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Numerical Analysis of Concrete using Discrete Elements

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A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (10 December 2016) | Viewed by 69856

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Prof. Dr. Erik Schlangen

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Faculty of Civil Engineering and Geosciences, Micromechanics Laboratory, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands
Interests: micromechanics of civil engineering materials; durability mechanics; self healing of materials; lattice modeling for fracture and transport
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Dear Colleagues,

Numerical analysis of concrete is widely used when designing concrete structures, but is also used when investigating the concrete material. Various techniques have been developed to perform an analysis of concrete at different scales, and to analyze different properties, behaviors and failures, or transport mechanisms. One of these analysis techniques makes use of Discrete Elements, and is also called lattice type models or lattice discrete particle models.

An area in which Discrete Elements are often applied is in fracture processes in concrete. Mechanical loading on the material or a structure leads to stresses, which result in localized cracking. It is known that models that use Discrete Elements are very well capable of simulating crack patterns that match perfectly with experimental findings. These models are especially suited when dealing with fractures in heterogeneous materials like concrete, where crack patterns are tortuous and follow the weakest link in the material. Additionally, materials that incorporate fibers are studied using Discrete Elements and even ductile behavior can be modeled realistically.

Another topic that can be tackled with these models is transport. Lattice type models are applied to study moisture flow, both in diffusion or permeability, through concrete. In addition, heat or gas flow in heterogeneous materials like concrete can be studied with lattice models.

A further challenge is the combination of mechanical loading and transport phenomena. Mechanical loading leads to cracks in the material, which enhances the transport. Furthermore, the transport leads to moisture or temperature gradients, which induce stresses that can propagate cracks.

The Discrete Element models are, on the one hand, adopted to study the basic mechanisms of mechanics or transport in both concrete materials and structures. On the other hand, they can be applied to study deterioration mechanisms like processes such as corrosion, restrained drying shrinkage, alkali-silica reaction, and the effect of those on the performance of a concrete structure.

Prof. Dr. Erik Schlangen
Guest Editor

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Keywords

Concrete
Numerical Modeling
Lattice models
Discrete Elements
Fracture
Transport
Material
Structure

Published Papers (11 papers)

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Research

6248 KiB

Open AccessArticle

Modeling Framework for Fracture in Multiscale Cement-Based Material Structures

by Zhiwei Qian, Erik Schlangen, Guang Ye and Klaas Van Breugel

Materials 2017, 10(6), 587; https://doi.org/10.3390/ma10060587 - 26 May 2017

Cited by 44 | Viewed by 4866

Abstract

Multiscale modeling for cement-based materials, such as concrete, is a relatively young subject, but there are already a number of different approaches to study different aspects of these classical materials. In this paper, the parameter-passing multiscale modeling scheme is established and applied to address the multiscale modeling problem for the integrated system of cement paste, mortar, and concrete. The block-by-block technique is employed to solve the length scale overlap challenge between the mortar level (0.1–10 mm) and the concrete level (1–40 mm). The microstructures of cement paste are simulated by the HYMOSTRUC3D model, and the material structures of mortar and concrete are simulated by the Anm material model. Afterwards the 3D lattice fracture model is used to evaluate their mechanical performance by simulating a uniaxial tensile test. The simulated output properties at a lower scale are passed to the next higher scale to serve as input local properties. A three-level multiscale lattice fracture analysis is demonstrated, including cement paste at the micrometer scale, mortar at the millimeter scale, and concrete at centimeter scale. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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6188 KiB

Open AccessFeature PaperArticle

Modeling Time-Dependent Behavior of Concrete Affected by Alkali Silica Reaction in Variable Environmental Conditions

by Mohammed Alnaggar, Giovanni Di Luzio and Gianluca Cusatis

Materials 2017, 10(5), 471; https://doi.org/10.3390/ma10050471 - 28 Apr 2017

Cited by 70 | Viewed by 6985

Abstract

Alkali Silica Reaction (ASR) is known to be a serious problem for concrete worldwide, especially in high humidity and high temperature regions. ASR is a slow process that develops over years to decades and it is influenced by changes in environmental and loading conditions of the structure. The problem becomes even more complicated if one recognizes that other phenomena like creep and shrinkage are coupled with ASR. This results in synergistic mechanisms that can not be easily understood without a comprehensive computational model. In this paper, coupling between creep, shrinkage and ASR is modeled within the Lattice Discrete Particle Model (LDPM) framework. In order to achieve this, a multi-physics formulation is used to compute the evolution of temperature, humidity, cement hydration, and ASR in both space and time, which is then used within physics-based formulations of cracking, creep and shrinkage. The overall model is calibrated and validated on the basis of experimental data available in the literature. Results show that even during free expansions (zero macroscopic stress), a significant degree of coupling exists because ASR induced expansions are relaxed by meso-scale creep driven by self-equilibriated stresses at the meso-scale. This explains and highlights the importance of considering ASR and other time dependent aging and deterioration phenomena at an appropriate length scale in coupled modeling approaches. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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8254 KiB

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Upscaling Cement Paste Microstructure to Obtain the Fracture, Shear, and Elastic Concrete Mechanical LDPM Parameters

by Gili Sherzer, Peng Gao, Erik Schlangen, Guang Ye and Erez Gal

Materials 2017, 10(3), 242; https://doi.org/10.3390/ma10030242 - 28 Feb 2017

Cited by 21 | Viewed by 7327

Abstract

Modeling the complex behavior of concrete for a specific mixture is a challenging task, as it requires bridging the cement scale and the concrete scale. We describe a multiscale analysis procedure for the modeling of concrete structures, in which material properties at the macro scale are evaluated based on lower scales. Concrete may be viewed over a range of scale sizes, from the atomic scale (10⁻¹⁰ m), which is characterized by the behavior of crystalline particles of hydrated Portland cement, to the macroscopic scale (10 m). The proposed multiscale framework is based on several models, including chemical analysis at the cement paste scale, a mechanical lattice model at the cement and mortar scales, geometrical aggregate distribution models at the mortar scale, and the Lattice Discrete Particle Model (LDPM) at the concrete scale. The analysis procedure starts from a known chemical and mechanical set of parameters of the cement paste, which are then used to evaluate the mechanical properties of the LDPM concrete parameters for the fracture, shear, and elastic responses of the concrete. Although a macroscopic validation study of this procedure is presented, future research should include a comparison to additional experiments in each scale. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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5372 KiB

Open AccessArticle

Lattice Modeling of Early-Age Behavior of Structural Concrete

by Yaming Pan, Armando Prado, Rocío Porras, Omar M. Hafez and John E. Bolander

Materials 2017, 10(3), 231; https://doi.org/10.3390/ma10030231 - 25 Feb 2017

Cited by 35 | Viewed by 5662

Abstract

The susceptibility of structural concrete to early-age cracking depends on material composition, methods of processing, structural boundary conditions, and a variety of environmental factors. Computational modeling offers a means for identifying primary factors and strategies for reducing cracking potential. Herein, lattice models are shown to be adept at simulating the thermal-hygral-mechanical phenomena that influence early-age cracking. In particular, this paper presents a lattice-based approach that utilizes a model of cementitious materials hydration to control the development of concrete properties, including stiffness, strength, and creep resistance. The approach is validated and used to simulate early-age cracking in concrete bridge decks. Structural configuration plays a key role in determining the magnitude and distribution of stresses caused by volume instabilities of the concrete material. Under restrained conditions, both thermal and hygral effects are found to be primary contributors to cracking potential. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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7331 KiB

Open AccessArticle

Mesoscale Characterization of Fracture Properties of Steel Fiber-Reinforced Concrete Using a Lattice–Particle Model

by Francisco Montero-Chacón, Héctor Cifuentes and Fernando Medina

Materials 2017, 10(2), 207; https://doi.org/10.3390/ma10020207 - 21 Feb 2017

Cited by 29 | Viewed by 6399

Abstract

This work presents a lattice–particle model for the analysis of steel fiber-reinforced concrete (SFRC). In this approach, fibers are explicitly modeled and connected to the concrete matrix lattice via interface elements. The interface behavior was calibrated by means of pullout tests and a range for the bond properties is proposed. The model was validated with analytical and experimental results under uniaxial tension and compression, demonstrating the ability of the model to correctly describe the effect of fiber volume fraction and distribution on fracture properties of SFRC. The lattice–particle model was integrated into a hierarchical homogenization-based scheme in which macroscopic material parameters are obtained from mesoscale simulations. Moreover, a representative volume element (RVE) analysis was carried out and the results shows that such an RVE does exist in the post-peak regime and until localization takes place. Finally, the multiscale upscaling strategy was successfully validated with three-point bending tests. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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6771 KiB

Open AccessArticle

Mesoscale Fracture Analysis of Multiphase Cementitious Composites Using Peridynamics

by Amin Yaghoobi, Mi G. Chorzepa, S. Sonny Kim and Stephan A.

Materials 2017, 10(2), 162; https://doi.org/10.3390/ma10020162 - 10 Feb 2017

Cited by 54 | Viewed by 7200

Abstract

Concrete is a complex heterogeneous material, and thus, it is important to develop numerical modeling methods to enhance the prediction accuracy of the fracture mechanism. In this study, a two-dimensional mesoscale model is developed using a non-ordinary state-based peridynamic (NOSBPD) method. Fracture in a concrete cube specimen subjected to pure tension is studied. The presence of heterogeneous materials consisting of coarse aggregates, interfacial transition zones, air voids and cementitious matrix is characterized as particle points in a two-dimensional mesoscale model. Coarse aggregates and voids are generated using uniform probability distributions, while a statistical study is provided to comprise the effect of random distributions of constituent materials. In obtaining the steady-state response, an incremental and iterativesolverisadopted for the dynamic relaxation method. Load-displacement curves and damage patterns are compared with available experimental and ﬁnite element analysis (FEA) results.Although the proposed model uses much simpler material damage models and discretization schemes, the load-displacementcurvesshownodifferencefromtheFEAresults. Furthermore,nomeshreﬁnement is necessary, as fracture is inherently characterized by bond breakages. Finally, a sensitivity study is conducted to understand the effect of aggregate volume fraction and porosity on the load capacity of the proposed mesoscale model Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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2089 KiB

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Boundary Layer Effect on Behavior of Discrete Models

by Jan Eliáš

Materials 2017, 10(2), 157; https://doi.org/10.3390/ma10020157 - 10 Feb 2017

Cited by 18 | Viewed by 3677

Abstract

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson’s ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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604 KiB

Open AccessArticle

An Extended Damage Plasticity Model for Shotcrete: Formulation and Comparison with Other Shotcrete Models

by Matthias Neuner, Peter Gamnitzer and Günter Hofstetter

Materials 2017, 10(1), 82; https://doi.org/10.3390/ma10010082 - 21 Jan 2017

Cited by 26 | Viewed by 6172 | Correction

Abstract

The aims of the present paper are (i) to briefly review single-field and multi-field shotcrete models proposed in the literature; (ii) to propose the extension of a damage-plasticity model for concrete to shotcrete; and (iii) to evaluate the capabilities of the proposed extended damage-plasticity model for shotcrete by comparing the predicted response with experimental data for shotcrete and with the response predicted by shotcrete models, available in the literature. The results of the evaluation will be used for recommendations concerning the application and further improvements of the investigated shotcrete models and they will serve as a basis for the design of a new lab test program, complementing the existing ones. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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5972 KiB

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Microscale Testing and Modelling of Cement Paste as Basis for Multi-Scale Modelling

by Hongzhi Zhang, Branko Šavija, Stefan Chaves Figueiredo, Mladena Lukovic and Erik Schlangen

Materials 2016, 9(11), 907; https://doi.org/10.3390/ma9110907 - 08 Nov 2016

Cited by 85 | Viewed by 7006

Abstract

This work aims to provide a method for numerically and experimentally investigating the fracture mechanism of cement paste at the microscale. For this purpose, a new procedure was proposed to prepare micro cement paste cubes (100 × 100 × 100 µm³) and beams with a square cross section of 400 × 400 µm². By loading the cubes to failure with a Berkovich indenter, the global mechanical properties of cement paste were obtained with the aid of a nano-indenter. Simultaneously the 3D images of cement paste with a resolution of 2 µm³/voxel were generated by applying X-ray microcomputed tomography to a micro beam. After image segmentation, a cubic volume with the same size as the experimental tested specimen was extracted from the segmented images and used as input in the lattice model to simulate the fracture process of this heterogeneous microstructure under indenter loading. The input parameters for lattice elements are local mechanical properties of different phases. These properties were calibrated from experimental measured load displacement diagrams and failure modes in which the same boundary condition as in simulation were applied. Finally, the modified lattice model was applied to predict the global performance of this microcube under uniaxial tension. The simulated Young’s modulus agrees well with the experimental data. With the method presented in this paper the framework for fitting and validation of the modelling at microscale was created, which forms a basis for multi-scale analysis of concrete. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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1074 KiB

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Three-Dimensional Network Model for Coupling of Fracture and Mass Transport in Quasi-Brittle Geomaterials

by Peter Grassl and John Bolander

Materials 2016, 9(9), 782; https://doi.org/10.3390/ma9090782 - 19 Sep 2016

Cited by 50 | Viewed by 6972

Abstract

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. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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9129 KiB

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A 3D Lattice Modelling Study of Drying Shrinkage Damage in Concrete Repair Systems

by Mladena Luković, Branko Šavija, Erik Schlangen, Guang Ye and Klaas Van Breugel

Materials 2016, 9(7), 575; https://doi.org/10.3390/ma9070575 - 14 Jul 2016

Cited by 43 | Viewed by 6531

Abstract

Differential shrinkage between repair material and concrete substrate is considered to be the main cause of premature failure of repair systems. The magnitude of induced stresses depends on many factors, for example the degree of restraint, moisture gradients caused by curing and drying conditions, type of repair material, etc. Numerical simulations combined with experimental observations can be of great use when determining the influence of these parameters on the performance of repair systems. In this work, a lattice type model was used to simulate first the moisture transport inside a repair system and then the resulting damage as a function of time. 3D simulations were performed, and damage patterns were qualitatively verified with experimental results and cracking tendencies in different brittle and ductile materials. The influence of substrate surface preparation, bond strength between the two materials, and thickness of the repair material were investigated. Benefits of using a specially tailored fibre reinforced material, namely strain hardening cementitious composite (SHCC), for controlling the damage development due to drying shrinkage in concrete repairs was also examined. Full article

(This article belongs to the Special Issue Numerical Analysis of Concrete using Discrete Elements)

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