Rotation Of Principal Directions Research Articles

Application of the Orthotropic Damage Growth Rule to Variable Principal Directions

The classical orthotropic brittle damage law [Kachanov (1958)] is applicable for principal directions of the stress tensor. When shear stresses are accounted, the principal directions of the stress tensor rotate with time and, hence, a tensorial formulation of the damage is required [Chow and Lu (1992)]. In general, current principal directions of the stress tensora, and of the damage tensorp3B do not coincide, however, when the principal axes of stress rotate due to the shear effect, the principal axes of damage follow them. The symmetric second rank damage tensor 2 [Murakami and Ohno (1981)] is applied, and the objective derivative Q of the damage tensor is adopted, to account for the effect of rotation of principal directions on the damage accumulation process. Then, a current transformation to the global coordinate system (sampling coordinate space) is performed. The similarity of deviators based on the flow theory and on the time hardening hypothesis, associated with the orthotropic damage growth rule, both written for current principal directions of stress, are taken as constitutive relationships for creep [Boyle and Spence (1983), Kachanov (1986)]. Three examples are considered: rotationally-symmetric disk subjected to stationary radial and tangential forces, disk subjected to sustained radial tension and multiple reverse torsion. and disk subjected to alternating body forces due to acceleration/breaking cycles.

Closure to “ Rotation of Principal Directions in Ko‐Consolidated Clay ” by Pierre‐Yves Hicher and Poul V. Lade (July, 1987, Vol. 113, No. 7)

Closure to “ <i>Rotation of Principal Directions in Ko‐Consolidated Clay</i> ” by Pierre‐Yves Hicher and Poul V. Lade (July, 1987, Vol. 113, No. 7)

Discussion of “ Rotation of Principal Directions in Ko‐Consolidated Clay ” by Pierre‐Yves Hicher and Poul V. Lade (July, 1987, Vol. 113, No. 7)

Discussion of “ <i>Rotation of Principal Directions in Ko‐Consolidated Clay</i> ” by Pierre‐Yves Hicher and Poul V. Lade (July, 1987, Vol. 113, No. 7)

Rotation of principal directions in Ko-consolidated clay : Hicher, P Y; Lade, P V J Geotech Engng Div ASCEV113, N7, July 1987, P774–788

Rotation of principal directions in Ko-consolidated clay : Hicher, P Y; Lade, P V J Geotech Engng Div ASCEV113, N7, July 1987, P774–788

Rotation of principal directions in Ko-consolidated clay : Hicher, P Y; Lade, P V J Geotech Engng Div ASCEV113, N7, July 1987, P774–788

Rotation of principal directions in Ko-consolidated clay : Hicher, P Y; Lade, P V J Geotech Engng Div ASCEV113, N7, July 1987, P774–788

Rotation of Principal Directions in K0‐Consolidated Clay

Monotonic and cyclic torsion shear and cubical triaxial tests were performed to study the influence of rotation of principal stress directions on the behavior of K0‐consolidated clay. The stress‐strain and pore‐pressure relations were clearly affected by stress rotation. Strength and pore‐pressure developments occurred faster in monotonic tests without stress rotation, but the effective friction angle was not affected by initial K0‐consolidation or stress rotation. In cyclic tests, two‐way stress rotation produced more rapid degradation, higher pore pressures, and larger strains than in tests with one‐way stress rotation and tests without stress rotation. Monotonic tests after cyclic loading showed that the effective stress failure condition was not influenced, but the stress‐strain behavior was affected by hardening due to cyclic loading.

Study of beam–soil interaction using finite element and centrifugal models

A comparison is presented between the results of centrifugal model tests and finite element analyses for the problem of load transfer to a rigid tie beam buried in sand. The finite element program utilized a nonlinear elastic (hyperbolic) soil constitutive relation, obtained from tests in simple shear. It was found that, for this particular type of problem, the finite element solution may reasonably represent the interaction between the beam and the surrounding soil. It is pointed out that this agreement does not ensure that the use of such finite element analyses would be justified in problems involving rotation of principal directions, and local unloading.The effect of compaction of the fill was investigated, and it was found that compaction leads to an increase in load transferred to the beam above that which is due to density effects alone.Key words: finite elements, centrifuge, models, soil–structure interaction, buried structures.

Experimental analysis of folding in simple shear

Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded. Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks. Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater. Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions. The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.