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When porous metal is loaded in compression, after initial elastic deformation early plastic flow sets in due to stress concentration around the pores. Plastic pore collapse causes a stiffening of the stress-strain curve as the material approaches the compacted state. When the loading is rapid, the closing of the pores and associated reduction in their perimeters causes acceleration of material in the neighborhood of each cavity even for constant strain-rate loading, and the associated inertia forces result in an effective rate-effect. This is a system effect due to the micro-dynamics of the porous material, and will be superposed on any material rate-effect. Specific examples of pore collapse and the associated rate effect are presented for an aluminum alloy, based on finite-element evaluations of the process.

The formulation of the differential or integro-differential equations governing the quasi-static stress analysis problem for linear viscoelastic bodies is considered, with particular reference to the initial conditions associated with sudden loading. If classical methods of solving the differential equations, such as the Laplace transform or integrating factor, are used, the need to evaluate the initial conditions after load application at t = 0+ presents difficulties. These can be avoided by working with the lower limit t = 0-, before load application, when the body is still undisturbed, and, in the case of direct integration of the equations, delta functions and their derivatives must then be incorporated into the analysis. Examples of both methods of approach are contrasted. The stress distribution in a spinning hollow circular cylinder with annihilating inner cavity is evaluated as an example which does not fall within the scope of the Laplace transform method of analysis. The procedures are justified through the application of the corresponding integral operators.

The propagation of plane waves in an elastic-plastic medium with displacement normal to the wave front is considered. A closed form solution for moderate unloading behind a shock-wave is developed, which determines the shock-wave attenuation. Yield strength and the influence of temperature change are taken into account. This solution enables the influence of various material characteristics to be assessed. The elastic-plastic solution is compared with the compressible fluid model which neglects yield influences, and with the rigid-plastic approximation in shear. In the particular problem treated, the former determines an appreciable difference in attenuation, while the latter provides only a poor approximation, since the elastic resilience in shear has an appreciable influence on the unloading characteristics.

Stimulated by the increasing use of plastics and polymers for components which must carry load, the theory and application of viscoelastic stress analysis has developed significantly in the four years since the last International Congress of Applied Mechanics. Certain aspects of the linear problem, published during this period, which have received particular attention from groups in the U.S.A., are summarized and reviewed in this paper. A brief introduction to these topics follows, with fuller assessment, including references, presented in subsequent sections.

Professor Hodge has clearly brought out the value of the use of the Tresca yield condition and associated flow rule in obtaining solutions of boundary value problems of plastic flow. In terms of Lode’s variables, this flow criterion appears to differ considerably from the experimental results of Taylor and Quinney: Phil. Trans. Roy. Soc., Lond., Ser. A 230, 323 (1931), and for this reason in the past the Mises flow law has been preferred in theoretical work. However, some recent solutions based on the Tresca criterion have been checked experimentally (J. Foulyes and E. T. Onat, Tests of behaviour of circular plates under transverse load, Brown University Report DA—3172/3, May 1955) and have been found to give remarkable agreement with experiment. In the problem of a loaded circular plate, the characteristics change from radial lines to logarithmic spirals at a certain radius and such a change was observed in markings on the plate surface. It seems therefore that solutions obtained by this method are more satisfactory than had been anticipated. The reason for this may be due to concentration of the corresponding points in the Lode diagram in the region of the diagonal in problems of non-homogeneous stress and strain, due to the freedom of the strain rate vector at the corners of the Tresca yield hexagon. It would seem worthwhile to look into this, for as Professor Hodge has shown, this technique offers an extremely powerful means of solution of plastic flow problems, which will be the more valuable when the basis for its accuracy is better understood.

The theory of the propagation of plastic waves developed independently by Taylor [1] and Karman [2] considers an invariant stress-strain relation which is independent of the rate of strain. Experimental measurements are in broadly satisfactory agreement with this theory for many metals, although reproducible discrepancies are observed which are thought to be due to the influence of the rate of strain in modifying the stress-strain relation [3]. Attempts to include a strain-rate influence, such as that by Malvern [4], have exhibited a marked improvement in predicting certain experimental observations, but have appeared to fail in the case of others. It is shown below that the major discrepancy with experiment which was considered to dictate against a theory of this type appears not to be valid.