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A sequentially coupled shape and topology optimization framework is presented in which the outer geometry and the internal topological layout of beam-type structures are optimized simultaneously. The outer geometry of the beam-type structures is parametrically described by non-uniform rational B-splines (NURBS), which guarantees a highly accurate description of the structural shape and enable an efficient control of the design domain with only a few control points. The computational efficiency of the coupled optimization approach is assured by applying a gradient-based optimization algorithm, for which the sensitivities are derived in closed form. The formulation of the coupled optimization approach is tailored toward 2.5D and full 3D representations of beam structures used in engineering applications. The 2.5D beam model, which has been taken from the literature, uses standard beam elements to simulate the beam response in the longitudinal direction, whereby the cross-sectional properties of the beam elements are calculated from additional 2D finite element method (FEM) analyses. A comparison study of a cantilever beam problem subjected to pure shape optimization and pure topology optimization illustrates that the 2.5D and 3D beam models lead to similar shape and topology designs, but that the 2.5D beam model has a significantly higher computational efficiency. Specifically, the computational times for the 2.5D model are about a factor 70 (shape optimization) and 1.4 (topology optimization) lower than for the 3D model, which indicates that in the coupled optimization approach the optimization of the shape provides the largest contribution to the higher computational efficiency of the 2.5D model. The coupled shape and topology optimization analysis subsequently performed on the 2.5D cantilever beam model demonstrates that the specific order at which the alternating shape and topology optimization increments are performed in the staggered update procedure turns out to have some influence on the computational speed and the value of the minimal compliance computed. Despite these differences, the final beam structures following from the different staggered update procedures illustrate how shape and topology can be efficiently optimized in an integrated, coupled fashion.

This contribution compares the performance of a monolithic and two staggered numerical update schemes for a coupled shape and topology optimization method for thin-walled beam structures. In order to limit the computational time of the optimization method, the thin-walled beam structures are modeled as 2.5D configurations. In this approach, 1D beam elements are used to simulate the beam response in the longitudinal direction, while the cross-sectional properties of the beam elements are calculated from additional 2D finite element method analyses. The sensitivities with respect to the shape and topology design variables are derived in closed form in order to take advantage of a computationally efficient, gradient-based optimization algorithm. The numerical examples concern basic circular and square thin-walled cantilever beam structures, as well as a more complex, non-prismatic thin-walled beam structure representative of a rotor blade used in a horizontal-axis wind turbine. For each numerical example the computational time and the solution computed by the monolithic and staggered update schemes are compared, which provides clear insight into the numerical efficiency of the solution procedure and the uniqueness of the computational result. Although the three different update schemes for the cases examined result in comparable optimized design concepts, the computational efficiency and the specific minimal compliance value found turn out to be rather sensitive to the algorithmic details of the numerical update scheme applied. Since the monolithic update scheme typically navigates a larger design space than the two staggered update schemes, for most cases examined it provides the lowest structural compliance. In the specific case whereby shape optimization (virtually) has no influence on the final, optimized beam configuration, the structural compliance computed by the monolithic scheme may relate to a local minimum that is less optimal compared to the value calculated by a staggered update scheme.

A coupled topology and domain shape optimization framework is presented that is based on incorporating the shape design variables of the design domain in the Solid Isotropic Material with Penalization topology optimization method. The shape and topology design variables are incrementally updated in a sequential fashion, using a staggered numerical update scheme. Non-Uniform Rational B-Splines are employed to parameterize the shape of the design domain. This not only guarantees a highly accurate description of the shape boundaries by means of smooth basis functions with compact support, but also enables an efficient control of the design domain with only a few control points. Furthermore, the optimization process is performed in a computationally efficient way by applying a gradient-based optimization algorithm, for which the sensitivities can be computed in closed form. The usefulness of the coupled optimization approach is demonstrated by analyzing several benchmark problems that are subjected to different types of initial conditions and domain bounds. The variation in simulation results denotes that a careful construction of the initial design domain is necessary and meaningful.

Recent experimental research by Reiter et al. (Cem. Concr. Res., 132:106047, 2020) indicates that the buildability of fresh concrete used in extrusion-based 3D printing processes can be significantly enhanced by chemically accelerating the curing process. In the present contribution the effect of accelerated curing on failure by plastic collapse and elastic buckling during 3D concrete printing is explored by incorporating a power-law curing function in the parametric 3D printing model developed by Suiker (Int. J. Mech Sci, 137:145–170, 2018). A structural yield criterion is derived for the case of accelerated curing, and the main advantages on the resistance against plastic collapse are demonstrated through a comparison of the predicted failure characteristics to those for linear curing and exponentially-decaying curing. Subsequently, the elastic buckling behaviour under accelerated curing is derived for a free wall configuration, and the competition between elastic buckling and plastic collapse of the free wall structure is assessed via the construction of failure mechanism maps. In addition, a modelling recipe is proposed for consistently accounting for the vertical deformations of layers in the prediction of structural failure during 3D concrete printing. The modelling of this effect may further increase the accuracy of the prediction of the number of layers at structural failure. For failure under plastic collapse, results are computed for linear curing, exponentially-decaying curing and accelerated curing. The model outcome for linear curing is used for a comparison with results from 3D concrete printing experiments recently presented in the literature, showing an excellent agreement. It is further demonstrated that the effect of vertical wall deformations on the prediction of failure by elastic buckling typically is minor, so that for this failure mechanism this contribution may be left out of consideration. All design graphs presented in this communication are generic, in a sense that they are not restricted to concrete, but can be applied for other printing materials as well.

Wood materials are characterized by complex, hierarchical material structures spanning across various length scales. The present work aims at establishing a relation between the hygro-elastic properties at the mesoscopic cellular level and the effective material response at the macroscopic level, both for softwood (spruce) and hardwood (balsa). The particular aim is to explore the influence on the effective hygro-elastic properties under variations in the meso-scale morphology. The multi-scale framework applied for this purpose uses the method of asymptotic homogenization, which allows to accurately and efficiently obtain the effective response of heterogeneous materials characterized by complex meso-structural geometries. The meso-structural model considered for softwood is based on a periodic, two-dimensional statistically representative volume element that is generated by a spatial repetition of tracheid cells. The tracheid cells are modeled as hexagonal elements characterized by a certain geometrical irregularity. The hardwood meso-structure consists of a region composed of hexagonal cellular fibers with large vessels embedded, which is connected to a ray region that is constructed of ray cells. The hardwood fibers are modeled as hexagonal cellular elements, similar to softwood tracheids. The rays are represented by quadrilateral cells oriented along the radial direction, whereby different arrangements are considered, i.e., the ray cells are either regularly stacked or organized as a staggered configuration. The interface between the fiber and ray regions may also be characterized by a regular or a staggered arrangement. The meso-structural models for softwood and hardwood are discretized by means of plane-strain, finite element models, which describe the hygro-elastic response of the wood material in the radial–tangential plane. For softwood, the sensitivity of the effective elastic and hygro-expansive properties is explored as a function of the geometrical irregularity of the tracheids. For hardwood, the effective properties are studied under a variation of the ray cell arrangement, the type of interface between ray and fiber regions, and the vessel volume fraction. The modeling results agree well with results obtained from other numerical homogenization studies and show to be in reasonable agreement with experimental data taken from the literature.

The structural failure of round and egg-shaped sewer pipes is investigated by means of laboratory experiments and finite element method analyses. Two different round pipes are considered, which have an inner diameter of 400 mm and 500 mm, and are respectively referred to as R400 and R500 sewer pipes. The egg-shaped pipe considered in this study has a horizontal inner diameter of 400 mm and a vertical inner diameter of 600 mm, and is labeled as the E400/600 sewer pipe. Sewer pipes with these dimensions are most commonly used in the Netherlands. In full-scale experimental tests the sewer pipe specimens are subjected to biaxial loading, whereby the horizontal pressure loading is set equal to 1/3 times the vertical pressure loading. This loading condition is representative of a sewer pipe embedded in a well-graded sandy gravel and subjected to neutral horizontal earth pressure. Apart from the global load–displacement behaviour, the local strain response is measured at various locations, which indicates how the applied load is distributed across the sewer pipe. The fracture pattern at catastrophic failure is recorded by means of cameras placed at the front side of the pipe specimen. The round pipes fail under the development of 4 distinctive failure cracks, which are located at the top and bottom of the sewer pipe, and halfway the left and right sides. The egg-shaped sewer pipes also fail under the development of 4 failure cracks, which emerge at the top and bottom of the pipe, and at the top-left and top-right sides. The round R500 pipe fails at the lowest ultimate failure load, which is, respectively, a factor of 1.16 and 2.25 smaller than the ultimate failure loads of the round R400 pipe and the egg-shaped E400/600 pipe. The FEM models of the round and egg-shaped pipes accurately predict both the failure response and the fracture pattern measured in the experiments. Accordingly, the FEM model of the round R400 sewer pipe is used to analyse the sensitivity of the overall failure response of the sewer pipe to various parameters, which are the load contact area, the ratio between the applied horizontal and vertical loads, the wall thickness of the sewer pipe, and the tensile strength, mode I toughness and Young’s modulus of the concrete. The variation of these parameters mimics how the load bearing capacity of a sewer pipe decreases under the effects of soil erosion, changes in lateral earth pressure, biochemical degradation, and ageing. The knowledge obtained from the experimental–numerical study may support the decision making process on maintenance and replacement of sewer systems.

This contribution studies failure by elastic buckling and plastic collapse during 3D concrete printing of wall structures. Four types of experiments were performed, which demonstrate the circumstances under which elastic buckling and plastic collapse occur, the effect of geometrical imperfections on the buckling response, the influence by the curing rate of the concrete material on the buckling stability, and the conditions leading to the successful printing of a complex, practical structure (a picnic table). The experimental results are compared to those computed by the parametric 3D printing model recently developed by Suiker (Int. J. Mech Sci, 137: 145–170, 2018), showing a very good agreement. The design formulas and design graphs deduced from the parametric model serve as a useful tool for accurately designing wall structures against failure during 3D concrete printing. Furthermore, they may be applied to optimize the process conditions during 3D printing, by providing the maximal printing velocity, the optimal geometrical characteristics, or the minimal amount of material required for adequately printing the structure.

Traditionally, Aerodynamic Shape Optimization (ASO) and Structural Topology Optimization (STO) are considered as two separate, consecutive stages in the aerostructural design process of wind turbine rotor blades. Since such a modeling strategy does not adequately account for the coupling effects between the blade aerodynamics and its structural performance, in this paper a Coupled Multi-objective Shape and Topology Optimization (CMSTO) approach is presented, which simultaneously optimizes the outer shape and the interior structural layout of the turbine blade from aerodynamic and structural requirements. The framework uses the weighted sum method, whereby the sum of the aerodynamic and structural objectives multiplied by specific weighting factors is minimized employing an incremental-iterative update procedure. The coupled optimization process is performed by sequentially carrying out shape and topology optimization steps for beam-type structures, in accordance with a staggered scheme. For the aerodynamic and structural optimizations the rotor power coefficient and the blade structural compliance are considered as the objectives, respectively. The aerodynamic response of the blade is evaluated by the Blade Element Momentum (BEM) method, which, together with a reduced beam-type Finite Element Method (FEM) model that simulates the structural response, facilitates the application of a gradient-based algorithm with analytical sensitivities. Accordingly, the computational efficiency of the CMSTO framework is warranted. The shape design variables are characterized by the locations of Non-Uniform Rational B-Splines (NURBS) control points that parameterize the blade outer shape. The topology design variables are represented by the relative densities assigned to the finite elements modeling the blade cross-sections, in correspondence with the Simplified Isotropic Material with Penalization (SIMP) method. The CMSTO framework is used to optimize the NREL 5 MW reference rotor blade, whereby the results are compared to those obtained from a separate ASO-STO approach and a pure STO approach. The rotor power coefficients calculated by the CMSTO and ASO-STO approaches are about 4% larger than that of the reference rotor blade. In addition, the blade structural compliance computed by the CMSTO approach is reduced by an extra 16% and 41% compared to the compliances found by ASO-STO and pure STO approaches, respectively. Such significant improvements clearly demonstrate the benefits of the CMSTO approach in the quest of wind turbines with higher power output and better structural performance.

In the present contribution, the effective mechanical, diffusive, and chemo-expansive properties of concrete arecomputed from a multi-scale and multi-physics approach. The distinctive features of the approach are that i) themechanical and diffusive responses are modelled in a coupled fashion (instead of separately, as is usually done),and that ii) the multi-scale model considers three different scales of observation, which allows for includingheterogeneous effects from both the micro- and meso-scales in the effective macro-scale properties of concrete.At the macro-scale, the concrete material is considered as homogeneous, whereas at the meso-scale it consists ofparticle aggregates embedded in a porous cement paste. At the micro-scale the porous cement paste is describedas a two-phase material, composed of a solid cement phase and saturated capillary pores. Adopting a two-levelasymptotic homogenization procedure, the effective meso-scale properties of the porous cement paste arecomputed first, using a unit cell that includes the cement paste and pore characteristics. Subsequently, theobtained meso-scale response of the porous cement paste, together with the aggregate characteristics, defines thematerial properties of a second unit cell, which is used for calculating the effective macro-scale response ofconcrete. The distributions of the pores and the aggregates within the unit cells are determined from a uniform,random distribution of points, and their radii are defined from a probability distribution function. The efficacy ofthe proposed framework is illustrated by studying the effective mesoscopic response of a porous cement paste,which demonstrates the influence of the micro-scale porosity and pore percolation. Next, the effective macroscopicresponse of concrete is analysed, by considering the influence of the aggregate volume fraction, themismatches in elastic stiffnesses and diffusivity between the aggregate and the cement paste, and the porosity.The computed effective properties are compared with experimental data from the literature, showing a goodagreement.

Crack channelling is predicted in a brittle coating-substrate system that is subjected to a moisture or temperature gradient in the thickness direction. Competing failure scenarios are identified, and are distinguished by the degree to which the coating-substrate interface delaminates, and whether this delamination is finite or unlimited in nature. Failure mechanism maps are constructed, and illustrate the sensitivity of the active crack channelling mechanism and associated channelling stress to the ratio of coating toughness to interfacial toughness, to the mismatch in elastic modulus and to the mismatch in coefficient of hygral or thermal expansion. The effect of the ratio of coating to substrate thickness upon the failure mechanism and channelling stress is also explored. Closed-form expressions for the steady-state delamination stress are derived, and are used to determine the transition value of moisture state that leads to unlimited delamination. Although the results are applicable to coating-substrate systems in a wide range of applications, the study focusses on the prediction of cracking in historical paintings due to indoor climate fluctuations, with the objective of helping museums developing strategies for the preservation of art objects. For this specific application, crack channelling with delamination needs to be avoided under all circumstances, as it may induce flaking of paint material. In historical paintings, the substrate thickness is typically more than ten times larger than the thickness of the paint layer; for such a system, the failure maps constructed from the numerical simulations indicate that paint delamination is absent if the delamination toughness is larger than approximately half of the mode I toughness of the paint layer. Further, the transition between crack channelling with and without delamination appears to be relatively insensitive to the mismatch in the elastic modulus of the substrate and paint layer. The failure maps developed in this work may provide a useful tool for museum conservators to identify the allowable indoor humidity and temperature fluctuations for which crack channelling with delamination is prevented in historical paintings.

Indoor climate fluctuations are regarded as one of the major risks for the emergence of damage in historical works of art. For a safe preservation of their art objects museums try to minimize this risk, which is typically done by imposing strict limitations on the indoor temperature and humidity conditions. The high energy demand resulting from this approach, however, undermines the aim of preeminent museums to execute a sustainable preservation strategy of their collections. A rational improvement of this aspect asks for detailed information on the history of museum objects, complemented by a thorough comprehension of the failure and deformation behaviour of museum objects under indoor climate fluctuations. Accordingly, in this paper the hygro-mechanical response of mock-ups of historical Dutch cabinet door panels made of oak wood is examined under several relative humidity variations. In specific, the mock-ups were subjected to (i) an instantaneous decrease of 40% relative humidity, (ii) eight successive, instantaneous drops of 5% relative humidity, and (iii) a varying relative humidity profile ranging between 35 and 71%. The shrinkage characteristics of mock-ups are translated to their damage susceptibility using an analytical hygro-mechanical bi-layer model. This model shows that restrained hygral shrinkage may originate from: (i) a difference in moisture content across the thickness direction of the panel, or (ii) a directional difference in the coefficient of hygroscopic expansions of structural components forming a coherent connection. The first type of shrinkage occurs in the outer regions of the panel thickness, while the second type of shrinkage takes place at the cleated ends. Further, by accounting for the age-dependency of the fracture strength of oak wood, a clear distinction can be made between the damage susceptibility of new door panels and historical door panels present in museum cabinets. The six main conclusions of the experimental study—conveniently summarized at the end of this paper—provide a scientific basis for the understanding of shrinkage cracks and dimensional changes observed on decorated oak wooden panels in historical Dutch cabinets, and thus may assist in advising museums on future sustainable preservation strategies and rational guidelines for indoor climate specifications.

Recent museum studies have indicated the appearance of cracks and dimensional changes on decorated oak panels in historical Dutch cabinets and panel paintings. A thorough analysis of these damage mechanisms is needed to obtain a comprehensive understanding of the causes of damage and to advise museums on future sustainable preservation strategies and rational guidelines for indoor climate specifications. For this purpose, a combined experimental-numerical characterization of the fracture behaviour of oak wood of various ages is presented in this communication. Three-point bending tests were performed on historical samples dated 1300 and 1668 A.D. and on new samples. The measured failure responses and fracture paths are compared against numerical results computed with a finite element model. The discrete fracture behaviour is accurately simulated by using a robust interface damage model in combination with a dissipation-based path-following technique. The results indicate that the samples dated 1300 A.D. show a quasi-brittle fracture response, while the samples dated 1668 A.D. and the new samples show a rather brittle failure response. Further, the local tensile strength of the oak wood decreases with age in an approximately linear fashion, thus indicating a so-called ageing effect. Numerical simulations show that, due to small imperfections at the notch tip of the specimen, the maximal load carrying capacity under three-point bending may decrease by maximally \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7 \%$$\end{document}7%. A comparison between a calibration of the experimental results by isotropic and orthotropic elastic models shows that the peak load is 10–\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$13\%$$\end{document}13% higher for the orthotropic elastic model. Finally, no significant dependence of the fracture toughness on the age of the oak wood and on the orientation of the fracture plane has been found. The strength and toughness values measured can be used as input for advanced numerical simulations on climate-induced damage in decorated oak wooden panels and panel paintings.

A fatigue interface damage model is presented that is based on combining a fatigue evolution law with a static interface damage model. The fatigue model elegantly enables the simulation of crack initiation and propagation in a computationally efficient and accurate way, accounting for mixed-mode loading conditions and fatigue loading of variable amplitude. The basic features of the fatigue model are explained by means of the response of an isotropic mode I specimen. In addition, the fatigue response of a fiber-epoxy specimen is analyzed, thereby illustrating the effects by load cycle blocks of different amplitude and the generation of plasticity on the fatigue life of the specimen. Finally, the fatigue response of a single lap joint is computed, showing that both the number of load cycles to failure and the evolution of local deformation correspond very well with experimental data reported in the literature.

This contribution studies failure by elastic buckling and plastic collapse of wall structures during extrusion-based 3D printing processes. Results obtained from the parametric 3D printing model recently developed by Suiker (Int J Mech Sci, 137: 145–170, 2018), among which closed-form expressions useful for engineering practice, are validated against results of dedicated FEM simulations and 3D concrete printing experiments. In the comparison with the FEM simulations, various types of wall structures are considered, which are subjected to linear and exponentially decaying curing processes at different curing rates. For almost all cases considered, the critical wall buckling length computed by the parametric model turns out to be in excellent agreement with the result from the FEM simulations. Some differences may occur for the particular case of a straight wall clamped along its vertical edges and subjected to a relatively high curing rate, which can be ascribed to the approximate form of the horizontal buckling shape used in the parametric model. The buckling responses computed by the two models for a wall structure with imperfections of different wavelengths under increasing deflection correctly approaches the corresponding bifurcation buckling length. Further, under a specific change of the material properties, the parametric model and the FEM model predict a similar transition in failure mechanism, from elastic buckling to plastic collapse. The experimental validation of the parametric model is directed towards walls manufactured by 3D concrete printing, whereby the effect of the material curing rate on the failure behaviour of the wall is explored by studying walls of various widths. At a relatively low curing rate, the experimental buckling load is well described when the parametric model uses a linear curing function. However, the experimental results suggest the extension of the linear curing function with a quadratic term if the curing process under a relatively long printing time is accelerated by thermal heating of the 3D printing facility. In conclusion, the present validation study confirms that the parametric model provides a useful research and design tool for the prediction of structural failure during extrusion-based 3D printing. The model can be applied to quickly and systematically explore the influence of the individual printing process parameters on the failure response of 3D-printed walls, which can be translated to directives regarding the optimisation of material usage and printing time.

© 2018 The Authors Numerically reproducing wind tunnel experimental tests of flow behavior around a pitching airfoil is a challenge, especially under the occurrence of dynamic stall at relatively high angles of attack. This not only requires the application of advanced turbulence models, but also asks for examining the influence of the most relevant model parameters in detail. This contribution presents the results of an extensive computational study of the unsteady flow around a pitching NACA0012 airfoil at a Reynolds number of 1.35 × 10 5 , as obtained by first performing 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations whereby the flow characteristics are simulated by the Transition SST turbulence model. The influence of a large number of parameters on the numerical results is investigated, namely the blockage ratio, computational grid resolution and y + value, time step size, inlet freestream turbulence properties, airfoil trailing edge detailing and turbulence model. Integral aerodynamic force coefficients and detailed flow patterns are analyzed and compared with measurements from wind tunnel experiments presented in the literature. For the best-performing parameters, an adequate agreement with the experimental tests is obtained for the upstroke phase, while for the downstroke phase some differences appear. These differences are investigated in more detail by considering the results from a 2.5D Large Eddy Simulation (LES), which provides deep and complementary insights into the flow behavior during dynamic stall at the selected Reynolds number. ispartof: JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS vol:183 pages:315-332 status: published

A multiscale approach termed the generalized grain cluster method (GGCM) is presented, which can be applied for the prediction of the macroscopic behavior of an aggregate of single crystal grains composing a multiphase material. The GGCM is based on the minimization of a functional that depends on the microscopic deformation gradients in the grains through the equilibrium requirements of the grains as well as kinematic compatibility between grains. By means of the specification of weighting factors it is possible to mimic responses falling between the Taylor and Sachs bounds. The numerical solution is computed with an incremental-iterative algorithm based on a constrained gradient descent method. For a multiscale analysis, the GCCM can be included at integration points of a standard finite element code to simulate macroscopic problems. A comparison with FEM direct numerical simulations illustrates that the computational time of the GGCM may be up to about an order of magnitude lower.

A multi-scale model for the analysis of granular systems is proposed, which combines the principles of a coupled FEM–DEM approach with a novel servo-control methodology for the implementation of appropriate micro-scale boundary conditions. A mesh convergence study is performed, whereby the results of a quasi-static biaxial compression test are compared with those obtained by direct numerical simulations. The comparison demonstrates the capability of the multi-scale method to realistically capture the macro-scale response, even for macroscopic domains characterized by a relatively coarse mesh; this makes it possible to accurately analyse large-scale granular systems in a computationally efficient manner. The multi-scale framework is applied to study in a systematic manner the role of individual micro-structural characteristics on the effective macro-scale response. The effect of particle contact friction, particle rotation, and initial fabric anisotropy on the overall response is considered, as measured in terms of the evolution of the effective stress, the volumetric deformation, the average coordination number and the induced anisotropy. The trends observed are in accordance with notions from physics, and observations from experiments and other DEM simulations presented in the literature. Hence, it is concluded that the present framework provides an adequate tool for exploring the effect of micro-structural characteristics on the macroscopic response of large-scale granular structures.

The efficiency and reliability of modern jet engines strongly depend on the performance of thermal barrier coatings (TBCs), which prevent melting and oxidation of the turbine blades' structural core. The system's lifetime is limited by cracks appearing in and in the vicinity of an oxide layer that grows in the TBC under thermal cycling. High replacement costs have led to an increased demand to identify, quantify and remedy damage in TBCs. An integrated experimental-numerical approach is presented for studying the main factors that contribute to damage, particularly interfacial irregularities. Damage at several stages of oxidation in TBCs is analyzed in samples with predefined interfacial irregularities. The model predicts the experimentally observed crack patterns, clearly quantifying the influence of imperfections and indicating that damage can be delayed by surface treatment. © 2009 Acta Materialia Inc.

Particulate materials loaded under uniaxial compression and tension are studied using the discrete element method. Self-healing of the damaged samples is activated through sintering, a process that effectively increases the contact adhesion (i.e. the tensile strength) between particles. The initial sample is prepared from spherical particles by applying high (isotropic) pressure, where particles in contact deform plastically and adhere to each other due to increased van der Waals forces. The result of this pressure-sintering is a solid sample from which the stress is released before uniaxial tension or compression is applied. Damage occurs "microscopically" through loss of contacts and thus loss of adhesion. In order to "self-heal" (part of) this damage, the system is sintered again, so that the adhesion at existing contacts in the damaged sample becomes stronger than originally. The stress-strain curves for the mechanically loaded samples are characterised by a peak-strength followed by a softening branch. Self-healing of an originally "weak" sample, up to a "strong" adhesion level, leads to qualitatively different stress-strain behaviour, dependent on the strain at which self-healing is applied. Interestingly, the response of the "weak" self-healed material is bounded by the damage response of the "strong" material. For an optimal self-healing of the particulate material, it is preferable to initiate the healing mechanism during the early stage of damage development, before the peak-strength is reached.

Micromechanically-based models are used to mimic the martensitic phase transformations in retained austenite and the elasto-plastic behavior of the adjacent ferritic phase. The numerical simulations concern TRIP steel samples with a finite number of grains of retained austenite embedded in a polycrystalline ferrite-based matrix. Parametric analyses are performed in order to investigate the effect of the variation of microstructural properties on the stability of retained austenite, and thus on the overall mechanical response. The microstructural parameters considered are (i) the initial volume fraction of the retained austenite, (ii) the elasto-plastic properties of the surrounding ferritic matrix, (iii) the crystallographic orientations of the ferritic and austenitic grains, and (iv) the carbon concentration in the retained austenite. The results show that the effective strength of TRIP steels increases with the carbon concentration in the retained austenite, but it depends non-monotonically on the initial volume fraction of retained austenite. It is shown that the overall strength and the martensitic transformation rate depend strongly on the crystallographic orientations of the grains and the properties of the surrounding matrix. This information is useful for the optimization of the mechanical characteristics of TRIP steels and the improvement of their processing parameters. The numerical predictions are in good qualitative agreement with experimental observations. © 2007 Elsevier B.V. All rights reserved.

In multiphase carbon steels, irreversible martensitic transformations from a parent austenitic phase are often accompanied by plastic deformations in the surrounding phases and damage growth in the martensitic product phase. In the present communication the interactions between these complex processes are studied through three-dimensional numerical analyses, where the response of the austenitic phase is simulated using a phase-changing damage model and the response of the surrounding matrix is mimicked with a plasticity model. A numerical update algorithm is provided for the phase-changing damage model, which is based on a fully implicit backward Euler scheme formulated within the framework of finite deformations. The consistent tangent operator for the model is computed using a numerical differentiation technique. Special attention is given to the robust and accurate treatment of the various constraints related to the volume fractions and damaged volume fractions of the transformation parent and product phases. The numerical analyses of a multiphase carbon steel microstructure illustrate the effect of the transformation, plasticity and damage processes on the overall stress-strain response and on the transformation and damage evolutions of the sample for various austenite crystal orientations. The computed responses are in qualitative agreement with experimental results reported in the literature. In terms of the numerical model, a variation study of the mesh density shows that the numerical results tend to converge upon mesh refinement. © 2007 IOP Publishing Ltd.

This paper discusses the triaxial testing of a ballast material and a subballast material, which are noncohesive, granular materials pically used for construction of a railway track substructure. Both static and cyclic triaxial tests were conducted. The cyclic triaxial tests simulated the behavior of these railway substructure materials under a large number of passing train wheels. The purpose of the static tests was to a priori identify the maximum stress level that could be applied in the cyclic tests, and to assess the strength and stiffness increase produced during the cyclic loading process. In order to accurately monitor the circumferential displacement during the static and cyclic tests, a new measuring device was developed. The experimental setup, the test procedure, and the test results are treated for the ballast and subballast materials. It is found that under cyclic loading the granular materials reveal a strong tendency to compact, even if the applied stress level is close to the static failure strength of the material. This compaction behavior generally causes a (significant) increase of the material strength and stiffness. Journal of Geotechnical and Geoenvironmental Engineering © ASCE.

A novel mesoscale granular continuum model is derived by homogenizing the mechanical behavior of six particles in contact forming an octahedron structure. The elastic behavior at the particle contacts is simulated in accordance with Hertz theory and the frictional behavior is taken into account by means of an evolution law for the contact shear stiffness. The mesoscale continuum model is calibrated on discrete element simulations of a cuboidal volume filled with identical spheres and loaded under axisymmetric compression. By imposing a set of radial deviatoric stress paths, the failure contour is computed in the deviatoric plane of the principal stress space. © ASCE / MARCH 2004.

The self-healing behaviour of materials with a particulate microstructure, which has experienced damage under uniaxial compression or tension, is studied with the Discrete Element Method. The stress-strain response of the particle system shows that the effective compressive and tensile strengths typically increase with the contact adhesion (i.e., the tensile strength between particles), where the effective compressive strength is about 5 times larger than the tensile strength. A sample with “weak” contact adhesion is self-healed by instantaneously increasing the contact adhesion at different deformation levels from weak to “strong”. The stress-strain curves of self-healed samples are bounded by an envelope curve that reflects the damage response of a sample that has a “strong” contact adhesion since the onset of loading. If self-healing is applied short before the peak stress is reached, the maximum sample strength will be close to maximum strength observed in the envelope curve. In contrast, if self-healing is initiated in the tensile softening regime, the maximum sample strength will be (significantly) less than the maximum strength related to the envelope curve.

SUMMARY A time integration scheme is presented for the martensitic phase transformation model developed in recent theoretical work of Turteltaub and Suiker (A multi-scale thermomechanical model for cubic to tetragonal martensitic phase transformations 2005; Transformation-induced plasticity in ferrous alloys 2005). The phase transformation model can be used for analysing transformation-induced plasticity (TRIP) phenomena in ferrous alloys. The microstructural information for the phase transformation model is provided by the crystallographic theory of martensitic transformations. The transformation characteristics depend on the specific transformation systems activated during a loading process. The time integration scheme is formulated within a framework of finite deformations, where the stressupdate algorithm is based on a fully implicit Euler backward discretization. A robust search algorithm is used for detecting the transformation systems activated during loading. The completion of the transformation process is prescribed by a constraint on the total martensitic volume fraction, which is accurately satisfied in the converged state using a sub-stepping algorithm. The computation of the consistent tangent operator is performed through a numerical differentiation method, which avoids the determination of extensive analytical derivatives and allows the model to be easily adapted if necessary. The ability of the algorithm to solve complex transformation-induced plasticity problems is illustrated with the aid of three-dimensional analyses, in which an aggregate of single-crystal grains of retained austenite embedded in a ferrite-based matrix is subjected to uniaxial tension. The response characteristics are in agreement with experimental findings of Jacques et al. (Philos. Mag. 2001; 81(7):1789; Metall. Mater. Trans. A 2001; 32A:2759) and Oliver et al. (Appl. Phys. A 2002; 74:S1143). Copyright 2005 John Wiley & Sons, Ltd.

This special issue of Philosophical Magazine contains contributions from both the computational geology and mechanics of materials communities, and deals with the modelling and numerical simulation...

The elastic-viscoplastic characteristics of the Perzyna model and the Consistency model are considered. Both theories are compared by assessing the evolution of the viscoplastic multiplier, the evolution of the internal variables and the loading/unloading conditions. An explicit expression is derived for the consistency parameter in the Consistency model. Accordingly, it is shown that the Consistency model and the Perzyna model can be treated in a novel, unified algorithmic fashion. Illustrative numerical examples are given to reveal the differences and the similarities between the models, and to elucidate the features of the proposed implicit numerical scheme.

In general, modelling of the mechanical behaviour of granular materials can be divided into two categories. Firstly, there are the discrete models, where the equilibrium conditions, the kinematic conditions and the constitutive behaviour are formulated for each individual particle with respect to its surrounding particles. Secondly, there are the continuum models, where the equilibrium conditions, the kinematic conditions and the constitutive behaviour are formulated for an assembly of particles using the continuum concepts of stress and strain. The advantage of discrete models in comparison to continuum models is that the heterogeneous effects on the particle level can be described more accurately. However, for most granular structures the number of particles is very large, which causes the number of equations that has to be solved for in a discrete system to become large as well.

Conventional homogenization theories developed for a matrix-inclusion system cannot be used for deriving the pressure-dependent elastic behaviour of a granular material. This is caused by the lack of a proper description of the high stress concentrations at the particle contacts. This paper discusses a more suitable homogenization theory, which follows from micro-structural considerations at the particle level. Accordingly, for an assembly of isotropically distributed, equal-sized spherical particles, expressions for the pressure-dependent shear modulus and the Poisson's ratio are derived. This is done for the case of hydrostatic compression. The derivation of these equations is based on the so-called best-fit hypothesis of the actual displacement field in the granular assembly. The usefulness of the equation derived for the shear modulus is illustrated via a comparison with experiment results. Copyright © 2000 John Wiley & Sons, Ltd.

Crack channelling in a brittle, flexural bilayer, composed of a coating adhering to a substrate of finite thickness, is addressed for the case of a uniform moisture content (or temperature) variation. The linear stress profile within the coating may lead to three different fracture mechanisms, which are a channelling crack with delamination absent, a channelling crack with delamination of finite length, and a channelling crack with delamination of unbounded extent. Failure mechanism maps illustrate the dependence of the active crack channelling mechanism, and the corresponding critical crack channelling stress, upon the stiffness mismatch between the layers and upon the ratio of interfacial toughness to coating toughness. Although the results are applicable to bilayers in a wide range of applications, the study focuses on the prediction of crack channelling in historical paintings. The significance of bending of the bilayer upon crack channelling is explored by comparing the fracture characteristics of the simply-supported, flexural bilayer with those of a rigidly supported bilayer that is constrained against bending. These two bilayer systems are representative of the different framing techniques commonly used for historical paintings, with the simply-supported bilayer reflecting a regular wooden panel that can bend freely, and the rigidly supported bilayer characterizing a wooden panel that does not bend as a result of cradle additions composed of several horizontal members and corresponding orthogonal cross-pieces. Independent of the type of framing technique applied, it is shown that crack channelling with delamination can be avoided in historical paintings when the delamination toughness exceeds the mode I toughness of the paint layer. Under these conditions paint flaking does not occur and the visual appearance of the painting is preserved. The failure maps constructed in this study provide a useful tool for museum conservators to identify acceptable indoor humidity and temperature variations such that historical paintings do not degrade by a combination of crack channelling and delamination.