfer codes to selected stress analysis codes; (3) developing the automated thermal load transfer module; and (4) verifying and documenting the module. In aircraft turbine engine hot section components, cyclic thermal stresses are the most important damage mechanism. Consequently, accurate and reliable prediction of thermal loads is essential to improving durability. To achieve this goal, a considerable effort over the past 20 years has been devoted to the acquisition of engine temperature test data, as well as the development of accurate, reliable, and efficient computer codes for the prediction of steady state and transient temperatures and for the calculation of elastic and inelastic cyclic stresses and strains in hot section components. There is a need for continued development of these codes, because the availability of more accurate analysis techniques for complex configurations has enabled engine designers to use more sophisticated designs to achieve higher cycle efficiency and reduce weight.
Maffeo, R. J.↗
Notes and comments on computational elastoplasticity - Some new models and their numerical implementation
The following topics are discussed in this paper: (1) the basic interactive nature of classical elasto-plasticity and a redefinition of elastic and plastic processes that facilitates numerical calculations, (2) generalized mid-point or end-point algorithms to determine the stress increment in an elastic-plastic solid from a given strain increment, (3) an endochronic (internal time) rate theory of time-independent plasticity which encompasses various multiple-yield-surface theories and nonlinear kinematic hardening theories as its specializations, and (4) comments on finite element and boundary element methods for solving boundary value problems in elasto-plasticity.
Atluri, S. N.↗