Tests have been carried out on thin closed-ended tubes of alpha brass subjected to various combinations of torque and internal pressure. The effect of loading, unloading, and reloading along different loading paths has been investigated, including the effect on the shape of the yield surface, and the form of the curve of representative stress and representative strain. The behavior of the material for initial loading suggests that the material is isotropic in the plane of the surface of the tube but is anisotropic in a radial direction. A form of yield criterion and representative stress which correlates these results has been deduced, but the results of the tests for the second loadings of the specimens cannot be correlated in terms of a nested set of similar yield surfaces. The evidence for or against the existence of corners or pointed vertices on the yield surface is inconclusive.

A differential stress-strain relation is derived for a medium composed of a hexagonal close-packed array of elastic spheres in contact. The stress-strain relation is based on the theory of elastic bodies in contact, and includes the effects of both normal and tangential components of contact forces. Results of an experiment performed as a test of the differential stress-strain relation are presented.

Equations for the stress distribution in plastic rotating cylinders are developed for both hollow and solid cylinders. It is assumed that the stress-strain relations may depend upon either the maximum shearing stress or the octahedral shearing stress and the corresponding shearing strain. A triaxiality factor proportional to the ratio of the hydrostatic tension to the octahedral shearing stress is introduced. This factor may be useful in evaluating the ductility of metals under combined stress.

A granular medium is idealized here by a model composed of contiguous like spheres arranged in a face-centered cubic lattice. Total stress-strain relations for this model are derived by integrating incremental relations, given previously by Duffy and Mindlin, for a loading program which consists of a uniaxial compression applied concurrently with a related isotropic pressure. Further, the failure stress in uniaxial compression is determined as a function of initial pressure. Results of experimental work are reported which agree with predictions of the theory.

The definitions given previously for work-hardening and perfect plasticity are broadened to cover viscous effects. As before, the system considered is isothermal and includes both the body and the time-dependent set of forces acting upon it. An external agency is supposed to apply an additional set of forces to the already loaded body. It is now postulated that the work done by the external agency on the additional displacements it produces is positive. Some of the restrictions thus imposed on permissible stress-strain relations are explored. Especial attention is paid to simple laws of creep. Uniqueness of solution also is studied.

When a layer of material embedded in an infinite medium is subject to a compression parallel with the layer an instability tends to develop which manifests itself in the folding of the layer. This phenomenon is examined here for the general case where the layer and the surrounding medium are both viscoelastic. This problem which was examined in preliminary form in an earlier publication [6] is treated here with particular attention to the effect of interfacial adherence of the layer and the medium, and to an evaluation of the amplitude of the folding. In general there is a lower and upper-critical value of the compressive load between which folding occurs with a finite rate of deformation. There appears also a dominant wave length, for which the rate of folding is maximum under a given load. The dominant wave length may or may not depend on the load. The effect of interfacial adherence while not negligible is not generally significant. The rate of folding increases very rapidly beyond a certain value of the viscosity ratio of the two media. A brief discussion is also included of the thermodynamic implications of incremental stress-strain relations in prestressed media.

A granular assemblage is represented by a model consisting of like spheres in contact arranged in a simple cubic lattice. Based on consideration of local contact forces and concomitant deformations, incremental stress-strain relations are derived and subsequently integrated, for certain types of loading, to yield total stress-strain relations. The integration is carried out for both a loading and an unloading process. A criterion of failure for the model is set up and the theory applied to a regimen of loading which gives rise to a plane state of stress.

Stress-strain relations are given for an initially isotropic material, which is macroscopically homogeneous, but inhomogeneous on a microscopic scale. An element of volume is considered to be composed of various portions, which can be represented by subelements showing secondary creep and isotropic work-hardening in plastic deformation. If the condition is imposed that all subelements of an element of volume are subjected to the same total strain, it is demonstrated that the inelastic stress-strain relations of the material show anisotropic strain-hardening, creep recovery, and primary and secondary creep due to the nonuniform energy dissipation in deformation of the sub-elements. Only quasi-static deformations under isothermal conditions are considered. The theory is restricted to small total strains.

This paper establishes conditions under which a wide or narrow adhesive scarf joint can have uniformly distributed adhesive stresses, and gives formulas for these stresses. The results are rigorously limited to linear adhesive stress-strain relations, but are such that they sometimes may be applicable in analyzing scarf-joint tests to destruction, even when appreciable inelastic deformation occurs. Previously published test data are found to have one of the failure-load variations with scarf angle to be considered in this paper. The analysis therefore should prove useful in design work within the elastic limit, and in some cases beyond it.

An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β ) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π /2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β . Numerical results for stresses and displacements are given in one case ( β = π /4) for various positions of the elastic-plastic boundary.

It is shown that a variational formula similar to the one expressing the principle of Haar and von Karman in the statically determinate problems of plasticity holds independently of the stress-strain relations and yield condition. In the variation of the elastic energy the part connected with the variation of the field must be distinguished from the part connected with the variation of the energy density. These points are illustrated by an example.

The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

A differential stress-strain relation is derived for a medium composed of a face-centered cubic array of elastic spheres in contact. The stress-strain relation is based on the theory of elastic bodies in contact, and includes the effects of both normal and tangential components of contact forces. A description is given of an experiment performed as a test of the contact theories and the differential stress-strain relation derived from them. The experiment consists of a determination of wave velocities and the accompanying rates of energy dissipation in granular bars composed of face-centered cubic arrays of spheres. Experimental results indicate a close agreement between the theoretical and experimental values of wave velocity. However, as in previous experiments with single contacts, the rate of energy dissipation is found to be proportional to the square of the maximum tangential contact force rather than to the cube, as predicted by the theory for small amplitudes.

It is well known that the use of Tresca’s yield condition frequently leads to a simpler system of equations for the stresses in a plastic solid than the use of the yield condition of Mises. However, in most cases where Tresca’s yield condition has been used, the flow rule associated with the Mises condition has been retained. Following Koiter, it is shown that further simplification results from the use of the flow rule associated with the Tresca condition. The reason for this is discussed in connection with two examples concerning the finite enlargement of a circular hole in an infinite sheet of perfectly plastic or work-hardening material. The second example is probably the first nontrivial case in which a problem of finite plastic deformation of a work-hardening material has been treated in closed form by the use of incremental stress-strain relations.

The influence of the loading program on the agreement between the predictions of the Hencky and the Prandtl-Reuss stress-strain relations for a perfectly plastic material is investigated in the case of the combined bending and twisting of thin-walled tubes. The agreement in the values of the bending and twisting moments is found to vary considerably with the particular loading program chosen. The analysis is extended to tubes composed of a work-hardening material. The bending and twisting moments are obtained numerically using the incremental approach for a square tube which is bent and then twisted. Owing to the large amount of labor involved in this solution, an approximate method using the concept of a “composite” beam is developed, and good agreement in the results is found with those obtained from the incremental solution.

This paper presents the results of an experimental study of the stress-strain relation of annealed 2S aluminum when subjected to compression impact. Two methods of securing a dynamic stress-strain curve are considered, namely, from the measurement of impact stress as a function of maximum plastic strain, and impact stress as a function of the impact velocity. The dynamic stress-strain curves obtained by these methods lie considerably above the static curve. The elevation in stress of the dynamic relations above the static relation increases progressively from zero at the elastic limit to about 20 per cent at a strain of 4.5 per cent. However, the two dynamic relations are not coincident which indicates that the behavior of the material cannot be described by a single stress-strain curve for all impact velocities. A family of stress-strain curves which differ slightly from each other and which depend upon the final strain is postulated in order to correlate both sets of data adequately.

Equations of motion of the three-dimensional finite oscillation theory are integrated across the plate thickness to obtain a second-order theory of oscillations for plates. For this purpose, components of the displacement vector are assumed to have power-series expansions in the transverse co-ordinate, and a systematic perturbation procedure in a nondimensional thickness parameter is used. Stress-strain relations include the hereditary damping.

The authors assess a plastic stress-strain law of anisotropic strain-hardening type which they previously developed on the basis of explicit consideration of the polycrystalline nature of metals and the mechanism of plastic deformation. The assumptions made are reviewed, together with the successes and limitations of the theory. The authors indicate the lines along which they feel that improvement of the theory is to be sought.