By Jacek Tejchman, Jerzy Bobiński
The e-book analyzes a quasi-static fracture strategy in concrete and bolstered concrete by way of constitutive versions formulated inside continuum mechanics. a continual and discontinuous modelling process was once used. utilizing a continual process, numerical analyses have been played utilizing a finite aspect approach and 4 diversified stronger continuum versions: isotropic elasto-plastic, isotropic harm and anisotropic smeared crack one. The types have been built with a attribute size of micro-structure by way of a non-local and a second-gradient conception. so that they may accurately describe the formation of localized zones with a undeniable thickness and spacing and a similar deterministic dimension impact. utilizing a discontinuous FE method, numerical result of cracks utilizing a cohesive crack version and XFEM have been provided which have been additionally accurately regularized. Finite point analyses have been played with concrete parts below monotonic uniaxial compression, uniaxial stress, bending and shear-extension. Concrete beams below 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 dimension influence used to be conscientiously investigated. when it comes to bolstered concrete specimens, FE calculations have been performed with bars, slim 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 identified within the medical literature laboratory and full-scale tests.
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Extra resources for Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM
34 Three point bend testing of notched beams: experimental results of vertical force versus deflection u for small- (a), medium- (b) and large-size beam (c) (Le Bellego et al. 2003) 2 Concrete and Reinforced Concrete Behaviour 29 Fig. 35 Experimental results of size effect in three-point bending tests (points – experimental results, line – size effect law by Bažant (Bažant and Planas 1998), D – specimen size, Do – characteristic size, B – parameter, ft – tensile strength) (Le Bellego et al. 2003) The beams under the constant bending moment failed by crushing of a compression zone around the peak load.
25) I1ε δ ij . 26) sij = σ ij − eij = ε ij − To describe the behaviour of concrete, a simplified elasto-plastic model was assumed. In the compression regime, a shear yield surface based on a linear Drucker-Prager criterion and isotropic hardening and softening was used (Bobiński 2006, Marzec et al. 2007, Majewski et al. 2008) (Fig. 1) 1 f1 = q + p tan ϕ − (1 − tan ϕ )σ c (κ 1 ) . 27) where q - Mises equivalent deviatioric stress, p – mean stress and ϕ – internal friction angle. The material hardening/softening was defined by the uniaxial compression stress σc(κ1), wherein κ1 is the hardening/softening parameter corresponding to the plastic vertical normal strain during uniaxial compression.