Showing papers by "Zdenek P. Bazant published in 1996"

Microplane Model for Concrete. I: Stress-Strain Boundaries and Finite Strain

Abstract: The paper presents an improvement of the microplane model for concrete—a constitutive model in which the nonlinear triaxial behavior is characterized by relations between the stress and strain components on a microplane of any orientation under the constraint that the strains on the microplane are the projections of the macroscopic strain tensor. The improvement is achieved by a new concept: the stress-strain boundaries, which can never be exceeded. The advantage of this new concept is that various boundaries and the elastic behavior can be defined as a function of different variables (strain components). Thus, whereas for compression the stress-strain boundaries are defined on the microplanes separately for volumetric and deviatoric components, for tension an additional boundary is defined in terms of the total normal strains. This is necessary to achieve a realistic triaxial response at large tensile strains. For microplane shear, a friction law with cohesion is introduced. The present model is simpler than the previous microplane model. Finally, the microplane model is generalized to finite, but only moderately large, strains. Verification and calibration by test data are left to a subsequent companion paper.

Size Effect and Fracture Characteristics of Composite Laminates

Abstract: Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/92{sub 2}]{sub s} crossply layup, and another set had a single-sided edge notch and a [0/{+-}45/90]{sub s} quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of {minus}0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on themore » basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.« less

Analysis of work-of-fracture method for measuring fracture energy of concrete

Abstract: The role that plastic-frictional energy dissipation in the fracture process zone plays in the work­ of-fracture method for measuring the fracture energy of concrete or other quasibrittle materials is analyzed, and a possible improvement of this method is proposed. It is shown that by measuring the unloading compliance at a sufficient number of states on the post-peak descending load-deflection curve, it is possible to calculate the pure fracture energy, representing the energy dissipated by the fracture process alone. However, this value of fracture energy is pertinent only if the material model (constitutive law and fracture law) used in structural analysis takes into account separately the fracture-damage deformations and the plastic-frictional deformations. Otherwise, one must use the conventional fracture energy, which includes plastic-frictional energy dissipation. Either type of fracture energy should properly be determined by extrapolation to infinite specimen size. Further, it is shown that the unloading compliancies to be used in the calculation of the pure fracture energy can be corrected to approximately eliminate the time-dependent effects (material viscoelasticity) and reverse plasticity. Finally, it is proposed to improve the work-of-fracture method by averaging the work done by fracture over only a central portion of the ligament. However, experiments are needed to check whether the specimen size required for this improved method would not be impracticably large.

Is No-Tension Design of Concrete or Rock Structures Always Safe?—Fracture Analysis

Abstract: Plain concrete structures such as dams or retaining walls, as well as rock structures such as tunnels, caverns, excavations, and rock slopes, have commonly been designed by elastic-perfectly plastic analysis in which the tensile yield strength of the material is taken as zero. The paper analyzes the safety of this "no­ tension" design in the light of the finiteness of the tensile strength of concrete or the tensile strength of rock between the joints. Through examples, it is demonstrated that: (1) the calculated length of cracks or cracking zones can correspond to an unstable state; (2) the uncracked ligament of the cross section, available for resisting horizontal shear loads, can be predicted much too large, compared to the fracture mechanics pre­ diction; (3) the calculated load-deflection diagram can lie lower than that obtained by fracture mechanics; (4) the no-tension load capacity for a combination of crack face pressure and loads remote from the crack front, calculated by elastic analysis on the basis of allowable compressive stress, can be higher than that obtained by fracture mechanics; and (5) an increase in the tensile strength of the material can cause the load capacity of the structure to decrease. Due to the size effect, these facts are true not only for zero fracture toughness (no-toughness design) but also for finite fracture toughness provided that the structure size is large enough. Several previous studies on the safety of no-tension design, including the finite-element analysis of a gravity dam, are also reviewed. It is concluded that if the no-tension limit design is used, the safety factors of concrete or rock structures cannot be guaranteed to have the specified values. Fracture mechanics is required for that.

Softening-Induced Dynamic Localization Instability: Seismic Damage in Frames

Abstract: This paper analyzes dynamic localization of damage in structures with softening inelastic hinges and studies implications for the seismic response of reinforced concrete or steel frames of buildings or bridges. First, the theory of limit points and bifurcation of the symmetric equilibrium path due to localization of softening damage is reviewed. It is proven that, near the state of static bifurcation or near the static limit point, the primary (symmetric) path of dynamic response or periodic response temporarily develops Liapunov-type dynamic instability such that imperfections representing deviations from the primary path grow exponentially or linearly while damage in the frame localizes into fewer softening hinges. The implication for seismic loading is that the kinetic energy of the structure must be absorbed by fewer hinges, which means faster collapse. The dynamic localizations are demonstrated by exact analytical solutions of torsional rotation of the floor of a symmetric and symmetrically excited frame, and of horizontal shear excitation of a building column. Static bifurcations with localization are also demonstrated for a portal frame, a multibay frame, and a multibay-multistory frame. The widely used simplification of a structure as a single-degree-of-freedom oscillator becomes invalid after the static bifurcation state is passed.

Modelling and Materials Science of Cement-Based Materials

Abstract: The second part of this review covers recent developments in modelling related to the materials science of cements. The specific goal is to formulate constitutive models based on the microstructure. Problems with simple numeric representation of the microstructure and scaling are discussed. Several new models are reviewed with a view towards defining the microstructure in terms that can be related directly to complex properties such as permeability, creep and shrinkage, and fracture of large-scale structures. Relationships to current constitutive models are discussed.

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

Comment on Hyperbolicity of Wave Problem for Valanis’ Global Damage Theory

Abstract: In a very interesting and stimulating recent paper, Valanis (199l) proposed a new type of nonlocal damage theory, called the global damage theory. Some conclusions of this paper, however, require further analysis, which is the purpose of this technical note. Offering as motivation some questionable and unfounded critical comments on the nonlocal damage theory originally proposed by Pijaudier-Cabot and Baiant (1987) and Baiant and Pijaudier-Cabot ( 1988), Valanis formulated a different theory and cltrimed it to be superior because, as he stated, it exhibits unconditional hyperbolicity of the wave problem. On closer scrutiny, though, Valanis' claim is found to be invalid, and for further development of nonlocal damage models it is important to understand why.