Computational model of mesoscopic structure of concrete for simulation of fracture processes

This paper describes mathematical modelling and computational tool for simulation of fracture processes of cementitious composites at the mesoscopic level. The tool relies on highly realistic 3D- and 2D-representations of the heterogeneous internal structure of concrete for understanding the micromechanics of aggregate–matrix interactions. The generation mechanism allows control of aggregate volume content, shape and size distribution. The allocation procedure proved capable to produce numerical concrete with aggregate distributions comparable to real concrete. The continuum was discretised into lattices of linear elements, for structural analyses. Compression, direct tension and wedge-splitting tests were simulated. Parametrical study was carried out to investigate effects of different material properties and proportions in concrete admixtures.     

Design of fracture resistant energy absorbing structures using elastoplastic topology optimization

This paper introduces a novel elastoplastic topology optimization method for fracture resistant energy absorbing structural designs. The target is to find the optimal structural topologies with high plastic work absorption capacity while constraining the fracture indicators below the prescribed constraints. As the two main fracture mechanisms in ductile metals, the ductile fracture and shear fracture criteria are considered using uncoupled CrachFEM fracture model. A consistent adjoint method is presented for the path-dependent sensitivity analysis under the plane stress assumption. Several numerical examples are carried out to demonstrate the effectiveness of the proposed method. It is shown that by constraining the fracture indicators, the optimized designs have a more uniform plastic work distribution and high ductility with a significant delay of failure points. This eventually leads to much better material utilization with enhanced ultimate energy absorption capacities.     

Limit load analysis of thick-walled concrete structures - a finite element approach to fracture

The paper illustrates the interaction of constitutive modelling and finite element solution techniques for limit load prediction of concrete structures.On the constitutive side, an engineering model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure. Upon intersection with the stress path the failure surface collapses for brittle behaviour according to one of three softening rules — no-tension, no-cohesion, and no-friction. The stress transfer accompanying the energy dissipation during local failure is modeled by several fracture rules which are examined with regard to ultimate load prediction.On the numerical side the effect of finite element idealization is studied first as far as ultimate load convergence is concerned. Subsequently, incremental tangential and initial load techniques are compared together with the effect of step size.Limit load analyses of a thick-walled concrete ring and a lined concrete reactor closure conclude the paper along with engineering examples.     

Crack band model of fracture in irregular lattices

An irregular lattice model is used to simulate mode I fracture in softening materials, such as concrete. Lattice geometry is based on a three-dimensional Voronoi discretization of the material domain. The Voronoi diagram provides scaling rules for the elemental stiffness relations, leading to an elastically uniform representation of the material for simple modes of straining. Fracture is represented using a crack band approach, in which the dimensions of the crack band are also scaled according to the Voronoi diagram. The material is viewed as homogeneous and the energy dissipation mechanisms active at finer scales are lumped into a cohesive crack relation. This energy conserving crack band approach is objective with respect to the irregular geometry of the lattice. Model accuracy and performance are demonstrated through simulated fracture testing of concrete specimens under uniaxial tension and flexural loadings. Basic qualities of the simulation approach, demonstrated here for homogeneous models of concrete, are applicable toward simulating fracture in multi-phase systems where material features are explicitly modeled.     

Mesoscale modeling of concrete: Geometry and numerics

Mesoscale analysis is a promising discipline for concrete mix design and damage prediction. Besides many other aspects, its success crucially depends on accurate modeling of the mesoscale geometry and efficient numerical analysis of high resolution, to both of which this article contributes. Mesoscale models of concrete include aggregates, cement stone and, optionally, interfacial transition zones. The present paper establishes transparent formulas for consistent numerical generation of aggregate sizes. Fast separation checks are applied to place ellipsoidal and in particular arbitrary shaped particles. The multigrid method enables efficient computation of very large heterogeneous mesoscale models. This is exemplified by linear finite element analysis of two-dimensional models. Corresponding results are confirmed by experiments and analytical models from literature. The influence of concrete mix parameters on effective elastic properties is studied.     

Simulating climate and energy policy with agent-based modelling: The Energy Modelling Laboratory (EMLab)

We present an approach to simulate climate and energy policy for the EU, using a flexible and modular agent-based modelling approach and a toolbox, called the Energy Modelling Laboratory (EMLab). The paper shortly reviews core challenges and approaches for modelling climate and energy policy in light of the energy transition. Afterwards, we present an agent-based model of investment in power generation that has addressed a variety of European energy policy questions. We describe the development of a flexible model core as well as modules on carbon and renewables policies, capacity mechanisms, investment behaviour and representation of intermittent renewables. We present an overview of modelling results, ongoing projects, a case study on current reforms of the EU ETS, and we show their relevance in the EU context.     

A knowledge graph-supported information fusion approach for multi-faceted conceptual modelling

It has become progressively more evident that a single data source is unable to comprehensively capture the variability of a multi-faceted concept, such as product design, driving behaviour or human trust, which has diverse semantic orientations. Therefore, multi-faceted conceptual modelling is often conducted based on multi-sourced data covering indispensable aspects, and information fusion is frequently applied to cope with the high dimensionality and data heterogeneity. The consideration of intra-facets relationships is also indispensable. In this context, a knowledge graph (KG), which can aggregate the relationships of multiple aspects by semantic associations, was exploited to facilitate the multi-faceted conceptual modelling based on heterogeneous and semantic-rich data. Firstly, rules of fault mechanism are extracted from the existing domain knowledge repository, and node attributes are extracted from multi-sourced data. Through abstraction and tokenisation of existing knowledge repository and concept-centric data, rules of fault mechanism were symbolised and integrated with the node attributes, which served as the entities for the concept-centric knowledge graph (CKG). Subsequently, the transformation of process data to a stack of temporal graphs was conducted under the CKG backbone. Lastly, the graph convolutional network (GCN) model was applied to extract temporal and attribute correlation features from the graphs, and a temporal convolution network (TCN) was built for conceptual modelling using these features. The effectiveness of the proposed approach and the close synergy between the KG-supported approach and multi-faceted conceptual modelling is demonstrated and substantiated in a case study using real-world data.     

Homogenization of material properties in additively manufactured structures

Additive manufacturing transforms material into three-dimensional parts incrementally, layer by layer or path by path. Subject to the build direction and machine resolution, an additively manufactured part deviates from its design model in terms of both geometry and mechanical performance. In particular, the material inside the fabricated part often exhibits spatially varying material distribution (heterogeneity) and direction dependent behavior (anisotropy), indicating that the design model is no longer a suitable surrogate to consistently estimate the mechanical performance of the printed component.We propose a new two-stage approach to modeling and estimating effective elastic properties of parts fabricated by fused deposition modeling (FDM) process. First, we construct an implicit representation of an effective mesoscale geometry–material model of the printed structure that captures the details of the particular process and published material information. This representation of mesoscale geometry and material of the printed structure is then homogenized at macro scale through a solution of an integral equation formulated using Green’s function. We show that the integral equation can be converted into a system of linear equations that is symmetric and positive definite and can be solved efficiently using conjugate gradient method and Fourier transform. The computed homogenized properties are validated by both finite element method and experiment results. The proposed two-stage approach can be used to estimate other effective material properties in a variety of additive manufacturing processes, whenever a similar effective mesoscale geometry–material model can be constructed.     

An application for the fracture characterisation of quasi-brittle materials taking into account fracture process zone influence

The paper introduces a Java application programmed for the advanced determination of the fracture characteristics of silicate-based materials failing in a quasi-brittle manner. The tool reconstructs the progress of a quasi-brittle fracture from the measured load–displacement curve and the knowledge of basic mechanical properties of the material. The main contribution of the proposed approach is that it takes the characteristics of the Fracture Process Zone (FPZ, particularly its extent, i.e. its size and shape) evolving at the tip of the propagating crack during the failure process into account and incorporates them into the fracture-mechanical parameter evaluation procedure(s). This approach is expected to substantially diminish the influence of the test specimen’s size/shape and the test geometry on the values of the parameters of nonlinear fracture models determined from the records of fracture tests on laboratory specimens. The application implements a developed technique for estimation of the size and shape of the FPZ. The technique is based on an amalgamation of several modelling concepts dealing with the failure of structural materials, i.e. multi-parameter linear elastic fracture mechanics, classical nonlinear fracture models for concrete (equivalent elastic crack and cohesive crack models), and the plasticity approach. The knowledge of the FPZ’s extent is employed for the relation of a part of the entire work of fracture to its characteristics within the presented approach. The verification and validation of the developed technique is performed via numerical simulations using the authors’ own computational code based on physical discretization of continuum and selected sets of experimental evidence published in the literature. Reasonable agreement is observed between the outputs of the presented semi-analytical technique and both the simulation results and the experimental data.     

Neural networks as material models within a multiscale approach

This paper shows the application of neural networks in a multiscale analysis of a reinforced concrete beam. A mesoscale model is presented, which simulates the pullout test of a reinforcement bar in concrete. By applying a homogenization procedure, a macroscopic stress vs. crack opening response is obtained from the mesoscale simulations. The neural network is used to approximate this relation in a macroscale simulation and replaces the material formulation of the interface layer between concrete and reinforcement, thus avoiding the computationally expensive parallel simulation on different scales.     

Design of experiments and energy dissipation analysis for a contact mechanics 3D model of frictional bolted lap joints

Bolted lap joints allow structural assemblies to be made. The answer to requirements, both static and dynamic, depends on the joint behaviour. Bolted joints are a primary source of energy dissipation in dynamic built-up and space structures among others. This paper presents an analysis of a bolted lap joint, subjected to a relative displacement after applying a pre-stress on the bolt in order to characterise the joint behaviour. For this purpose a 3D modelling is made by means of finite elements, using design techniques of experiments (DOE) to fit constitutive contact parameters. The theoretical results relative to elasto-plastic hysteresis cycles of the joint are experimentally validated. Finally, the preload effect and the magnitude of the displacement on the non-linear joint behaviour are analysed to determine equivalent stiffness and dissipated energy in the hysterical loops of the joint.     

Experimental investigation and finite element modelling of the effects of flow velocities on a skewed integral bridge

This paper presents finite element modelling of the effects of different flow velocities on the structural behaviour of a skewed integral bridge. Flow velocities affect the scour depths at the piles of a bridge and thus affect its structural behaviour. Laboratory tests on a scaled-down hydraulic model along with numerical modelling were performed to simulate the structural behaviour of the scoured integral bridge. A finite element package was used for the numerical modelling work, and the displacements and strains corresponding to the measured locations on the physical model were extracted. The experimental and numerical results for the case of maximum scour depths were compared.     

Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

Three-dimensional modelling and full-scale testing of stone arch bridges

Existing test results of full-scale in-service masonry arch bridges are analysed to determine appropriate material properties for the modelling of this structural type. Three-dimensional nonlinear finite element models of three masonry arch bridges are generated using a commercially available finite element package. The behaviour of the masonry is replicated by use of a solid element that can have its stiffness modified by the development of cracks and crushing. The fill is modelled as a Drucker–Prager material, and the interface between the masonry and the fill is characterised as a frictional contact surface. The bridges are modelled under service loads, and the model results are compared to the results of a program of field testing of the structures. It is found that the assumption of a reasonable set of material properties, based on visual observations of the material and construction of the structure, implemented through a program of three-dimensional nonlinear finite element analysis enable good predictions of the actual behaviour of a masonry arch bridge.     

A fibre model for push-over analysis of underdesigned reinforced concrete frames

Most of the existing reinforced concrete buildings were designed according to early seismic provisions or, sometimes, without applying any seismic provision. Some problems of strength and ductility, like insufficient shear strength, pull-out of rebars, local mechanisms, etc., could characterize their structural behaviour. The above mentioned topics lead to a number of problems in the evaluation of the seismic behaviour of reinforced concrete (RC) frames. Therefore the assessment of existing RC structures requires advanced tools. A refined model and numerical procedure for the non-linear analysis of reinforced concrete frames is presented. The current version of the model proposed is capable of describing the non-linear behaviour of underdesigned reinforced concrete frames including brittle modes of failure. Selected results of an experimental–theoretical comparison are presented to show the capabilities of this model. The results show the capacity of the model of describing both the global behaviour and the local deformation at service and ultimate state.     

Optimal design of prestressed concrete pipes using linear programming

Non cylinder composite typ: prestressed concrete pipes extensively used in India for high pressure water supply lines are being designed at present by the conventional ‘analysis’ type structural design process. Geometric properties are assumed and then analysis is carried out, for checking accepted design behaviour or safe pressure carrying capacity. The authors here, have considered design behaviour at various loading stages and pressures, as an input in the design process called ‘synthesis’ and geometric properties are generated as an output. Optimal design solution is found using well known linear programming technique. Illustrative design example considering Veeranam Lake—Madras 230 km pipe line, shows substantial economy over conventionally designed pipes.     

A three-dimensional finite element program to predict ultimate fracture failure load

A finite element computer program using an eight-noded three-dimensional isoparametric finite element is developed to predict the initiation and propagation of fracture, load-displacement history and failure load in elastoplastic structural systems subjected to monotonically increasing loads. Isotropie material is considered. The program is based on small deformation theory and uses an incremental loading technique to load the structure. The approach uses two types of piecewise linear approximations for the non-linear portion of the actual uniaxial stress-strain curve for the material: (i) the tangent modulus concept and (ii) the secant modulus concept. Either the St. Venant or von Mises yielding criteria can be used to predict yielding or fracture. Three different methods of calculating element principal stresses/strains are incorporated to apply the yield criterion. The energy at fracture is redistributed by using the ‘zero modulus unload-reload scheme’. Two different problems are solved using the developed program to demonstrate its capabilities and accuracy: (i) a center cracked panel and (ii) a tubular T-connection. The results obtained by the finite element analyses compare well with the available results from experimental tests on similar specimens.     

Multiscale Modeling of Concrete

In this paper, a mesoscale model of concrete is presented, which considers particles, matrix material and the interfacial transition zone (ITZ) as separate constituents. Particles are represented as ellipsoides, generated according to a prescribed grading curve and placed randomly into the specimen. Algorithms are proposed to generate realistic particle configurations efficiently. The nonlinear behavior is simulated with a cohesive interface model for the ITZ. For the matrix material, different damage/plasticity models are investigated. The simulation of localization requires to regularize the solution, which is performed by using integral type nonlocal models with strain or displacement averaging. Due to the complexity of a mesoscale model for a realistic structure, a multiscale method to couple the homogeneous macroscale with the heterogeneous mesoscale model in a concurrent embedded approach is proposed. This allows an adaptive transition from a full macroscale model to a multiscale model, where only the relevant parts are resolved on a finer scale. Special emphasis is placed on the investigation of different coupling schemes between the different scales, such as the mortar method and the arlequin method, and a discussion of their advantages and disadvantages within the current context. The applicability of the proposed methodology is illustrated for a variety of examples in tension and compression.     

Online end-use energy disaggregation via jump linear models

This paper presents two iterative algorithms for non-intrusive appliance load monitoring, which aims to decompose the aggregate power consumption only measured at the household level into the contributions of the individual electric appliances. The approaches are based on modelling the total power consumption as a combination of jump linear sub-models, each of them describing the behaviour of the individual appliance. Dynamic-programming and multi-model Kalman filtering techniques are used to reconstruct the power consumptions at the single-appliance level from the aggregate power in an iterative way.