Showing papers in "International Applied Mechanics in 1985"

Mutual effect of a circular surface crack and a free boundary in an axisymmetric problem of the fracture of an incompressible half space in compression along the crack plane

Abstract: In the case where a deformable solid containing a crack which is planar in plan is acted upon only by forces parallel to the crack plane, the stress intensity factors obtained in linear fracture mechanics are equal to zero [6, 8] Fracture criteria of the Griffith-Irwin type cannot be used, and instead use is made of the stability criterion proposed earlier [2] in the framework of the three-dimensional linearized theory of stability [I] A general approach to such problems in the coordinates of the initial strain state was proposed in the monograph [3], where a detailed bibliography was also given The approach is based on the use of general solutions of the equations of the linearized theory of stability with uniform subcritical states

Stability of a series of fibers in an elastic matrix at small subcritical deformations

Abstract: 1. The comparison in Table 2 confirms the good convergence of the chosen method, which allows sufficiently accurate results to be obtained. 2. Qualitatively, the dependence of the critical deformation on the rigidity is analogous for problems with one and two fibers. The minimal values of the deformation in Table 1 are shown by bold type in Table 1. 3. Comparison with results for one (Fig. 2) and two (Figs. 3 and 4) fibers shows a great distance with respect to the limiting load, i. e., the limiting loads for a series of fibers are less (for forms I and III than for one or two fibers. This indicates that the interaction of a series of fibers in stability loss is even stronger. 4. As shown by the results (Table 1), stability loss is in form I, but for very closely spaced fibers and small rigidity ratios form III has an advantage: for example, for δ/R=2.2 and E(1)/E≤500; for δ/R=2.5 and E(1)/E≤100; for δ/R=3 and E(1)/E≤200. 5. Comparison of the results obtained with the critical deformation for a single fiber shows that, within limits of error of 10%, for small rigidity ratios even when δ/R=5, the interaction of the fibers cannot be taken into account (Table 1). For large ratios E(1)/E, mutual influence appears only for large δ/R; when E(1)/E=1000, the fibers interact slightly only for δ/R>7 (Fig. 2, Table 1). This is somewhat greater than for the results obtained for two fibers (Figs. 3 and 4).

Three-dimensional stability theory of deformed bodies. Internal instability

Abstract: In studying internal instability effects for elastic (which is fully obvious) and elastoplastic models of deformable bodies the approximate approach [12, 15] in the three-dimensional stability theory leads to results which disagree quantitatively and qualitatively with the corresponding results of the three-dimensional linearzed stability theory of deformable bodies (the second variant of the theory of small subcritical deformations). In this connection, in studying internal instability effects for various models of deformable bodies, in which elastic or elastoplastic deformations are substantial, the use of this approximate approach is recommended.