Joško Ožbolt

Microplane model for concrete with relaxed kinematic constraint

Abstract In the paper, the microplane material model for concrete based on the relaxed kinematic constraint is presented. The model is aimed to be used for three-dimensional damage and fracture analysis of concrete and reinforced concrete structures in the framework of smeared crack approach. In the microplane model, the material is characterized by a relation between the stress and strain components on planes of various orientations. These planes may be imagined to represent the damage planes or weak planes in the microstructure, such as contact layers between aggregate pieces in concrete. The tensorial invariance restrictions need not be directly enforced. They are automatically satisfied by superimposing in a suitable manner the responses from all the microplanes. To realistically model concrete under compressive load, for each microplane, the total strain tensor has to be decomposed into the normal (volumetric and deviatoric) and shear strain component. It is shown that for dominant tensile load the decomposition of the normal microplane strain into volumetric and deviatoric part, together with the fact that the tensile strength of concrete is an order of magnitude smaller than its compressive strength, leads to unrealistic model response. To keep the conceptual simplicity, the model is improved in the framework of the kinematic microplane theory, however, the kinematic constraint at the microplane level is relaxed. The proposed approach finds its physical background in the discontinuity of the strain field. It is demonstrated that the improved model correctly predicts the concrete response for dominant tensile load. The implementation of the initial anisotropy and the modeling of concrete for cyclic loading is also discussed. Comparison with a number of test data for different stress–strain histories shows a good agreement. The model has been recently implemented into a two- and three-dimensional finite element code and coupled with the localization limiter of local (crack band) and nonlocal integral type.

NUMERICAL SMEARED FRACTURE ANALYSIS: NONLOCAL MICROCRACK INTERACTION APPROACH

SUMMARY A recently proposed new nonlocal concept based on microcrack interactions is discussed, its implementation in a smeared cracking finite element code for concrete is presented, numerical studies are reported, and comparisons with experimental results are made. The nonlocality is not merely a mathematical device to prevent excessive spurious localization into a zone of zero volume but is a necessary physical consequence of microcrack interactions. Since the constitutive law itself is strictly local, the new nonlocal concept can be combined with any type of constitutive law for strain-softening nonlocal damage, which is here chosen to be the micro plane model. A simple method is formulated to approximately identify the material parameters in the model from the basic characteristics of concrete such as the tensile strength, fracture energy and maximum aggregate size. The results of finite element analysis are shown to be mesh insensitive, and good convergence is obtained. Cracking damage is found to localize into a volume whose size and shape depend on the macroscopic concrete properties as well as the current stress-strain state. Although the damage is considered to be tensile on the microlevel, due solely to mode I microcracks, the new non local model can describe well not only mode I fracture tests but also complex shear-dominated and mixed-mode types of failure such a diagonal shear, and can do so for the same values of material parameters (which was not the case for previous nonlocal models). Most importantly, the new nonlocal model can correctly capture the size effect of quasibrittle fracture, in approximate agreement with Bazanfs size effect law.

Modeling damage in concrete caused by corrosion of reinforcement: coupled 3D FE model

Reinforced concrete structures, which are exposed to aggressive environmental conditions, such as structures close to the sea or highway bridges and garages exposed to de-icing salts, often exhibit damage due to corrosion. Damage is usually manifested in the form of cracking and spalling of concrete cover caused by expansion of corrosion products around reinforcement. The reparation of corroded structure is related with relatively high direct and indirect costs. Therefore, it is of great importance to have a model, which is able to realistically predict influence of corrosion on the safety and durability of reinforced concrete structures. In the present contribution a 3D chemo-hygro-thermo-mechanical model for concrete is presented. In the model the interaction between non-mechanical influences (distribution of temperature, humidity, oxygen, chloride and rust) and mechanical properties of concrete (damage), is accounted for. The mechanical part of the model is based on the microplane model. It has recently been shown that the model is able to realistically describe the processes before and after depassivation of reinforcement and that it correctly accounts for the interaction between mechanical (damage) and non-mechanical processes in concrete. In the present paper application of the model is illustrated on two numerical examples. The first demonstrates the influence of expansion of corrosion products on damage of the beam specimen in cases with and without accounting for the transport of rust through cracks. It is shown that the transport of corrosion products through cracks can significantly influence the corrosion induced damage. In the second example the numerically predicted crack patterns due to corrosion of reinforcement in a beam are compared with experimental results. The influence of the anode–cathode regions on the corrosion induced damage is investigated. The comparison between numerical results and experimental evidence shows that the model is able to realistically predict experimentally observed crack pattern and that the position of anode and cathode strongly influences the crack pattern and corrosion rate.

Numerical Study of Mixed-Mode Fracture in Concrete

In the present paper, the finite element code based on the microplane model is used for the analysis of typical concrete mixed-mode geometries — the notched beam, the doubleedge-notched specimen and the dowel disk specimen. The local smeared fracture finite element analysis is carried out. As a regularization procedure, the crack band method is used. The aim of the study was to investigate whether the smeared fracture finite element analysis is able to predict mixed-mode fracture of concrete. Comparison between experimental and numerical results shows that the used code predicts structural response and crack pattern realistically for all investigated cases. It is shown that for the most of studied geometries the mixed-mode fracture mechanism dominates at crack initiation. However, with increase of the crack length mode I fracture becomes dominant and finally specimens fail in failure mode I.

Size effect on the concrete cone pull-out load

In the present paper the failure mechanism and size effect of the concrete cone resistance is reviewed and studied. The influence of material and geometrical parameters on the failure mode and size effect is investigated. In the numerical studies the smeared crack finite element analysis, based on the microplane material model for concrete, was used. Both, experimental and numerical results show that there is a strong size effect on the nominal concrete cone pull-out strength. It is demonstrated that besides the embedment depth the scaling of the head of the stud as well as the scaling of the concrete member influence the nominal strength.

Modelling processes related to corrosion of reinforcement in concrete: coupled 3D finite element model

Abstract Aggressive environmental conditions, such as exposure to the sea climate or use of de-icing salts, have a strong influence on durability of reinforced concrete (RC) structures due to reinforcement corrosion-induced damage. In the present paper, a recently developed three-dimensional (3D) chemo-hygro-thermo-mechanical model for concrete is briefly discussed. The model was implemented into a 3D finite element code and its application is illustrated through numerical analysis of a RC beam-end specimen with stirrups, exposed to aggressive environmental conditions. Damage of concrete cover due to expansion of corrosion products and transport of rust through concrete pores and cracks are computed. Subsequently, the influence of corrosion-induced damage of concrete cover on pull-out resistance of deformed reinforcement is investigated. The comparison between numerical results and experimental evidence shows that the complex coupled mathematical model is able to realistically predict the phenomena related to corrosion of steel reinforcement in concrete.

Influence of Surface Reinforcement, Member Thickness, and Cracked Concrete on Tensile Capacity of Anchor Bolts

An extensive numerical study was carried out to evaluate the influence of concrete member thickness and orthogonal surface reinforcement on the tensile capacity and performance of anchor bolts in u ...

Tensile Capacity of Anchor Bolts in Uncracked Concrete: Influence of Member Thickness and Anchor’s Head Size

This study evaluated the influence of concrete member thickness and size of anchor head on the tensile capacity and performance of anchor bolts in concrete. Anchor bolts at various embedment depths ...

Dynamic Fracture of Concrete–3D Numerical Study of Compact Tension Specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. For concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. Moreover, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 to 600 m/s.

Modeling of reinforced concrete by the non-local microplane model

This paper reviews some recent results of non-local finite element fracture analysis of concrete structures using a non-local microplane material model. The microplane model and recently introduced non-local microcrack interaction approach are described briefly. It is demonstrated that the model used in smeared fracture finite element analysis does not exhibit mesh sensitivity. Results of a three-dimensional numerical study of fastening elements pulled out from cracked and uncracked reinforced concrete plates are shown. The capability of the model for correct prediction of the structural size effect is supported by one numerical example. In all examples numerical results are compared with experimental evidence and reasonably good agreement is observed.