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.

This is a review of the results of several selected theoretical studies concerned with the localized kinking, or microbuckling, of aligned fiber composite materials subjected to compression in the fiber direction. Compressive kinking is of primary concern in polymer matrix composites, for which kinking failure can limit the compressive strength to a value that is usually much lower than the tensile strength. A similar situation can occur in carbon matrix fiber composites. Compressive kinking failure may be understood on the basis of an elementary theoretical approach that ignores the influence of bending resistance of the reinforcing fibers, but takes into account the nonlinearity of composite constitutive relations as well as the effects of initial imperfections in fiber alignment. Kink bands bounded by fiber breaks are produced by deformations that occur after the attainment of peak compressive loads. The theoretical calculation of the widths of such kink bands does require consideration of fiber bending resistance; on the other hand, the results for kink width are not sensitive to the sizes of initial fiber misalignments. Progress in the study of the following additional kinking topics is summarized briefly: correlation of static kinking strength and random fiber misalignment; effects of shear and transverse loads on static kinking; viscoelastic and creep kinking; kinking fatigue; and a phenomenological theory of kinking “toughness”.

We consider the buckling of an ensemble of infinitely long columns, with initial deflections, resting on nonlinear elastic foundations. The initial deflections are assumed to be Gaussian stationary random functions of known autocorrelation, and the problem is solved by the method of equivalent linearization. We find that each column in the ensemble has the same buckling load that depends only on the autocorrelation of the initial deflection functions. Results are presented for columns whose initial deflection functions have an exponential-cosine autocorrelation.

Exact tensor equations of equilibrium are derived for nonlinear membrane shell theory and small perturbations of pressurized membrane shells. Approximate equations (for sufficiently small initial strains and rotations) for small perturbations of pressurized membrane shells are also given. Exact equations for the general nonlinear shell theory (including bending) are discussed, and approximate equations (again for small initial strains and rotations) are derived for the small perturbations, buckling, and vibration of stressed shells. These last equations are given in an Appendix in lines-of-curvature coordinates in classical notation.

With the use of J 2 deformation theory, the stress-concentration factor at a circular hole in an infinite sheet of strain-hardening material subjected to equal biaxial tension at infinity is found for a variety of representative materials. The analysis exploits a transformation which permits the calculation of the stress-concentration factor without determining the stress distribution in the sheet. Subsequent calculations reveal that, for a monotonically increasing applied stress, the stress history at all points in the sheet is nearly radial.