By Jacek Tejchman, Jerzy Bobiński
The booklet analyzes a quasi-static fracture method in concrete and strengthened concrete by way of constitutive versions formulated inside of continuum mechanics. a continual and discontinuous modelling process was once used. utilizing a continual method, numerical analyses have been played utilizing a finite point strategy and 4 diversified more advantageous continuum types: isotropic elasto-plastic, isotropic harm and anisotropic smeared crack one. The versions have been built with a attribute size of micro-structure by way of a non-local and a second-gradient thought. in order that they may well effectively describe the formation of localized zones with a undeniable thickness and spacing and a similar deterministic measurement influence. utilizing a discontinuous FE procedure, numerical result of cracks utilizing a cohesive crack version and XFEM have been offered which have been additionally competently regularized. Finite point analyses have been played with concrete parts below monotonic uniaxial compression, uniaxial pressure, bending and shear-extension. Concrete beams less than cyclic loading have been additionally simulated utilizing a coupled elasto-plastic-damage process. Numerical simulations have been played at macro- and meso-level of concrete. A stochastic and deterministic measurement influence used to be conscientiously investigated. relating to strengthened concrete specimens, FE calculations have been conducted with bars, narrow and brief beams, columns, corbels and tanks. Tensile and shear failure mechanisms have been studied. Numerical effects have been in comparison with effects from corresponding personal and recognized within the medical literature laboratory and full-scale tests.
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Additional resources for Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM
This Chapter presents continuous models to describe concrete behaviour in a quasi-static regime during monotonic and cyclic loading. In the case of monotonic loading, isotropic elasto-plastic, isotropic damage and smeared crack model, and in the case of cyclic loading elasto-plastic-damage models are described. An integral-type non-local and a second gradient approaches to model strain localization are introduced. In addition, bond-slip laws are presented. : within non-linear elasticity (Palaniswamy and Shah 1974), linear fracture mechanics (Bažant and Cedolin 1979, Hilleborg 1985), endochronic theory (Bažant and Bhat 1976, Bažant and Shieh 1978), micro-plane theory (Bažant and Ožbolt 1990, Jirásek 1999), plasticity (Willam and Warnke 1975, Ottosen 1977, Hsieh et al.
If f=g, the flow rule is associated. 9) During plastic deformation, a stress state remains on the boundary of the elastic/plastic region f (σ ij + dσ ij , κ + d κ ) = 0 . 10 may be rewritten in a rate form as (similarly to Eq. 2) df df d σ ij + dκ = 0 . 11 are known as consistency conditions and allow to determine the magnitude of the plastic strain increment. 12) where H = −( ∂f ). 13) The proportionality factor dλ is equal to ∂f T e ) Cijkl d ε kl ∂σ ij dλ = . 14) The parameter ξ=1, if f=0 and κ>0, otherwise ξ=0.
Behaviour of concrete under biaxial stresses. : Calibration of nonlocal damage model from size effect tests. : Schubversuche an einfeldigen Stahlbetonbalken mit und ohne Schubbewehrung. Stb. : Grundlagen zur Bemessung im Stahlbetonbau. : Bond of reinforcement under controlled confinement. : Shapes of loading surfaces of concrete models and their influence on the peak load and failure mode in structural analyses. : Tensile tests and failure analysis of concrete. : Influence of cracking in the presence of free water on the mechanical behaviour of concrete.