Download Continuous and Discontinuous Modelling of Fracture in by Jacek Tejchman, Jerzy Bobiński PDF

By Jacek Tejchman, Jerzy Bobiński

The booklet analyzes a quasi-static fracture technique in concrete and bolstered concrete through constitutive versions formulated inside of continuum mechanics. a continuing and discontinuous modelling procedure was once used. utilizing a continual process, numerical analyses have been played utilizing a finite point technique and 4 assorted better continuum types: isotropic elasto-plastic, isotropic harm and anisotropic smeared crack one. The types have been outfitted with a attribute size of micro-structure via a non-local and a second-gradient concept. so that they may perhaps safely describe the formation of localized zones with a definite thickness and spacing and a comparable deterministic dimension impression. utilizing a discontinuous FE strategy, numerical result of cracks utilizing a cohesive crack version and XFEM have been offered that have been additionally correctly regularized. Finite aspect analyses have been played with concrete parts less than monotonic uniaxial compression, uniaxial rigidity, bending and shear-extension. Concrete beams less than cyclic loading have been additionally simulated utilizing a coupled elasto-plastic-damage technique. Numerical simulations have been played at macro- and meso-level of concrete. A stochastic and deterministic dimension impression was once rigorously investigated. in relation 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 clinical literature laboratory and full-scale tests.

Show description

Read Online or Download Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM PDF

Best intelligence & semantics books

Constraint Reasoning for Differential Models

Evaluating the key good points of biophysical inadequacy was once similar with the illustration of differential equations. procedure dynamics is frequently modeled with the expressive strength of the present period constraints framework. it truly is transparent that crucial version was once via differential equations yet there has been no approach of expressing a differential equation as a constraint and combine it in the constraints framework.

Soft Methods for Integrated Uncertainty Modelling (Advances in Soft Computing)

This edited quantity is the complaints of the 2006 foreign convention on delicate equipment in likelihood and facts (SMPS 2006) hosted by way of the unreal Intelligence workforce on the college of Bristol, among 5-7 September 2006. this is often the 3rd of a chain of biennial meetings prepared in 2002 by means of the structures learn Institute from the Polish Academy of Sciences in Warsaw, and in 2004 via the dep. of records and Operational study on the college of Oviedo in Spain.

Theory of Fuzzy Computation

The ebook presents the 1st complete size exploration of fuzzy computability. It describes the idea of fuzziness and current the basis of computability thought. It then offers some of the ways to fuzzy computability. this article presents a glimpse into different methods during this sector, that is very important for researchers so as to have a transparent view of the sphere.

Degradations and Instabilities in Geomaterials

This publication provides the main recents advancements within the modelling of degradations (of thermo-chemo-mechanical foundation) and of bifurcations and instabilities (leading to localized or diffuse failure modes) occurring in geomaterials (soils, rocks, concrete). functions (landslides, rockfalls, particles flows, concrete and rock growing older, and so on.

Additional info for Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM

Sample text

2002), Huerta et al. (2003) and Jirásek (2004a). e. material brittleness. The material softening starts when the when the equivalent strain measure reaches the initial threshold κ0 (material hardening is neglected). The parameter β determines the rate of the damage growth (larger value of β causes a faster damage growth). In one dimensional problems, for ε → ∞ (uniaxial tension), the stress approaches the value of (1 − α )Eκ 0 (Fig. 4b). 1 Local Models for Monotonic Loading 57 The constitutive isotropic damage model for concrete requires the following 5 material constants: E, υ, κ0, α and β (Eq.

30) where ψ is the dilatancy angle (ψ≠φ). The increments of plastic strains dε ij were p calculated as d ε ijp = d κ1 ∂g1 d κ1 ∂q ∂p = + tanψ ( ). 31) b) Fig. 1 Drucker-Prager criterion in the space of principal stresses (a) and on the plane q-p (b) In turn, in the tensile regime, a Rankine criterion was used with the yield function f2 using isotropic hardening and softening defined as (Bobiński 2006, Marzec et al. 2007, Majewski et al. 2008) (Fig. 32) where σi – principal stresses, σt – tensile yield stress and κ2 – softening parameter (equal to the maximum principal plastic strain ε1p ).

The total strains ε ij were decomposed into the elastic ε ije and inelastic crack strains ε ijcr ε ij = ε ije + ε ijcr . 53) Between the concrete stresses and cracked strains, the following relationship was valid (in a local coordinate system) cr cr σ ij = Cijkl ε kl cr with the secant cracked stiffness matrix Cijkl (defined only for open cracks). Fig. 1 Local Models for Monotonic Loading 61 Fig. 6 Relationships between normal crack stress versus normal crack strain in softening range during loading, unloading and reloading (de Borst 1986) cr The matrix Cijkl was assumed to be diagonal.

Download PDF sample

Rated 4.63 of 5 – based on 42 votes