Jerzy Bobiński

Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM

The book analyzes a quasi-static fracture process in concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, numerical analyses were performed using a finite element method and four different enhanced continuum models: isotropic elasto-plastic, isotropic damage and anisotropic smeared crack one. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory. So they could properly describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. Using a discontinuous FE approach, numerical results of cracks using a cohesive crack model and XFEM were presented which were also properly regularized. Finite element analyses were performed with concrete elements under monotonic uniaxial compression, uniaxial tension, bending and shear-extension. Concrete beams under cyclic loading were also simulated using a coupled elasto-plastic-damage approach. Numerical simulations were performed at macro- and meso-level of concrete. A stochastic and deterministic size effect was carefully investigated. In the case of reinforced concrete specimens, FE calculations were carried out with bars, slender and short beams, columns, corbels and tanks. Tensile and shear failure mechanisms were studied. Numerical results were compared with results from corresponding own and known in the scientific literature laboratory and full-scale tests.

Mesoscopic Modelling of Strain Localization in Plain Concrete

The Chapter deals with modelling of strain localization in concrete at meso-scale. Concrete was considered as a composite material by distinguishing three phases: cement matrix, aggregate and interfacial transition zones. For FE calculations, an isotropic damage model with non-local softening was used. The simulations were carried out with concrete specimens under uniaxial tension and bending. The effect of aggregate density, aggregate size, aggregate distribution, aggregate shape, aggregate stiffness, aggregate size distribution, characteristic length and specimen size was investigated. The representative volume element was also determined.

Simulations of Shear Zones and Cracks in Engineering Materials Using eXtended Finite Element Method

Numerical simulations of cracks and shear zones in quasi-brittle materials are presented. Extended Finite Element Method is used to describe both cracks and shear zones. In a description of tensile cracks, a Rankine criterion is assumed. A discrete Mohr-Coulomb law is adopted for simulations of shear zones. Results of simple numerical tests: uniaxial tension, bending and biaxial compression are demonstrated.

A constitutive law with improved continuous-discontinuous description of fracture in concrete

Paper presents an improved version of the constitutive model which combines a continuous and discontinuous crack’s description to simulate the concrete under tensile dominated loads. In a continuum regime, a plasticity model with a Rankine failure criterion and an associated flow rule was used. To describe the width of strain localization and to obtain mesh-independent results, the continuum constitutive law was equipped with a characteristic length of micro-structure by applying a non-local theory in an integral format. For describing displacement jumps along/across cracks, the eXtended Finite Element Method (XFEM) was used. A transition algorithm between a non-local continuum model and XFEM was formulated. A transfer function was introduced to enable a gradual switch from a continuous (smeared) to discontinuous (discrete) softening process. Several benchmarks were numerically simulated with a dominated mode-I (e.g. uniaxial tension and bending) and under mixed-mode conditions.

Concrete and Reinforced Concrete Behaviour

This chapter describes briefly the most important mechanical properties of concrete, reinforcement and reinforced concrete elements in a static and dynamic regime. In addition, bond-slip between reinforcement and concrete is discussed. Attention is laid on a size effect in concrete and reinforced concrete elements.

Continuous and Discontinuous Modelling of Fracture in Plain Concrete under Monotonic Loading

This Chapter presents the FE results of continuous and discontinuous modelling of fracture in plain concrete under monotonic loading. Tests of uniaxial compression, uniaxial extension, bending and shear –extension were simulated.

Continuous Approach to Concrete

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.

Deterministic and Statistical Size Effect in Plain Concrete

The numerical FE investigations of a deterministic and stochastic size effect in concrete beams of a similar geometry under three point bending were performed within an elasto-plasticity with a non-local softening. The FE analyses were carried out with four different sizes of notched and unnotched beams. Deterministic calculations were performed with a uniform distribution of the tensile strength. In turn, in stochastic calculations, the tensile strength took the form of random correlated spatial fields described by a truncated Gaussian distribution. In order to reduce the number of stochastic realizations without losing the calculation accuracy, Latin hypercube sampling was applied. The numerical outcomes were compared with the size effect law by Bažant and by Carpinteri.

Continuous Modelling of Fracture in Plain Concrete under Cyclic Loading

The enhanced coupled elasto-plastic damage models with non-local softening proposed by Pamin and de Borst (1999) (called model ‘1’), by Carol et al. (2001) and by Hansen and Willam (2001) (called model ‘2’), by Meschke et al. (1998) (called model ‘3’) and Marzec and Tejchman (2009, 2010, 2011) (called model ‘4’) described in detail in Chapter 3.2 were used in FE calculations. Quasistatic FE results were compared with corresponding laboratory tests on concrete specimens: dog-bone shaped specimen under monotonic uniaxial tension (van Vliet and van Mier 2000) and notched beams under cyclic loading (Hordijk 1991, Perdikaris and Romeo 1995).

Final Conclusions and Future Research Directions

The book analyzes quasi-static fracture in plain concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, analyses were performed using a finite element method and four different continuum concrete models: enhanced isotropic elasto-plastic, enhanced isotropic damage, enhanced anisotropic smeared crack and enhanced coupled elasto-plastic-damage model. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory, so they could describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. FE results converged to a finite size of localized zones via mesh refinement. In addition, numerical results of cracks in plain concrete using a discontinuous approach including cohesive (interface) elements and XFEM were presented which were also properly regularized. Numerical results were compared with corresponding laboratory tests from the scientific literature and own tests.