Identifying elastoplastic parameters with Bayes' theorem considering double error sources and model uncertainty

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 ▲]

h- and p-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics

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 ▲]

Linear smoothed extended finite element method for fatigue crack growth simulations

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 ▲]

Simple and extensible plate and shell finite element models through automatic code generation tools

in Computers and Structures (2018), 209

A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore ... [more ▼]

A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore, it is often not straightforward to adapt existing implementations to emerging frontier problems in thin structural mechanics including nonlinear material behaviour, complex microstructures, multi-physical couplings, or active materials. We show that by using a high-level mathematical modelling strategy and automatic code generation tools, a wide range of advanced plate and shell finite element models can be generated easily and efficiently, including: the linear and non-linear geometrically exact Naghdi shell models, the Marguerre-von K ́arm ́an shallow shell model, and the Reissner-Mindlin plate model. To solve shear and membrane-locking issues, we use: a novel re-interpretation of the Mixed Interpolation of Tensorial Component (MITC) procedure as a mixed-hybridisable finite element method, and a high polynomial order Partial Selective Reduced Integration (PSRI) method. The effectiveness of these approaches and the ease of writing solvers is illustrated through a large set of verification tests and demo codes, collected in an open-source library, FEniCS-Shells, that extends the FEniCS Project finite element problem solving environment. [less ▲]

The elastic properties of composites reinforced by a transversely isotropic random fibre-network

in Composite Structures (2018), 208

This research stems from the idea of introducing a fibre-network structure into composites aiming to enhance the stiffness and strength of the composites. A novel new type of composites reinforced by a ... [more ▼]

This research stems from the idea of introducing a fibre-network structure into composites aiming to enhance the stiffness and strength of the composites. A novel new type of composites reinforced by a tranversely isotropic fibre-network in which the fibres are devided into continuous segments and randomly distributed has been proposed and found to have improved elastic properties compared to other conventional fibre or particle composites mainly due to the introduction of cross linkers among the fibres. Combining with the effects of Poisson’s ratio of the constituent materials, the fibre network composite can exhibit extraordinary stiffness. A simplified analytical model has also been proposed for comparison with the numerical results, showing close prediction of the stiffness of the fibre-network composites. Moreover, as a plate structure, the thickness of the fibre network composite is adjustable and can be tailored according to the dimensions and mechanical properties as demanded in industry. [less ▲]

Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization

in Computer Methods in Applied Mechanics and Engineering (2018)

Partition of unity enrichment is known to significantly enhance the accuracy of the finite element method by allowing the incorporation of known characteristics of the solution in the approximation space ... [more ▼]

Partition of unity enrichment is known to significantly enhance the accuracy of the finite element method by allowing the incorporation of known characteristics of the solution in the approximation space. However, in several cases it can further cause conditioning problems for which a number of remedies have been proposed in the framework of the extended/generalized finite element method (XFEM/GFEM). Those solutions often involve significant modifications to the initial method and result in increased implementation complexity. In the present work, a simple procedure for the local near-orthogonalization of enrichment functions is introduced, which significantly improves the conditioning of the resulting system matrices, while requiring only minor modifications to the initial method. Although application to different types of enrichment functions is possible, the resulting scheme is specialized for the singular enrichment functions used in linear elastic fracture mechanics and tested through benchmark problems. [less ▲]

Identifying material parameter distributions of fibers with extremely limited experimental efforts

Scientific Conference (2018, July 22)

Data-driven modelling and simulation: fracture and medical simulations

Presentation (2018, February 08)

Predicting failure in aircraft structures – simulating fracture across scales and times You could fly every day of your life in a commercial aircraft for twenty thousand years without suffering a fatal ... [more ▼]

Predicting failure in aircraft structures – simulating fracture across scales and times You could fly every day of your life in a commercial aircraft for twenty thousand years without suffering a fatal accident. This extraordinary level of safety is the product of decades of engineering and materials science research. Simultaneously, engineers have strived to produce lighter and stronger aircraft, with increased range and metals have thus been gradually replaced by lighter advanced composite materials which take up more than half of the structural weight of today's most advanced aircraft. Such progress has been largely enabled by modeling and simulation of materials and structures, which have revolutionized design by enabling engineers to investigate virtually various design strategies. This presentation will focus on the challenges which have been posed, are posed, and will be posed to such modeling and simulation tools in the strive to predict the durability of lighter, stronger, longer-ranging and more reliable aircraft. [less ▲]

Multiple crack detection in 3D using a stable XFEM and global optimization

in Computational Mechanics (2018)

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid ... [more ▼]

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity. [less ▲]

3D meso-scale modelling of foamed concrete based on X-ray Computed Tomography

in Construction and Building Materials (2018), 188

Foamed concrete has been widely used in infrastructure construction and poses new challenges to design and modelling. This paper investigates the behaviour of foamed concrete with the help of X-ray ... [more ▼]

Foamed concrete has been widely used in infrastructure construction and poses new challenges to design and modelling. This paper investigates the behaviour of foamed concrete with the help of X-ray Computed Tomography (XCT), which is capable of characterising the microstructure of foamed concrete. An in situ compressive test-XCT scan is carried out to observe the failure mechanism of foamed concrete by XCT when subjected to compression load. A meso-scale simulation based on XCT images is conducted to simulate the behaviour of foamed concrete. An algorithm that directly reconstructs the meso-scale model from XCT images is developed. The experimental and numerical results show that foamed concrete exhibits a significant change in mechanical behaviour; it is less brittle compared to the response of dense samples. However, the reduction in the level of brittleness is accompanied by a significant decrease in compressive strength. Failure development inside samples is successfully captured by the XCT scan and the meso-scale modelling. The topology of foamed structures, in particular the chain of interconnected pores, influences the failure mechanism of foamed concrete. The combination of XCT scan and meso-scale modelling provides a comprehensive framework to understand the mechanical behaviour of foamed concrete. [less ▲]