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

Based on the premise that large-scale failure of sea ice is governed by fracture mechanics, recently validated by Dempsey's in situ tests of fracture specimens of a record-breaking size, this two-part study applies fracture mechanics and asymptotic approach to obtain approximate explicit formulas for the size effect in two fundamental problems. In the present Part I, the load capacity of a floating ice plate subjected to vertical load is determined, and in Part II, which follows, the horizontal force exerted by an ice plate moving against a fixed structure is analyzed in a similar manner. The resulting formulas for vertical loading agree with previous sophisticated numerical fracture simulations as well with the limited field tests of vertical penetration that exist. The results contrast with the classical predictions of material strength or plasticity theories, which in general exhibit no size effect on the nominal strength of the structure. ©2002 ASME

/pdf/scaling-of-sea-ice-fracture-part-i-vertical-penetration-5bn6g4aq8q.pdf

Scaling of Sea Ice Fracture—Part I: Vertical Penetration

M<>d< 11/ (o.,;pw,.) .~..,.\",.''''' \"''''~ oj <OftVtIt -..I-.no. -. --.\"\" \"\" I~ _ 0/,10< ri,..qj..\" ., .. , 1M 'P«\"\"\"\" .,'\". <,II. <W. ~ilh . <i'<~m/\"MI\"I \"O,,1t ., 1M;, \",M,.\"\", • • \"b,lmd 10 IN\" '0\"\",\" ., .... \" OXHl! fIN<'<, n.'~I ...... ' ....,. ,,,,,,,,,,ie.u, ,1.,11., \".<1 110m >lUI • • riM •• 1:1:', TIl. 1tK><., \"\"\"'''''., \"\"\" -.w.d Nt ~ /0 • _ .,,\"10 \"\"\"'I< 1_\"\", __ _/~\" did ,i« _~ st>«_ 1M _ oj _ III «> UO« / (I_I /\",<1\"\" ~ _ J_ '\" I>t _, J \"\" __ ..... Mil ...... r'/O< _ . 1M ~ _tty _,\"\"'. _ ... u\"\"\",,,,,, oj '''' _ '''''''''''P''K'D ,_ -..I>t • *. .If ..... ' m«M.i>no <n>iII, \",,,,n,,,, \"\"'~. ,,_ \"\"'\"\" ,.,1\"._ ,\",\"\" TIot ,;,<-#/\"\" '\" .... ~\"...\"\" .~\" P<iJ • • \"lfm.\" of 'M .i\" oj ,., j'OC'\"\"'PftXW , ..... ~''' it\"\" jO<,\"G '. I>t \"\"' '', ,It, stirn, '\" I\"' Mod< I !\"\"\"u\", \"\"-........ ,\"\"\"-.. \", .. ' --, .... --:_\"'-\"\"'\" -.... ~ , ... \"'_--.

Antiplane Shear Fracture Tests (Mode III)

Based on a mathematical model developed in the preceding Part I of this study, a numerical analysis of the process of decontamination of radionuclides from concrete by microwave heating is conducted. The aim is to determine the required microwave power and predict whether and when the contaminated surface layer of concrete spalls off. As customary, the finite element method is used for the stress and fracture analysis. However, as a departure from previous studies, the finite volume method is adopted to treat the heat and moisture transfer, in order to prevent spurious numerical oscillations that plagued the finite element response at moving sharp interface between the saturated and unsaturated concrete, and to deal accurately with the jumps in permeability and in sorption isotherm slope across the interface. The effects of wall thickness, reinforcing bars, microwave frequency, and power are studied numerically. As a byproduct of this analysis, the mechanism of spalling of rapidly heated concrete is clarified.

/pdf/decontamination-of-radionuclides-from-concrete-by-microwave-43kmkxwasp.pdf

Decontamination of Radionuclides from Concrete by Microwave Heating. II: Computations

Propagation of a crack from the tensile face of a beam causes postpeak softening, i.e., the bending moment decreases at increasing rotation of the hinge. Examples are unreinforced concrete beams and plates, foundations plinths, retaining walls, tunnel linings, or arch dams. Softening in an inelastic hinge is also caused by compression crushing of concrete. This happens in reinforced concrete beams that are prestressed, overreinforced, retrofitted by laminates, or subjected to a large enough axial compressive force, which is typical of columns as well as frames or arches with a large enough horizontal thrust. Hinge softening may also be caused by plastic buckling of flanges in deep thin-wall steel beams. An inevitable consequence of inelastic hinge softening in statically indeterminate structures requiring more than one inelastic hinge to fail is a size effect. Although finite element solutions are possible, general analytical formulas for the size effect in such structures do not exist, because of the complexity of response. The idea of this two-part paper is to exploit the technique of asymptotic matching in order to derive approximate formulas for the entire size range. Exact analytical solutions of the nominal strength of structure are derived for the large-size asymptotic case, for which the hinges soften one by one rather than simultaneously, and for the small-size asymptotic case, for which the classical plastic limit analysis applies. Matching these asymptotic solutions by a smooth formula then yields simple, yet general, size effect laws for the peaks and troughs of the load-deflection diagram through the entire size range. The size effect found is very different from the classical size effect in quasibrittle structures failing due to a single dominant crack. The theory is developed in the present Part I, and analysis of its implications is relegated to Part II.

/pdf/asymptotic-matching-analysis-of-scaling-of-structural-2y898oafe9.pdf

Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. I: Theory

The workshop of the above title took place in Paris, France where 36 invitees made presentations followed by extensive discussions. The themes covered at the workshop are discussed and are as as follows: observation and measurement of damage and localization; micromechanics of fracture and micro-macro relaionships; stability, bifurcation, and localization; nonlocal models, and localization limiters and size effect. Although it would not be possible formulate to conclusions acceptable to all, certain views appeared to reflect a broad consensus. In static, time-independent modeling of the tensile fracture of concrete and geomaterials, the structural size effect is widely regarded as the key macroscopic consequence of fracture, and the most important yardstick for the evaluation of various theories. It is noted that the knowledge of the effect of the loading rate due to viscoplastic behavior, and especially the general effect of load and deformation history is rather limited. These and other observations are discussed.

Zdenek P. Bazant

Papers

Scaling of Sea Ice Fracture—Part I: Vertical Penetration

Antiplane Shear Fracture Tests (Mode III)

Decontamination of Radionuclides from Concrete by Microwave Heating. II: Computations

Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. I: Theory

France‐U.S. Workshop on Strain Localization and Size Effect Due to Cracking and Damage