An Elastic Solution Of The Laterally Constrained Circular Cylinder Under Uniaxial Loading

One of the more widespread experimental procedures currently used in experimental rock and soil mechanics work involves the use of a short circular cylinder loaded axially between nonrigid end plates1-5 (Fig. 1a and b). It is widely recognized 6 that a number of undesirable features are connected with this test procedure ; the most noteworthy of these is the development of a nonuniform stress distribution throughout the specimen resulting from an elastic mismatch between the specimen and the end plates. In general, the end plates and specimen possess different elastic properties. As a result of this elastic mismatch, the uniform distribution of stress and strain applied to the end plates is altered at the interface, the degree of which is dependent not only on the magnitude of the elastic mismatch but also on whether there is any relative movement between the specimen and the end plate. A convenient measure of the elastic mismatch is the ratio (vp/Ep) / (v8/E3), where v and E are Poisson's ratio and Young's modulus and the subscripts s and p refer to the specimen and end plate, respectively. For most tests that use steel end plates, (v8/E8) is greater than (vp/Ep) ; i.e., the specimen tends to expand or contract laterally more than the end plates. Because of the frictional restraint offered by the end plates, shearing stresses are developed at the interface that, for compression testing, act inward producing a "clamping" effect (Fig. lc). The effect of this "clamping" is to produce a state of triaxial stress throughout the specimen. Fig. Id illustrates the coordinate system and stress nomenclature used. In a homogeneous, elastic two-dimensional plate loaded uniaxially at the edge, a uniform stress distribution is obtained at a distance from the