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Multiscale fracture: a natural connection between reduced order models and homogenisation Bordas, Stéphane ; Beex, Lars ; Chen, Li et al Scientific Conference (2019, May 13) Detailed reference viewed: 162 (14 UL)Displacement based polytopal elements a strain smoothing and scaled boundary approach Bordas, Stéphane ; Scientific Conference (2019, May 03) Detailed reference viewed: 177 (12 UL)ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS ; ; Bordas, Stéphane et al Scientific Conference (2019, April 11) We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼] We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲] Detailed reference viewed: 330 (24 UL)A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics ; Bordas, Stéphane ; et al in Acta Mechanica (2019), 230 In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM ... [more ▼] In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard interpolation, the weighted strain filed can be obtained, which will be utilized to construct the discretized system equations. The validity of the presented method is fully investigated through several numerical examples. From these results, it is shown that compared with standard XFEM, the presented method can achieve much better accuracy, efficiency and higher convergence, when dealing with fracture analysis. [less ▲] Detailed reference viewed: 53 (0 UL)A unified polygonal locking-free thin/thick smoothed plate element ; ; et al in Composite Structures (2019), 219 A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary ... [more ▼] A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary polygons and on each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The plate is made of functionally graded material with effective properties computed using the rule of mixtures. The influence of various parameters, viz., the plate aspect ratio and the material gradient index on the static bending response and the first fundamental frequency is numerically studied. It is seen that the proposed element: (a) has proper rank; (b) does not require derivatives of shape functions and hence no isoparametric mapping required; (c) independent of shape and size of elements and (d) is free from shear locking. [less ▲] Detailed reference viewed: 89 (0 UL)Introduction to Isogeometric Analysis Bordas, Stéphane ; Lian, Haojie ; Ding, Chensen Report (2019) Detailed reference viewed: 122 (8 UL)A unified enrichment approach addressing blending and conditioning issues in enriched finite elements ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2019), 349 We present a combination of techniques to improve the convergence and conditioning properties of partition of unity (PU) enriched finite element methods. By applying these techniques to different types of ... [more ▼] We present a combination of techniques to improve the convergence and conditioning properties of partition of unity (PU) enriched finite element methods. By applying these techniques to different types of enrichment functions, namely polynomial, discontinuous and singular, higher order convergence rates can be obtained while keeping condition number growth rates similar to the ones corresponding to standard finite elements. [less ▲] Detailed reference viewed: 89 (0 UL)Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties Ding, Chensen ; ; et al in Computer Methods in Applied Mechanics and Engineering (2019), 349 Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially ... [more ▼] Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decomposition accelerated Monte Carlo stochastic isogeometric method (IGA-POD-MCS) for stochastic analysis of exactly represented (composite) structures. This approach particularly enables high-dimensional material uncertainties wherein the characteristics of each element are independent. And the novelties include: (1) the structural geometry is exactly modeled thanks to isogeometric analysis (IGA), as well as providing more accurate deterministic and stochastic solutions, (2) we innovatively consider high-dimensional and independent material uncertainties by separating the stochastic mesh from the IGA mesh, and modeling different stochastic elements to have different (independent) uncertainty behaviors, (3) the classical Monte Carlo simulation (MCS) is employed to universally solve the high-dimensional uncertainty problem. However, to circumvent its computational expense, we employ model order reduction via proper orthogonal decomposition (POD) into the IGA coupled MCS stochastic analysis. In particular, we observe that this work decouples all IGA elements and hence permits independent uncertainty models easily, thereby the engineering problem is modeled to be more realistic and authentic. Several illustrative numerical examples verify the proposed IGA-POD-MCS approach is effective and efficient; and the larger the scale of the problem is, the more advantageous the method will become. [less ▲] Detailed reference viewed: 47 (2 UL)A simple and robust computational homogenization approach for heterogeneous particulate composites ; ; et al in Computer Methods in Applied Mechanics and Engineering (2019), 349 In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM ... [more ▼] In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM with multiscale finite element methods (MsFEM). The multi-split XFEM is capable to model multiple discontinuities in a single element which leads to reduction in the number of mesh elements, whereas MsFEM helps in reducing the computational time. Strain energy based homogenization has been implemented on an RVE (having volume fraction of heterogeneities up to 50%) for evaluating the elastic properties. From macro-element size analysis, we estimate that the RVE edge length must be 5 times the edge length of the macro-element. The directional analysis has been performed to verify the isotropic behavior of the material, whereas contrast analysis has been done to check the numerical accuracy of the proposed scheme. A level set correction (LSC) based on higher order shape functions has been proposed to reduce mapping errors of level set values. It is also observed that multi-split MsXFEM is about 16 times computationally more efficient than MsXFEM for 50% volume of heterogeneities. [less ▲] Detailed reference viewed: 66 (0 UL)Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Bordas, Stéphane Learning material (2019) Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Detailed reference viewed: 590 (24 UL)B-Spline FEM for Time-Harmonic Acoustic Scattering and Propagation ; ; Bordas, Stéphane in Journal of Theoretical and Computational Acoustics (2019), 27 We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing ... [more ▼] We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing Boundary Conditions (ABCs) are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the numerical method, in particular of the size of the pollution error. Numerical results performed with high-order basis functions (third or fourth order) showed no visible pollution error even for very high frequencies. To prove the ability of the method to increase its accuracy in the high frequency regime, we show how to implement a high-order Padé-type ABC on the fictitious outer boundary. The above-mentioned properties combined with exact geometrical representation make B-Spline FEM a very promising platform to solve high-frequency acoustic problems. [less ▲] Detailed reference viewed: 71 (1 UL)A one point integration rule over star convex polytopes ; ; et al in Computers and Structures (2019), 215 In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it ... [more ▼] In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor’s expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. The convergence properties, the accuracy and the efficacy of the one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲] Detailed reference viewed: 78 (0 UL)Model I cohesive zone models of different rank coals ; Lian, Haojie ; et al in International Journal of Rock Mechanics and Mining Sciences (2019), 115 The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals ... [more ▼] The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals and anthracite, through disk-shaped compact tension tests. Firstly, the experiments show that with the coal rank rising, the critical crack separation displacements and the degrees of the nonlinearity of the softening function decline gradually. By fitting the experimental data with the four commonly used cohesive zone models including the power law, the exponential law, the bilinear law and the linear law, the best-fitted model for each rank of coals was identified and the corresponding parameters were found. Secondly, to arrive at a general CZM formulation for the different rank coals, Karihaloo’s polynomial law was employed, which also gave better fit to the experimental data compared with the aforementioned four CZMs. After obtaining the CZM for coals, fracture energy was evaluated which is equal to the area under the softening curve. With the increase of the coal rank, the fracture energy reduces but its coefficient of variation increases. Thirdly, the geometric characteristics of fractures in different rank coals are studied. The lower rank coals have more tortuous crack propagation paths and larger roughness coefficients, whereas the higher rank coals possess wider average fracture apertures. Lastly, in order to further test the applicability of the obtained cohesion-separation laws, we implemented the Karihaloo’s polynomial CZM and the bilinear CZM into the cohesive elements of ABAQUS® using the user-subroutine VUMAT, and thereby simulated the crack propagation in single-edge notched beams made of weakly caking coals, fat coals, and meager-lean coals, respectively. It is found that the numerical results based on Karihaloo’s polynomial CZM have a better agreement with the experimental data than the bilinear CZM [less ▲] Detailed reference viewed: 67 (0 UL)Meshing or not meshing - Iso/sub/super-geometric analysis (adaptive unfitted methods for real-time simulations) Immersed collocation methods
Bordas, Stéphane Scientific Conference (2019, January 04) Detailed reference viewed: 283 (41 UL)A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al in Archives of Computational Methods in Engineering (2019) The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already ... [more ▼] The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress–strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress–strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions. [less ▲] Detailed reference viewed: 722 (111 UL)Identifying elastoplastic parameters with Bayes' theorem considering double error sources and model uncertainty Rappel, Hussein ; Beex, Lars ; et al in Probabilistic Engineering Mechanics (2019), 55 We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in ... [more ▼] We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more. [less ▲] Detailed reference viewed: 396 (67 UL)Geometrical and material uncertainties for the mechanics of composites ; Bordas, Stéphane ; et al Scientific Conference (2019) Detailed reference viewed: 139 (15 UL)h- and p-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics ; ; et al in Computers and Mathematics with Applications (2018), 77(9), 2369-2395 In this work, we demonstrate the application of PHT-splines for time-harmonic acoustic problems, modeled by the Helmholtz equation. Solutions of the Helmholtz equation have two features: global ... [more ▼] In this work, we demonstrate the application of PHT-splines for time-harmonic acoustic problems, modeled by the Helmholtz equation. Solutions of the Helmholtz equation have two features: global oscillations associated with the wave number and local gradients caused by geometrical irregularities. We show that after a sufficient number of degrees of freedom is used to approximate global oscillations, adaptive refinement can capture local features of the solution. We compare residual-based and recovery-based error estimators and investigate the performance of -refinement. The simulations are done in the context of recently introduced Geometry Independent Field approximaTion (GIFT), where PHT-splines are only used to approximate the solution, while the computational domain is parameterized with NURBS. This approach builds on the natural adaptation ability of PHT-splines and avoids the re-parameterization of the NURBS geometry during the solution refinement process. [less ▲] Detailed reference viewed: 92 (0 UL)The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses ; Lian, Haojie ; et al in International Journal of Rock Mechanics and Mining Sciences (2018), 113 To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for ... [more ▼] To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for hydraulic tests in the experiments. According to the experimental results of the relationships between the hydraulic gradient and the flow rate, it is demonstrated that the Forchheimer's equation can offer a good description of the non-Darcy flow in rough fractures. In addition, the coefficients A and B in Forchheimer's equation are sensitive to the fracture geometric characteristics, and their values also increase as the confining stress rises, mainly owing to the reduction of the hydraulic aperture and the heterogeneous distribution of the interconnected void areas with the confining stress rising. Then, the surface and interior geometric properties of rough fractures were quantitatively characterized with the peak asperity height and the box-counting fractal dimension of the heterogeneous distribution of the interconnected void areas, respectively. Furthermore, an empirical relationship between the fractal dimension D and the fracture apertures was constructed according to the experimental results. Lastly, a quantitative model was proposed to represent the relationship between the fracture geometric characteristics and the non-Darcy coefficient . This model was further used to link the non-linear coefficient of Forchheimer's equation and the critical Reynold number with the fracture geometric characteristics. The proposed models were validated by the experimental data and would be helpful to characterize the non-Darcy flow behavior in rough fractures under various confining stresses. [less ▲] Detailed reference viewed: 60 (0 UL)Linear smoothed extended finite element method for fatigue crack growth simulations ; ; et al in Engineering Fracture Mechanics (2018), 206 In this paper, the recently proposed linear smoothed extended finite element method (LSmXFEM) is employed to simulate the fatigue crack growth. Unlike the conventional extended finite element method, the ... [more ▼] In this paper, the recently proposed linear smoothed extended finite element method (LSmXFEM) is employed to simulate the fatigue crack growth. Unlike the conventional extended finite element method, the LSmXFEM does not require special numerical integration technique to integrate the terms in the stiffness matrix. The stress intensity factors (SIFs) are evaluated by using the domain form of the interaction integral technique. The fatigue crack growth rate is evaluated using the generalized Paris’ law in conjunction with the maximum hoop stress criterion. The robustness of the method is demonstrated with a few examples for which the results are available in the literature. Then, the fatigue crack growth from the numerical simulation is compared with the experimental investigations performed on CR5 grade cold formed steel. It is seen that the fatigue life and the crack path obtained from the proposed method is in close agreement with the experimental observation. [less ▲] Detailed reference viewed: 76 (0 UL) |
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