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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Elastoplastic transverse properties of a unidirectional fibre reinforced composite

An approximate theoretical study is made to predict the overall transverse elastoplastic properties of a unidirectional fibre reinforced composite. Based on the simplest deformation theory of plasticity, the overall transverse polyaxial elastoplastic constitutive equations for an incompressible composite are obtained. A simple formula is suggested to evaluate the average stress in the fibres. Furthermore, with the prediction of the overall transverse elastic moduli of a compressible composite, the overall transverse uniaxial stress-strain curve for a compressible composite in the entire elastic-plastic range is obtained. A detailed example is given for a Boron-Aluminum composite. Comparison is made with the experimental and theoretical work done by General Dynamics and Adams respectively.

Huang, W.-C.↗
NASA NTRS1975

Application of boundary integral equations to elastoplastic problems

The application of boundary integral equations to elastoplastic problems is reviewed. Details of the analysis as applied to torsion problems and to plane problems is discussed. Results are presented for the elastoplastic torsion of a square cross section bar and for the plane problem of notched beams. A comparison of different formulations as well as comparisons with experimental results are presented.

Mendelson, A.↗
NASA NTRS1975

Application of boundary integral equations to elastoplastic problems

The application of the boundary integral equation method (BIE) to the elastoplastic torsion problem is considered. It is found that the BIE is very suitable for the elastoplastic analysis of the torsion of prismatic bars. A comparison of the BIE with the finite difference method shows savings for the BIE concerning the number of unknowns which have to be determined and also a much faster convergence rate. Attention is given to the problem of an edge-notched beam in pure bending, taking into account a biharmonic formulation and a displacement formulation.

Mendelson, A.↗
NASA NTRS1972

Nonlinear waves in a rate-sensitive, elastoplastic material.

Discussion of two classes of closed form solutions of one-dimensional, unsteady motion of a rate-sensitive elastoplastic material. One class of these solutions is self-similar and is deduced from the invariant theorems of continuous groups of transformations. The second class of solutions is obtained by searching for one-dimensional wave motions with constant speeds of propagation. Applications of these solutions to unsteady motions behind propagating discontinuities are considered.

Burniston, E. E.↗
NASA NTRS1974

Application of boundary integral method to elastoplastic analysis of v-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problems. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single edge notch and subjected to pure bending. The boundary integral equation method reduced the non-homogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with the method of successive elastic solutions.

Rzasnicki, W.↗
NASA NTRS1974

Application of boundary integral method to elastoplastic analysis of V-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problem. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single-edge notch and subjected to pure bending. The boundary integral equation method reduced the inhomogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with a method of successive elastic solutions.

Rzasnicki, W.↗
NASA NTRS1974

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Osias, J. R.↗
NASA NTRS1974

An elastoplastic analysis of a uniaxially loaded sheet with an interference-fit bolt

The stresses and strains in a uniaxially loaded sheet with an unloaded interference-fit bolt were calculated by an elastoplastic finite-element analysis. The material properties represented a 7075-T6 aluminum alloy sheet and a steel bolt. The analysis considered the two ideal cases of no slip and no friction at the bolt-sheet interface for a single combination of bolt diameter, interference level, and cyclic loading. When the bolt was inserted, the sheet deformed plastically near the hole; the first tensile load cycle produced additional yielding, but subsequent cycles to the same level caused only elastic cyclic stresses. These stresses together with fatigue data for unnotched specimens were used to estimate crack initiation periods and initiation sites. The cases analyzed with interference-fit bolts were predicted to have crack initiation periods which were about 50 times that for a clearance-fit bolt. Crack initiation was predicted to occur on the transverse axis at a distance of about one radius from the hole.

Crews, J. H., Jr.↗
NASA NTRS1974

A method for determining local elastoplastic stress and strain in metallurgically bonded notched laminates subjected to a loading cycle

A semianalytical method was developed for determining elastoplastic cyclic stresses and strains at notch roots in metallurgically bonded metal laminates. The method is based on the Neuber equation, which was used with an effective stress-strain curve for the laminate. It was applied to laminates containing a circular hole which were subjected to one cycle of reversed loading. The laminates consisted of two elasto-perfectly-plastic materials with different yield strengths and with either equal or different Young's moduli. A laminate of high-strength titanium alloy with alternate layers of commercially pure titanium was also analyzed. The accuracy of the method was evaluated by comparing the stresses and strains with those calculated from a finite-element analysis. The results estimated by the simple method based on the Neuber equation agreed closely with the results computed from the more elaborate finite-element analysis.

Sova, J. A.↗
NASA NTRS1975

Solution of elastoplastic torsion problem by boundary integral method

The boundary integral method was applied to the elastoplastic analysis of the torsion of prismatic bars, and the results are compared with those obtained by the finite difference method. Although fewer unknowns were used, very good accuracy was obtained with the boundary integral method. Both simply and multiply connected bodies can be handled with equal ease.

Mendelson, A.↗
NASA NTRS1975

Application of boundary integral method to elastoplastic analysis of V-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problems. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single edge notch and subjected to pure bending. The boundary integral equation method reduced the nonhomogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with the method of successive elastic solutions.

Rzasnicki, W.↗
NASA NTRS1982

Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem

The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into elastic and plastic parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stabiity properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.

Pinsky, P. M.↗
NASA NTRS1982

Three-dimensional elastoplastic stress analysis of unidirectional boron/aluminum composites

A three dimensional elastoplastic finite element micromechanical model was developed to study the state of stress around a broken fibers in a unidirectional composite. A boron/aluminum composite consisting of 50 percent by volume of fibers in a square array and subjected to an axial loading is taken as a specific example. This loading in the fiber direction is applied in small increments, by prescribing increments of boundary displacement, until the first failure occurs. The effect of reduced material properties of the aluminum matrix material at elevated temperature is also studied. The results are presented in the form of stress contours and stress-strain plots.

Mahishi, J. M.↗
NASA NTRS1984

Initial postbuckling analysis of elastoplastic thin-shear structures

The design of thin shell structures with respect to elastoplastic buckling requires an extended analysis of the influence of initial imperfections. For conservative design, the most critical defect should be assumed with the maximum allowable magnitude. This defect is closely related to the initial postbuckling behavior. An algorithm is given for the quasi-static analysis of the postbuckling behavior of structures that exhibit multiple buckling points. the algorithm based upon an energy criterion allows the computation of the critical perturbation which will be employed for the definition of the critical defect. For computational efficiency, the algorithm uses the reduced basis technique with automatic update of the modal basis. The method is applied to the axisymmetric buckling of cylindrical shells under axial compression, and conclusions are given for future research.

E G Carnoy↗