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.

Softening Instability: Part II—Localization Into Ellipsoidal Regions

Abstract: Extending the preceding study of exact solutions for finite-size strain-softening regions in layers and infinite space, exact solution of localization instability is ob­ tained for the localization of strain into an ellipsoidal region in an infinite solid. The solution exploits Eshelby's theorem for eigenstrains in elliptical inclusions in an in­ finite elastic solid. The special cases of localization of strain into a spherical region in three dimensions and into a circular region in two dimensions are further solved for finite solids-spheres in 3D and circles in 2D. The solutions show that even if the body is infinite the localization into finite regions of such shapes cannot take place at the start of strain-softening (a state corresponding to the peak of the stress-strain diagram) but at a finite strain-softening slope. If the size of the body relative to the size of the softening region is decreased and the boundary is restrained, homogeneous strain-softening remains stable into a larger strain. The results also can be used as checks for finite element programs for strain-softening. The present solutions determine only stability of equilibration states but not bifurcations of the equilibrium path.

Fracture and Damage in Quasibrittle Structures: Experiment, modeling and computation

Abstract: Understanding of failure of quasibrittle materials is of paramount importance in many engineering fields. This subject has become a broad and important field of considerable mathematical complexity, with many competing models and unsolved problems. Attention in this volume focuses on concrete, rock, masonry, toughened ceramics, ice and other quasib

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.