Showing papers by "Zdenek P. Bazant published in 1975"

Elastodynamic Near-Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials

Abstract: The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The 2-dimensional near-tip displacement fields are assumed in the general form r/sup P/ T(t, c) K(theta, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(theta, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(theta, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.

Saturated Sand as an Inelastic Two-Phase Medium.

Abstract: The inelastic densification produced by shear straining saturated sands is opposed by the elasticity of the pore water and leads to a pore pressure increase, which causes a decrease in the intergranular frictional forces and consequent liquefaction of the sand mass. This inelastic densification is accompanied by an inelastic strain of the fluid phase, and the magnitude of the developed pore water pressure is the product of the inelastic densification and the densification compliance, the latter being approximately equal to the drained compressibility of the sand. The tangent elastic moduli are expressed in terms of the drained and undrained compressibilities of the two-phase medium and the compressibilities of water and the solid matter forming the grains. It is demonstrated that the volume change of the grains due to intergranular stresses has a negligible effect on the material parameters, even though it roughly equals the volume change of the grains due to the pore water pressure, which has an appreciable effect. Typical values are calculated for the material parameters.

Micromechanics Model for Creep of Anisotropic Clay

Abstract: Clays frequently possess a fabric with a preferred particle orientation and the creep properties of such clays are therefore anisotropic. A two-dimensional microstructural model to describe this creep response is developed. The model is based on a triangular cell of three particles sliding over each other at a rate predicted by rate-process theory. Equating the rate of energy dissipation within the cell to that of the macroscopic continuum leads to the determination of the tangential viscosity matrix and the matrix of the nonviscous stress components, both of which are stress dependent. The anisotropic creep viscosity parametres then are obtained by a statistical averaging procedure based on the probability density of the particle orientation distribution, as determined by x-ray diffraction. The resulting model is able to predict the directional differences in the creep rate and the stress dependence of creep in clays with anisotropic fabric. Undrained creep tests were conducted on specimens cut in various directions from both isotropically and anisotropically consolidated kaolinite samples.

Elastodynamic near-tip stress and displacement fields for rapidly propagating cracks in orthotropic materials.

Abstract: The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The 2-dimensional near-tip displacement fields are assumed in the general form r/sup P/ T(t, c) K(theta, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(theta, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(theta, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.

Finite Element for Buckling of Curved Beams and Shells with Shear

Abstract: Inclusion of shear deformations allows the bending theory to be extended to relatively thick beams and shells and, at the same time, simplifies the finite element formulation for both thick and thin beams because monotonic convergence may be achieved without ensuring continuity of displacement derivatives between adjacent elements. Consequently, on may use low order interpolation polynomials, including linear ones. This is particularly useful in the case of curved beams because with higher order interpolation polynomials it is very difficult to satisfy exactly the conditions of no self-staining at rigid body rotations and of availability of all constant strain states, while with linear displacement interpolation polynomials and a straight shape of the element these requirements are easily met.