Showing papers by "Zdenek P. Bazant published in 1983"
TL;DR: In this article, it is shown that orthotropic models do not satisfy the form-invariance condition for initially isotropic solids, i.e., the condition that the response predicted by the model must be the same for any choice of coordinate axes in the initial stress-free state.
Abstract: Incrementally linear constitutive equations that are characterized by an orthotropic tangential stiffness or compliance matrix have recently become widely used in finite element analysis of concrete structures and soils. It does not seem to be, however, widely appreciated that such constitutive equations are limited to loading histories in which the prinicipal stress directions do not rotate, and that a violation of this condition can sometimes have serious consequences. It is demonstrated that in such a case the orthotropic models do not satisfy the form‐invariance condition for initially isotropic solids, i.e., the condition that the response predicted by the model must be the same for any choice of coordinate axes in the initial stress‐free state. An example shows that the results obtained for various such choices can be rather different. The problem cannot be avoided by rotating the axes of orthotropy during the loading process so as to keep them parallel to the principal stress axes, first, because t...
102 citations
01 May 1983
TL;DR: In this article, a triaxial stress-strain relation is proposed to describe gradual strain-softening with reduction of tensile stress to zero, which is applicable under general loading, including rotating principal stress directions.
Abstract: : Dynamic fracture analysis of concrete structures necessitates a triaxial stress-strain relation that describes gradual strain-softening with reduction of tensile stress to zero. A new model which does that and is applicable under general loading, including rotating principal stress directions, is a proposed. It is based on accumulating stress relaxations due to microcracking from the planes of all orientation within the microstructure. Comparisons with tensile test data are given.
71 citations
TL;DR: In this article, the spacing and width of cracks in a parallel crack system were analyzed using the energy criterion of fracture mechanics as well as the strength criterion, and the results indicated satisfactory agreement with existing test data, and lend theoretical support to one aspect of the empirical Gergely-Lutz formula obtained by statistical regression analysis of test data.
Abstract: The spacing and width of cracks in a parallel crack system is approximately analyzed using the energy criterion of fracture mechanics as well as the strength criterion. The energy criterion indicates that the crack spacing is a function of the axial strain of the bars and also depends on bar spacing, bar diameter, fracture energy of concrete, and its elastic modulus. Both the energy and strength criteria yield a minimum strain necessary to produce any cracks. The energy criterion and the bond slip conditions further yield a lower bound on possible spacing of continuous cracks. The rules for the formation of shorter, partial length, cracks are also set up. Approximate expressions for the crack width at, and away, from the bars are derived. Numerical comparisons indicate satisfactory agreement with existing test data, and lend theoretical support to one aspect of the empirical Gergely-Lutz formula obtained by statistical regression analysis of test data. Finally, formation of skew cracks in a biaxially stressed and biaxially reinforced plate is analyzed and a crack spacing formula is derived for one typical case.
66 citations
TL;DR: In this article, a uniaxial constitutive equation describing the deviations from the linear principle of superposition of aging concrete at constant moisture content and temperature is presented, where both the creep increase (flow) at high stress and the stiffening (adaptation) due to low sustained compressive stress are modeled.
Abstract: A uniaxial constitutive equation describing the deviations from the linear principle of superposition of aging concrete at constant moisture content and temperature is presented. Both the creep increase (flow) at high stress and the stiffening (adaptation) due to low sustained compressive stress are modeled, the latter being of principal interest. The constitutive equation expresses the creep rate as a history integral with a singular kernel involving the time lag of creep strain. The integral has the property that the strain response is proportional to the stress history but depends nonlinearly on the stress history when nonproportional stress histories are superposed. The double power law for aging creep is a special limiting case. The constitutive relation is also explained in terms of the rate-process (activation energy) theory for the rate of bond ruptures causing creep. For structural creep problems, a corresponding step-by-step integration algorithm which correctly captures the asymptotic properties of the integral is also developed. A good agreement with test data from the literature is achieved.
15 citations
TL;DR: In this paper, a simplified theory for predicting the spacing of cracks in a parallel crack system in reinforced concrete was presented, based on the formulas for the stress caused by a concentrated force in a halfspace.
Abstract: In a companion paper by Bazant and Oh, a simplified theory for predicting the spacing of cracks in a parallel crack system in reinforced concrete was presented. In this paper a different approximate analysis yields about the same result. For this purpose, a solution based on the formulas for the stress caused by a concentrated force in a halfspace is used.
7 citations