G.I Barenblatt

Bio: G.I Barenblatt is an academic researcher. The author has contributed to research in topics: Axial symmetry. The author has an hindex of 1, co-authored 1 publications receiving 1003 citations.

Crack band theory for fracture of concrete

Abstract: A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.

Cohesive force across the tip of a longitudinal‐shear crack and Griffith's specific surface energy

Abstract: The cohesive force across the fault plane is considered in order to understand the physical mechanism of rupture at the tip of a longitudinal-shear crack. The elastic field around the tip of a crack and the condition of rupture growth are systematically derived from the assumption that the cohesive force is given as a function of the displacement discontinuity. This assumption is more physically meaningful than those originally used by G. I. Barenblatt in 1959 and 1962. The stress field around the tip is calculated for several models of cohesive force, and is shown to be nonsingular even at the tip. The condition of rupture growth that is used to determine the rupture velocity turns out to be equivalent to the Griffith criterion and the relation employed by B. V. Kostrov in 1966, but the specific surface energy is defined more clearly in this paper.

Progressive Delamination Using Interface Elements

Abstract: The paper describes a method for modelling progressive mixed-mode delamination in fibre composites. The procedure, which is incorporated within the non-linear finite element method, is based on the use of interface elements in conjunction with softening relationships between the stresses and the relative displacements. Fracture mechanics is indirectly introduced by relating the areas under the stress/displacement curves to the critical fracture energies.

A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. Part II. Applications of the model

Abstract: We construct an earthquake source model which provides a complete description of acceleration power spectra of direct body waves. The model is a specific form of the barrier model proposed by Aki et al. (1977). According to this specific barrier model, the fault surface is visualized as composed of an aggregate of circular cracks which represent areas of localized slip, and the strong motion is assumed to be generated by the stationary occurrence of these localized ruptures as the rupture front propagates. The acceleration power spectra of direct S waves are described by their peak value P and an effective bandwidth Δ f. P scales proportionally to the width of the causative fault and to the square of local stress drop which is proportional to the ratio of maximum slip over the barrier interval. Δ f is specified by the corner frequency and a cutoff frequency which presumably originates from fault nonelasticity and is considered to be inversely proportional to the cohesive zone size. From these spectra and an estimate of the duration of faulting, measures of strong motion intensity such as rms and maximum acceleration can be inferred. Results of the application of the model to strong motion observations of various events are reported in Part II.