Finite element solutions, for a bilinear material model, were obtained to establish a correspondence between the response of the plane strain wedge and its axisymmetric counterpart, the cone. The results of the study enable a better understanding of the process of penetration of soils by penetrometers and piles, as well as the failure mechanism of deep foundations (piles and anchor plates). The second topic concerns the 'steady-state plane-strain free rolling of a rigid roller in clays.
The problem is approximately solved for small loads by obtaining the exact solution of two problems encompassing the problem of interest; the first is a steady state with a geometry close to that of the roll and the second is an immediate resolution of the rolling process, but is not a steady state. Details of the construction of the field with characteristics in a front failure mode Physical plane for a front failure mode Hodograph of figure. Typical field characteristics for a trailing edge junction. Details of the construction of the field of.
Steady-state free rotation under plane strain of a smooth rigid cylinder in a perfectly plastic rigid half-space. Various idealizations of the rolling process (a} Problem A: the ironing plate problem (b} Problem B: immediate solution (c) Giving a half space by a rigid punch (d} Marshall's conjecture about with the cheap one.
CHAPTER I
Invoking isotropy again, we can show that slip lines are features of the velocity field. Along the front boundary of the ABC plastic domain, we have a smooth surface with predefined properties. This method, which requires changes to the deformable medium model, such as the introduction of compressibility, has not been implemented.
After assuming the location of part of the divide, Nr. unique evidence could be obtained. Reading curves for modeling clay~ . rigid plastic material in the loading part of the basket. Part C fits into a cut made in slider B; it has properly spaced holes to allow fixing of.
The indenter is driven through the clay by the movement of the drive head of the machine. During the movement of the indenter, a deformation pattern is recorded in the center plane by distortion of the grid. The assumption of the technique is that the slope of the convergence curve is non-positive.
Szechy, C., “Some Experimental Observations Concerning the Size and Distribution of Settlements, 11 Proceedings of the 7th Int.
CHAPTER II
Let us consider the plane strain problem of the rigid symmetric wedge shown in Fig. be shown. This means that AB is considered a property of the plastic domain; (2) in order to meet the steady-state requirements, it is assumed that the free surface AD is straight and at an angle y, given by Equation (5), to the horizontal. To determine the effect of wedge angle on the results, wedges with half angles.
2L. 2) The load required to produce a steady state in the first test was found to be 5% greater than that in the second test. We conclude that the steady state of the wedge problem is indeed developed and is independent of the initial geometry. In addition, a certain area of contact with the back of the wedge is present in the test results.
The rigid domain in front of the wedge, which according to the theory suffers no deformation, actually deforms in the test. One such mechanism involving a rigid part in front of the wedge was reported in the indentation of a half space with a rigid wedge [15]. In the same figure, the distorted mesh is shown; it bears a strong resemblance to the wedge with ~ = 45°.
This is most obvious in the far field, i.e. at the boundary of the rigid domain with the plastic zone.
CHAPTER III
The plate is inclined with an angle ~. O < ~ < rr/4), to the horizontal and its lowest point is at the same level of the surface of the half space. A pile in front of the plate acts with the half space as ~ continuum and has a contact length L with the plate. Let p be the contact pressure at the interface, ~ the counterclockwise slope of the plate to the horizontal and k the flow stress in shear, then.
The non-plastic zone outside ABE DC is at rest and is therefore located at origin 0 of the hodograph. The velocity field is given by Figure III-7, which differs from III-5 by a shift from the origin 0 by an amount U. Along AB, the surface of the plate previously assumed to be smooth gives no energy dissipation.
The problem of the ironing plate is solved assuming that the heap in front of the plate is an isosceles triangle, Fig. For small values of ~ (say O < ~ < 10°), which is the region of interest in applications to the roll theory of Chapter IV, a summary of the dimensions and permanent horizontal deformation o is given in Figure. Part AB is a circular arc with the same radius R as that of the cylinder and a center of curvature O' that lies vertically above A. The cylinder must be mounted so that the center 0 coincides with 0 1 and then an instantaneous horizontal velocity U, to the right, becomes 0.
This is an exact solution and will prove to be valid in the case where the surface of the wedge has the form GABDF, fig. For the indentation problem shown in the figure described earlier, we now represent a plastic field lying in front of the cylinder. The horizontal velocity U on the right is given instantaneously at the center of the cylinder 0 along with the clockwise angular velocity w of the cylinder about O.
The origin of the hodograph lies at 00 and the heavy lines represent jumps in speed. Noting that the jump at any point on the rim of the cylinder is parallel. The shape of the zone outside the plastic zone being ambiguous for the current solution, we can consider the vertical BDE or horizontal DF in Fig.
The direction of the shear stresses and the shear strain rates at any point in the plastic zone have the same sign, satisfying the positive force of the dissipation condition. Details regarding the velocity field in the case of a frontal disturbance may be useful to the reader in noting the interchange of the a and f3 lines.
CHAPTER IV
The stationary free-rolling problem of a rigid cylinder is then properly formulated and an ideal plasticity chosen to account for losses. The first is a stationary solution to a problem with a geometry that is not exactly cylinder geometry, and the second is an instantaneous solution to a cylinder geometry but is not stationary. When checked against existing empirical formulas for wheel rolling on clay, the predicted rolling resistance compares favorably.
The nature of the sink to absorb the force released by external forces is undoubtedly a cornerstone for any theory dealing with this subject. Two types of slip are considered, the first is called "Reynolds slip", which is present in part of the contact area and results from the difference in elastic compliance between the rolling and static parts. The contact area between the ball and the plate was assumed to consist of a semicircle when projected onto the horizon, with the center of the semicircle lying directly below the center of the ball.
Using this assumption and measuring the applied forces, an average value of the contact stress was calculated, which was found to depend on the yield pressure of the softer metal. To rationalize these results, Eldredge and Tabor argued that rolling resistance is primarily due to plastic movement of the plate in front of the ball. Thus, the use of plasticity takes into account, firstly, the large permanent deformations of the plate material and, secondly, the almost uniform distribution of stresses at the contact.
Obviously, due to the complexity of the problem, no real plasticity analysis was performed; nevertheless the rolling resistance H. Theoretically speaking, the problem of plane deformation of a cylinder is much simpler than the problem of a three-dimensional ball. However, the bullet drag formula has not been extended to the cylinder, presumably due to the absence of an accurate plasticity analysis.
Since no more distinct permanent deformation was found for large n, and because of the assumed connection between plasticity and large deformation, Tabor and followers rejected plasticity. Unfortunately, a is not only a material constant, but depends on the loads and attenuations of the problem [4]. Although it can account for the effect of particular parameters (such as rotational speed) on rolling resistance, viscoelasticity.
