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...

/pdf/theoretical-stress-strain-model-for-confined-concrete-3eemamm28s.pdf

Theoretical stress strain model for confined concrete

http://mech.spbstu.ru/images/b/bd/Potyondy_Cundall_2004_A_bonded-particle_model_for_rock.pdf

A bonded-particle model for rock

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.

/pdf/crack-band-theory-for-fracture-of-concrete-4hm1hrkirl.pdf

Crack band theory for fracture of concrete

A plastic-damage model for concrete

National Institute of Standards and Technology における超伝導研究及び生活

The original publication is available at the publisher’s web site: http://link.springer.com/article/10.1617/s11527-014-0485-2/fulltext.html#copyrightInformation.
This article is accepted for publication, it is copyrighted by RILEM, and readers must contact RILEM for permission to reprint or use the material in any form.

/pdf/rilem-draft-recommendation-tc-242-mdc-multi-decade-creep-and-8hsmmgkmvy.pdf

RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis. Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability

The previously developed microprestress-solidification theory for concrete creep and shrinkage is generalized for the effect of temperature ~not exceeding 100°C!. The solidification model separates the viscoelasticity of the solid constituent, the cement gel, from the chemical aging of material caused by solidification of cement and characterized by the growth of volume fraction of hydration products. This permits considering the viscoelastic constituent as non-aging. The temperature dependence of the rates of creep and of volume growth is characterized by two transformed time variables based on the activation energies of hydration and creep. The concept of microprestress achieves a grand unification of theory in which the long-term aging and all transient hygrothermal effects simply become different consequences of one and the same physical phenomenon. The microprestress, which is independent of the applied load, is initially produced by incompatible volume changes in the microstructure during hydration, and later builds up when changes of moisture content and temperature create a thermodynamic imbalance between the chemical potentials of vapor and adsorbed water in the nanopores of cement gel. As recently shown, this simultaneously captures two basic effects: First, the creep decreases with increasing age at loading after the growth of the volume fraction of hydrated cement has ceased; and, second, the drying creep, i.e., the transient creep increases due to drying ~Pickett effect! which overpowers the effect of steady-state moisture content ~i.e., less moisture—less creep !. Now it is demonstrated that the microprestress buildup and relaxation also captures a third effect: The transitional thermal creep, i.e., the transient creep increase due to temperature change. For computations, an efficient ~exponential-type! integration algorithm is developed. Finite element simulations, in which the apparent creep due to microcracking is taken into account separately, are used to identify the consti- tutive parameters and a satisfactory agreement with typical test data is achieved.

/pdf/temperature-effect-on-concrete-creep-modeled-by-4ef71yd4w3.pdf

Temperature Effect on Concrete Creep Modeled by Microprestress-Solidification Theory

It is shown that the linear creep law of concrete can be characterized, with any desired accuracy, by a rate-type creep law that can be interpreted by a Maxwell chain model of time-variable viscosities and spring moduli. Identification of these parameters from the test data is accomplished by expanding into Direchlet series the relaxation curves, which in turn are computed from the measured creep curves. The identification has a unique solution if a certain smoothing condition is imposed upon the relaxation spectra. The formulation is useful for the step-by-step time integration of large finite element systems because it makes the storage of stress history unnecessary. For this purpose a new, unconditionally stable numerical algorithm is presented, allowing an arbitrary increase of the time step as the creep rate decays. The rate-type formulation permits establishing a correlation with the rate processes in the microstructure and thus opens the way toward rational generations to variable tempeature and water content. The previously developed Kelvin-type chain also permits such a correlation, but its identification from test data is more complicated.

Rate-type creep law of aging concrete based on maxwell chain

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

Zdenek P. Bazant

Papers

RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis. Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability

Temperature Effect on Concrete Creep Modeled by Microprestress-Solidification Theory

Rate-type creep law of aging concrete based on maxwell chain

Size Effect and Fracture Characteristics of Composite Laminates

Fracture Properties and Brittleness of High-Strength Concrete