Zdenek P. Bazant

Bio: Zdenek P. Bazant is an academic researcher from Northwestern University. The author has contributed to research in topics: Creep & Fracture mechanics. The author has an hindex of 82, co-authored 301 publications receiving 20908 citations. Previous affiliations of Zdenek P. Bazant include École Polytechnique Fédérale de Lausanne & Rensselaer Polytechnic Institute.

Fracture properties and brittlenesss of high-strength concrete

Abstract: The size effect method for determining material fracture characteristics, as previously proposed by Bazant is applied to typical high-strength concrete. Geometrically similar 3-point bending specimens are tested and the measured peak load values are used to obtain the fracture energy, the fracture toughness, the effective length of the fracture process zone, and the effective critical crack tip opening displacement. The brittleness of the material is shown to be objectively quantified through the size-effect method. Comparing the material fracture properties obtained with those of normal strength concrete shows that an increase of 16 % in compressive srength causes: (1) increase of fracture toughness; (2) decrease of effective fracture process zone length; (3) more than doubling of the brittleness number. The brittleness number, however, is still not high enough to permit the use of linear elastic fracture mechanics. The R-curves are demonstrated to derive according to the size effect law exclusively from the maximum loads of specimens of various sizes and yield remarkably good predictions of the load-deflection curves.

Finite strain analysis of deformations of quasibrittle material during missile impact and penetration

Abstract: Zdenek P. Bazant,* Fellow. ASME, Mark D. Adley,t and Yuyin Xiang* ~ Department of Civil Engineering Northwestern University. Evanston. Illinois 60208 U.S. Army Engineers Waterways Experiment Station Vicksburg, Mississippi 31980-6199 The conference presentation deab with thref' problems iuvolved in hnite element analysis of the impact of missiles into reinforced concrete walls and their penetration through t.he walls: (1) Formulation of the constitut.ive law for complex nonlinear triaxial behavior of concrete. including the strain-softening damage; (2) extension of the formulation to very large finite sW',ins; and (3) application of the model in dynamic finite element analysis. Only problem (2) is discussed in some detail in this brief paper. Because the Biot strain tensor has a clear physical meaning even for very large finite strains, its use is preferable in the fitting of complex triaxial test data. It is shown that the constitutive relation can be conveniently formulated as a relation of the Biot strain tensor to the back-rotated Cauchy stress tensor, and the justification of this form of the constitutive relation is given. INTRODUCTION Impact of missiles and their penetration through concrete walls generates strains of the order of 100% near the missile. The constitutive law used in the analysis must be applicable to such enormous strains. For some metal-forming problems. adequate incremental formulations in an updated Lagrangeall frame of reference have been obtained by finite strain g~npralization of constitutive models of incremental plasticity. such as von Mises plasticity. These formulations are well established. Such formulations have been tried for concrete. but with little success. The main reason is that the constit.utive law of concrete is much more complex. A sophisticated nonlinear triaxial constitutive model which that been shown to give excellent results for concrete at small strains is thl' microplane model. Its available form. however. requires a total rat.her than incremental Lagrangean frame of reference. Hibbitt et al. (1994) use in ABAQUS a hyperleastic constitutive law in the form of a relation of the Cauchy stress tensor to the left Cauchy-Green strain tensor. But such a formulation does not seem possible for concrete. As far as the total Lagrangean formulations are concerned, the available models deal mainly with elastomers, which do not exhibit damage and strain-softening and can be formulated on the basis of a simple, easily identified. elastic potential. such as a low-order polynomial in the principal stretches. This

Part III: Drying Creep

Abstract: The practical model for predicting creep and shrinkage developed in Parts I and II is extended to creep at drying environment and constant temperature. The increase of creep due to drying is related to shrinkage. Formulas for determining material parameters from concrete strength and mix composition are presented and verified by extensive comparisons with test data from the literature. INTRODUCfION The prediction models for shrinkage and basic creep, developed in Parts I and II, must now be extended to cover creep in a drying environment. The expressions describing this behavior were developed in a preceding work [4] e), and they were shown to allow good fits of test data. However, each data set was fitted indivi­ dually, and no formulas that correlate the material parameters and predict them from the given concrete strength and mix composition were derived. This will be done in this part, in which data analysis of un­ precedented scope (24 different mixtures) will be undertaken.

Theoretical stress strain model for confined concrete

Abstract: A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concret...

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.