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For corrosion-induced cracking in reinforced concrete, naturally occurring corrosion rates are so low that rust accumulates often over tens of years near the surface of the reinforcement bars before sufficient pressure in the surrounding concrete is generated to induce cracking in the concrete cover. To speed up the process, corrosion tests with impressed currents have been developed in which the corrosion rate is controlled to be so high that cracking of the concrete cover occurs within a few days. Extrapolating the results of these accelerated tests to those of naturally occurring corrosion requires an understanding of the influence of long-term creep deformations of concrete on the corrosion-induced cracking process. In mathematical models in the literature, creep deformations are often ignored for accelerated but considered for natural corrosion rates in the form of an effective modulus. Here, three numerical models of increasing complexity are proposed with the aim to investigate the effect of creep on corrosion-induced cracking. The simplest approach is based on an uncracked axis-symmetric thick-walled cylinder combined with a plastic limit on the radial pressure-induced by the accumulation of rust. The model with intermediate complexity comprises a thick-walled cylinder model divided into an inner cracked and an outer uncracked layer. The most comprehensive model consists of a thick-walled cylinder discretised by a three-dimensional lattice approach. Basic creep is predicted in all three approaches by means of the B3 model developed by Ba\v{z}ant and co-workers. Time dependence of strength of concrete is modelled using fib Model Code expressions. It is shown that for the comprehensive lattice model, creep has limited influence on critical corrosion penetration, which indicates that the dependence of the critical corrosion penetration on corrosion rate must have other sources.

Network modelling of water retention and conductivity of porous geomaterials based on filling and emptying of pores requires the use of a computational cell which is a representative volume element of the material. The conditions for the existence of a representative volume element are that with increasing cell size the statistical results of multiple random cells approach a constant mean and zero coefficient of variation of the macroscopic property. In this study, random network analyses were carried out to determine the mean and coefficient of variation of degree of saturation and conductivity for varying capillary suction and cell size. For water retention, a representative volume element was obtained for the entire range of capillary suction investigated. For conductivity, a representative volume element was obtained for most of the range of capillary suction, but there is a small range of capillary suction for which the coefficient of variation does not reduce with increasing size of the computational cell, due to onset and termination of percolation of the wetting fluid (during wetting and drying, respectively).

The initiation of fluid-induced fracture in formations of permeable geomaterials subjected to quasi-stationary flow processes (drained response) can be strongly affected by Biot's coefficient and the size of the formation. The aim of this paper is to analyse the influence of these parameters on the initial fracture process of a thick-walled hollow permeable sphere subjected to fluid injection in the hole. Assuming that fracture patterns are distributed uniformly during the hardening stage of the fracture initiation process, the coupled fluid-solid problem is described by a nonlinear ordinary differential equation, which is solved numerically by means of finite differences combined with shooting and Newton methods. The finite difference code has also been validated in the elastic range, i.e., before initiation of fracture, against an original closed-form analytical solution of the above differential equation. The results show that the nominal strength of the sphere increases with increasing Biot's coefficient and decreases with increasing size.

The width of fracture process zones in geomaterials is commonly assumed to depend on the type of heterogeneity of the material. Still, very few techniques exist, which link the type of heterogeneity to the width of the fracture process zone. Here, fracture processes in geomaterials are numerically investigated with structural network approaches, whereby the heterogeneity in the form of large aggregates and low volume fibres is modelled geometrically as poly-dispersed ellipsoids and mono-dispersed line segments, respectively. The influence of aggregates, fibres and combinations of both on fracture processes in direct tensile tests of periodic cells is investigated. For all studied heterogeneities, the fracture process zone localises at the start of the softening regime into a rough fracture. For aggregates, the width of the fracture process zone is greater than for analyses without aggregates. Fibres also increase the initial width of the fracture process zone and, in addition, result in a widening of this zone due to fibre pull out.

Differential shrinkage in particulate quasi-brittle materials causes microcracking which reduces durability in these materials by increasing their mass transport properties. A hydro-mechanical three-dimensional periodic network approach was used to investigate the influence of particle and specimen size on the specimen permeability. The particulate quasi-brittle materials studied here consist of stiff elastic particles, and a softer matrix and interfacial transition zones between matrix and particles exhibiting nonlinear material responses. An incrementally applied uniform eigenstrain, along with a damage-plasticity constitutive model, are used to describe the shrinkage and cracking processes of the matrix and interfacial transition zones. The results showed that increasing particle diameter at constant volume fraction increases the crack widths and, therefore, permeability, which confirms previously obtained 2D modelling results. Furthermore, it was demonstrated that specimen thickness has, in comparison to the influence of particle size, a small influence on permeability increase due to microcracking.

Dual three-dimensional networks of structural and transport elements were combined to model the effect of fracture on mass transport in quasi-brittle geomaterials. Element connectivity of the structural network, representing elasticity and fracture, was defined by the Delaunay tessellation of a random set of points. The connectivity of transport elements within the transport network was defined by the Voronoi tessellation of the same set of points. A new discretisation strategy for domain boundaries was developed to apply boundary conditions for the coupled analyses. The properties of transport elements were chosen to evolve with the crack opening values of neighbouring structural elements. Through benchmark comparisons involving non-stationary transport and fracture, the proposed dual network approach was shown to be objective with respect to element size and orientation.

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biot's coefficient.

Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress-strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated by fitting load-displacement curves and dissipated energy profiles for direct tension to the results of mesoscale analyses performed using a discrete model. These analyses are set up so that the results are independent of boundaries. Then, the models are applied to two-dimensional simulations of three-point bending tests with a sharp notch, a V-type notch, and a smooth boundary without a notch. The performance of the nonlocal approaches in modelling of fracture near nonconvex boundaries is evaluated by comparison of load-displacement curves and dissipated energy profiles along the beam ligament with the results of meso-scale simulations. As an alternative approach, elastoplasticity combined with nonlocal or over-nonlocal damage is also included in the comparative study.

A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse the failure of concrete structures. The aim is to obtain a model, which describes the important characteristics of the failure process of concrete subjected to multiaxial loading. This is achieved by combining an effective stress based plasticity model with a damage model based on plastic and elastic strain measures. The model response in tension, uni-, bi- and triaxial compression is compared to experimental results. The model describes well the increase in strength and displacement capacity for increasing confinement levels. Furthermore, the model is applied to the structural analyses of tensile and compressive failure., Comment: arXiv admin note: text overlap with arXiv:1103.1288

The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is determined numerically by evaluating the average of spatial distribution of dissipated energy densities of random meso-scale analyses. The influence of size and boundary conditions on the fracture process zone in concrete is investigated by comparing the results for beams of different sizes and boundary conditions.

A lattice approach is used to describe the mechanical interaction of a corroding reinforcement bar, the surrounding concrete and the interface between steel reinforcement and concrete. The cross-section of the ribbed reinforcement bar is taken to be circular, assuming that the interaction of the ribs of the deformed reinforcement bar and the surrounding concrete can be captured by a cap-plasticity interface model. The expansive corrosion process is represented by an Eigenstrain in the lattice elements forming the interface between concrete and reinforcement. Several pull-out tests with varying degree of corrosion are analysed. The numerical results are compared with experiments reported in the literature. The influence of the properties of concrete are studied. The proposed lattice approach offers insight into corrosion induced cracking and its influence on bond strength., Comment: Submitted to Cement and Concrete Composites

A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse concrete structures subjected to dynamic loading. The aim is to obtain a model, which requires input parameters with clear physical meanings. The model should describe the important characteristics of concrete subjected to multiaxial and rate-depending loading. This is achieved by combining an effective stress based plasticity model with an isotropic damage model based on plastic and elastic strain measures. The model response in tension, uni-, bi- and tri-axial compression is compared to experimental results in the literature., Comment: Preprint. Submitted to Eurodyn 2011, 8th International Conference on Structural Dynamics, Leuven, Belgium, 2011

The present work involves the discrete modelling of corrosion induced cracking and its influence on the bond between reinforcement and concrete. A lattice approach is used to describe the mechanical interaction of a corroding reinforcement bar, the surrounding concrete and the interface between steel reinforcement and concrete. The cross-section of the ribbed reinforcement bar is taken to be circular, assuming that the interaction of the ribs of the deformed reinforcement bar and the surrounding concrete is included in a cap-plasticity interface model. The expansion of the corrosion product is represented by an eigenstrain in the lattice elements forming the interface. The lattice modelling approach is applied to the analysis of corrosion induced cracking and its influence of the bond strength. The model capabilities are assessed by comparing results of analyses with those from unconfined pull-out tests reported in the literature. Future work will investigate the influence of the stiffness of interface elements and the effect of lateral confinement on corrosion induced cracking., Comment: Preprint of conference paper for Fracture Mechanics of Concrete and Concrete Structures, South Korea, 2010

Concrete subjected to combined compressive stresses and temperature loading exhibits compressive strains, which are considerably greater than for concrete subjected to compressive stresses alone. This phenomenon is called transient thermal creep or load induced thermal strain and is usually modeled by macroscopic phenomenological constitutive laws which have only limited predictive capabilities. In the present study a meso-scale modeling approach is proposed in which the macroscopically observed transient thermal creep results from the mismatch of thermal expansions of the meso-scale constituents. The meso-structure of concrete is idealized as a two-dimensional three phase material consisting of aggregates, matrix and interfacial transition zones (ITZ). The nonlinear material response of the phases are described by a damage-plasticity interface model. The meso-scale approach was applied to analyze compressed concrete specimens subjected to uniform temperature histories and the analysis results were compared to experimental results reported in the literature., Comment: Accepted in Journal of Engineering Mechanics - ASCE

In this paper, the influence of aggregate size and volume fraction on shrinkage induced micro-cracking and permeability of concrete and mortar was investigated. Nonlinear finite element analyses of model concrete and mortar specimens were performed. The aggregate diameter was varied between 2 and 16 mm. Furthermore, a range of volume fractions between 0.1 and 0.5 was studied. The nonlinear analyses were based on a 2D lattice approach in which aggregates were simplified as monosized cylindrical inclusions. The analysis results were interpreted by means of crack width and change of permeability. The results show that increasing aggregate diameter (at equal volume fraction) and decreasing volume fraction (at equal aggregate diameter) greatly increases permeability., Comment: 12th International Conference on Fracture (ICF 12)

Microbond tests composed of single fibre and matrix droplet are often used to determine the properties of fibre reinforced composites. Interfacial shear strength is quantified by the maximum pull-out force assuming a uniform stress distribution along the fibre. Here, nonlinear finite element analyses are performed to investigate the validity of this assumption., Comment: Submitted to 17th international conference on composite materials (ICCM-17)

A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is approximated by an analysis of a two-dimensional cell with periodic boundary conditions. The spatial distribution of dissipated energy density at the meso-scale of concrete is determined. The size and shape of the deterministic FPZ is obtained as the average of random meso-scale analyses. Additionally, periodicity of the discretisation is prescribed to avoid influences of the boundaries of the periodic cell on fracture patterns. The results of these analyses are then used to calibrate an integral-type nonlocal model., Comment: Submitted to International Journal of Solids and Structures, January 29, 2009

A damage-plasticity constitutive model for the description of fracture in plain concrete is presented. Two approaches, the local model comprising the adjustment of the softening modulus and the nonlocal model based on spatial averaging of history variables, are applied to the analysis of a concrete bar subjected to uniaxial tension and to a three-point bending test. The influence of mesh size and the decomposition into damage and plasticity components are discussed. It is shown that for the two examples studied, both approaches result in mesh-independent results. However, the nonlocal model, which relies on spatial averaging of history variables, exhibits sensitivity with respect to boundary conditions, which requires further studies., Comment: Revised version. Resubmitted to Engineering and Computational Mechanics

The present parametric study deals with the meso-scale modelling of concrete subjected to cyclic compression, which exhibits hysteresis loops during unloading and reloading. Concrete is idealised as a two-dimensional three-phase composite made of aggregates, mortar and interfacial transition zones (ITZs). The meso-scale modelling approach relies on the hypothesis that the hysteresis loops are caused by localised permanent displacements, which result in nonlinear fracture processes during unloading and reloading. A parametric study is carried out to investigate how aggregate density and size, amount of permanent displacements in the ITZ and the mortar, and the ITZ strength influence the hysteresis loops obtained with the meso-scale modelling approach.

In this paper, the influence of aggregate size and volume fraction on shrinkage induced micro-cracking and permeability of concrete and mortar was investigated. Nonlinear finite element analyses of model concrete and mortar specimens with regular and random aggregate arrangements were performed. The aggregate diameter was varied between 2 and 16 mm. Furthermore, a range of volume fractions between 0.1 and 0.5 was studied. The nonlinear analyses were based on a 2D lattice approach in which aggregates were simplified as monosized cylindrical inclusions. The analysis results were interpreted by means of crack length, crack width and change of permeability. The results show that increasing aggregate diameter (at equal volume fraction) and decreasing volume fraction (at equal aggregate diameter), increases crack width and consequently greatly increases permeability., Comment: Submitted to Cement and Concrete Research

This paper presents a lattice approach to model the influence of cracking on inviscid flow in concrete. A mechanical lattice model based on a damage-plasticity constitutive model was combined with a new dual lattice of conduit elements for flow analysis. The diffusivity of the conduit elements depends on the crack-opening obtained from the mechanical lattice. The coupled lattice model was applied to several benchmark tests for aligned and random lattices. The results for mechanical loading and flow analysis obtained with the new approach were shown to be independent of the size of lattice elements used., Comment: Accepted in Cement and Concrete Composites