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Abstract: Abstract The state-of-the-art locking-free meshfree Galerkin formulation for modeling the Reissner–Mindlin plate problems is plagued by the following issues: (1) the requirement of a large enough kernel support size in avoiding kernel instability because of the quadratic basis in meeting the Kirchhoff mode reproducing condition, as well as (2) the tedious construction of the conforming representative domains and the smoothed strain in the stabilized conforming integration scheme. This study introduces an efficient and stabilized approach that circumvents the above-mentioned issues. A quasi-consistent reproducing kernel approximation is first developed to enable a smaller kernel support size to be used without the moment matrix singularity issue under a controllable loss of completeness; thus, the approximation construction is accelerated. Then, a bending consistent nodal integration method is proposed where the bending consistency in Galerkin formulation is achieved via an assumed strain approach without using the conforming cell. A variational multiscale stabilization method from our earlier research is implemented to avoid low energy instability while maintaining the locking-free property. The performance of the present formulation is validated in several benchmark problems. PubDate: 2022-12-01

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Abstract: Abstract The approximation of steady-state vibrations within non-linear dynamical systems is well-established in academics and is becoming increasingly important in industry. However, the complexity and the number of degrees of freedom of application-oriented industrial models demand efficient approximation methods for steady-state solutions. One possible approach to that problem are hybrid approximation schemes, which combine advantages of standard methods from the literature. The common ground of these methods is their description of the steady-state dynamics of a system solely based on the degrees of freedom affected directly by non-linearity—the so-called non-linear degrees of freedom. This contribution proposes a new hybrid method for approximating periodic solutions of systems with localised non-linearities. The motion of the non-linear degrees of freedom is approximated using the Finite Difference method, whilst the motion of the linear degrees of freedom is treated with the Harmonic Balance method. An application to a chain of oscillators showing stick-slip oscillations is used to demonstrate the performance of the proposed hybrid framework. A comparison with both pure Finite Difference and Harmonic Balance method reveals a noticeable increase in efficiency for larger systems, whilst keeping an excellent approximation quality for the strongly non-linear solution parts. PubDate: 2022-12-01

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Abstract: Abstract We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems. PubDate: 2022-12-01

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Abstract: Abstract This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at least \(C^2\) -continuity, which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom. PubDate: 2022-12-01

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Abstract: Abstract This contribution picks up on a novel approach for a first order homogenization procedure based on the Irving-Kirkwood theory and provides a finite element implementation as well as applications to beam and plate structures. It does not have the fundamental problems of dependency from representative volume element (RVE) size in determining the shear and torsional stiffness for beams and plates, that is present in classic Hill-Mandel methods. Due to the possibility of using minimal boundary conditions whilst simultaneously reusing existing homogenization algorithms, creation of models and numerical implementation are much more straight forward. The presented theory and FE formulation are limited to materially and geometrically linear problems. The approach to determining shear stiffness is based on the assumption of a quadratic shear stress distribution over the height (and width in case of the beam), which causes warping of the cross-section under transverse shear loading. Results for the homogenization scheme are shown for various beam and plate configurations and compared to values from well known analytical solutions or computed full scale models. PubDate: 2022-12-01

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Abstract: Abstract Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results. PubDate: 2022-12-01

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Abstract: Abstract Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future of monitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results. PubDate: 2022-12-01

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Abstract: Abstract Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model has shown many advantages in this field. In this contribution, we present significant aspects related to the relaxed micromorphic model realization with the finite element method (FEM). The variational problem is derived and different FEM-formulations for the two-dimensional case are presented. These are a nodal standard formulation \(H^1({{\mathcal {B}}}) \times H^1({{\mathcal {B}}})\) and a nodal-edge formulation \(H^1({{\mathcal {B}}}) \times H({\text {curl}}, {{\mathcal {B}}})\) , where the latter employs the Nédélec space. In this framework, the implementation of higher-order Nédélec elements is not trivial and requires some technicalities which are demonstrated. We discuss the computational convergence behavior of Lagrange-type and tangential-conforming finite element discretizations. Moreover, we analyze the characteristic length effect on the different components of the model and reveal how the size-effect property is captured via this characteristic length parameter. PubDate: 2022-12-01

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Abstract: Abstract This paper presents a novel approach to coupling beam and solid elements. Connecting standard beam elements with solid elements results in a situation where the solid part of the model covers the cross-sectional deformation, while at the beam part assumptions only consider the rigid body movement of the cross-section. Therefore, kinematic assumptions do not include cross-section deformations such as warping and contraction. Due to this restriction, spurious stresses occur at the transition zone. To circumvent this problem, this contribution introduces a mixed hybrid transition element based on an extended Hu–Washizu functional. The extension allows the cross-section to contract and warp. Compared with other approaches that include these phenomena, precomputation of the warping function is unnecessary. The present approach considers the cross-sectional deformation using local variables. On the solid interface, there are only displacement degrees of freedom (depending on the solid discretization), whereas on the beam interface, there are two displacement degrees of freedom and one rotation. This allows beam-like parts of the solid model to be replaced with standard beam elements without affecting the overall accuracy of the model. Besides solid–beam coupling, the proposed formulation can also be used to apply beam-like boundary conditions as well as stress resultants to the solid interface. For the sake of simplicity and without restricting generality, the underlying element formulation is introduced for the 2D linear elastic case. Numerical examples demonstrate that the transition element causes no spurious stress distributions on the solid part. The results of full solid models are compared with mixed beam–solid models. PubDate: 2022-12-01

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Abstract: Abstract Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining accurate solutions remain challenging. Immersed boundary techniques provide elegant solutions for such problems. Enrichment methods alleviate the need for generating conforming analysis grids by capturing discontinuities within mesh elements. Additionally, increased accuracy of physical responses and geometry description can be achieved with higher-order approximation bases. In particular, using B-splines has become popular with the development of IsoGeometric Analysis. In this work, an eXtended IsoGeometric Analysis (XIGA) approach is proposed for multi-material problems. The computational domain geometry is described implicitly by level set functions. A novel generalized Heaviside enrichment strategy is employed to accommodate an arbitrary number of materials without artificially stiffening the physical response. Higher-order B-spline functions are used for both geometry representation and analysis. Boundary and interface conditions are enforced weakly via Nitsche’s method, and a new face-oriented ghost stabilization methodology is used to mitigate numerical instabilities arising from small material integration subdomains. Two- and three-dimensional heat transfer and elasticity problems are solved to validate the approach. Numerical studies provide insight into the ability to handle multiple materials considering sharp-edged and curved interfaces, as well as the impact of higher-order bases and stabilization on the solution accuracy and conditioning. PubDate: 2022-12-01

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Abstract: Abstract In this paper the formulation of hybrid-Trefftz displacement finite elements for transient problems in three-dimensional elastic media is derived. The mathematical model is derived from the classical theory of elasticity. The governing domain and boundary equations are discretized in time using a wavelet basis expansion to yield a series of spectral problems which only depend on space. Displacements are the main approximation in the domain of the element (displacement model) and tractions are approximated on the essential boundaries (hybrid formulation). The displacement trial functions are constrained to satisfy exactly the domain equations (Trefftz constraint), and consist of one family of compression waves and two families of shear waves. The problem is reduced to solving an algebraic system whose unknowns are the weights of the displacement bases. Strains and stresses are derived from the displacement approximations through the compatibility and elasticity equations. The formulation is implemented as a new module in FreeHyTE, an open-source and user-friendly Trefftz platform. Numerical tests have been carried out with the new 3D FreeHyTE module implemented with the functions derived in this paper and the results are satisfactory. PubDate: 2022-12-01

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Abstract: Abstract In this article, we propose a data-driven multi-flaw detection strategy based on deep learning and the boundary element method (BEM). In the training phase, BEM is implemented to generate the database, while the block LU decomposition technique is employed to reduce the computational cost. Then the Convolutional Neural Networks (CNNs) are adopted as a deep learning model to find the relationship between the input signals and the geometries of flaws through the training process. In the test phase, the performance of trained models will be evaluated with unseen data. As a typical inverse problem, the solution to a flaw detection problem is not always unique. In the present work, we demonstrate that such non-uniqueness is detrimental to the training process, and avoid them through some specific treatments. In order to enhance the robustness of the model, the idea of data augmentation is introduced to flaw detection tasks. The numerical results show that the presented model could produce accurate predictions in both single- and multi-flaw detection tasks with proper training. Additionally, data augmentation could significantly help against the noise. PubDate: 2022-11-23

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Abstract: Abstract Under fatigue loading, the stiffness decrease in short-fiber reinforced polymers reflects the gradual degradation of the material. Thus, both measuring and modeling this stiffness is critical to investigate and understand the entire fatigue process. Besides evolving damage, viscoelastic effects within the polymer influence the measured dynamic stiffness. In this paper, we study the influence of a linear viscoelastic material model for the matrix on the obtained dynamic stiffness and extend an elastic multiscale fatigue-damage model to viscoelasticity. Our contribution is two-fold. First, we revisit the complex-valued elastic models known in the literature to predict the asymptotic periodic orbit of a viscoelastic material. For small phase shifts in an isotropic linear viscoelastic material, we show through numerical experiments that a real-valued computation of an “elastic” material is sufficient to approximate the dynamic stiffness of a microstructure with a generalized Maxwell material and equal Poisson’s ratios in every element as matrix, reinforced by elastic inclusions. This makes standard solvers applicable to fiber-reinforced thermoplastics. Secondly, we propose a viscoelastic fatigue-damage model for the thermoplastic matrix based on decoupling of the time scales where viscoelastic and fatigue-damage effects manifest. We demonstrate the capability of the multiscale model to predict the dynamic stiffness evolution under fatigue loading of short-fiber reinforced polybutylene terephthalate (PBT) by a validation with experimental results. PubDate: 2022-11-22

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Abstract: Abstract This paper presents a predictive computational framework for surrogate modeling of pressure field and optimization of pressure sensor placement for wind engineering applications. Firstly, a machine learning-derived surrogate model, trained by high-fidelity simulation data using finite element-based CFD and informed by a turbulence model, is developed to construct the full-field pressure from scattered sensor measurements in near real-time. Then, the surrogate pressure model is embedded in another neural network (NN) for optimizing pressure sensor placement. The goal of the NN-based optimizer is to learn the best layout of a fixed number of pressure sensors over the structural surface to deliver the most accurate full-field pressure prediction for various inflow wind conditions. We deploy the model to a representative low-rise building subjected to different wind conditions. The performance of the proposed framework is assessed by comparing the predicted results with finite element-based CFD simulation results. The framework shows excellent accuracy and efficiency, which could be potentially integrated with structural health monitoring to enable digital twins of civil structures. PubDate: 2022-11-21

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Abstract: Abstract We propose a data-driven framework to increase the computational efficiency of the explicit finite element method in the structural analysis of soft tissue. An encoder–decoder long short-term memory deep neural network is trained based on the data produced by an explicit, distributed finite element solver. We leverage this network to predict synchronized displacements at shared nodes, minimizing the amount of communication between processors. We perform extensive numerical experiments to quantify the accuracy and stability of the proposed synchronization-avoiding algorithm. PubDate: 2022-11-15

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Abstract: Abstract In this research work, the radial basis function finite difference method (RBF-FD) is further developed to solve one- and two-dimensional boundary value problems in linear elasticity. The related differentiation weights are generated by using the extended version of the RBF utilizing a polynomial basis. The type of the RBF is restricted to polyharmonic splines (PHS), i.e., a combination of the odd m-order PHS \(\phi (r)=r^m\) with additional polynomials up to degree p will serve as the basis. Furthermore, a new residual-based adaptive point-cloud refinement algorithm will be presented and its numerical performance will be demonstrated. The computational efficiency of the PHS RBF-FD approach is tested by means of the relative errors measured in \(\ell _2\) -norm on several representative benchmark problems with smooth and non-smooth solutions, using h-adaptive, uniform, and quasi-uniform point-cloud refinement. PubDate: 2022-11-14

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Abstract: Abstract This article considers an inverse problem for a Cosserat rod where we are given only the position of the centreline of the rod and must solve for external forces and torques as well as the orientation of the cross sections of the centreline. We formulate the inverse problem as an optimal control problem using the position of the centreline as an objective function with the external force and torque as control variables, with meaningful regularisation of the orientations. A monolithic, implicit numerical scheme is proposed in the sense that primal and adjoint equations are solved in a fully-coupled manner and all the nonlinear coefficients of the governing partial differential equations are updated to the current state variables. The forward formulation, determining rod configuration from external forces and torques, is first validated by a numerical benchmark; the solvability and stability of the inverse problem are then tested using data from forward simulations. The proposed optimal control method is motivated by reconstruction of the orientations of a rod’s cross sections, with its centreline being captured through imaging protocols. As a case study, we take the locomotion of the nematode, Caenorhabditis elegans. In this study we take laboratory data for its centreline and infer its cross-section orientation (muscle locations) with the control force and torque being interpreted as the reaction force, activated by C. elegans’ muscles, from the surrounding fluids. This method thus combines the mathematical modelling and laboratory data to study the locomotion of C. elegans, which gives us insights into the potential anatomical orientation of the worm beyond what can be observed through the laboratory data. The paper is completed with several additional remarks explaining the theoretical and technical details of the model. PubDate: 2022-11-14

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Abstract: Abstract We aim to enhance the stability of finite element models of dynamic structural contact with multiphase granular soils which are described by advanced soil plasticity models that can simulate monotonic and cyclic behaviour of multiphase soils. Often, numerical oscillations cannot be avoided in these contact models and can cause advanced soil models to significantly overshoot stress, leading to unrealistic discontinuities in the stress paths. This situation can challenge the stability of the stress integration scheme and the global finite element solver and lead to the early termination of the analysis. We specifically address the issue of stress overshooting by presenting novel solutions and the corresponding stress integration schemes for a representative soil model for unsaturated granular soils. Also, several examples are provided to evaluate the integration scheme and show the advantages and limitations of the proposed overshooting solutions in solving a contact-impact problem involving unsaturated granular soils. PubDate: 2022-11-14

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Abstract: Abstract A novel computational approach to predicting fatigue crack initiation life in additively manufactured microlattice structures is proposed based on a recently developed microplasticity-based constitutive theory. The key idea is to use the concept of (micro)plastic dissipation as the driving factor to model fatigue degradation in additively manufactured metallic microlattice. An ad-hoc curve-fitting procedure is proposed to calibrate the introduced material constitutive parameters efficiently. The well-calibrated model is employed to obtain fatigue life predictions for microlattices through a diverse set of RVE-based finite element fatigue simulations. The model’s predictive capabilities are verified by comparing the simulation results with experimental fatigue data reported in the literature. The overall approach constitutes a unified setting for fatigue life prediction of additively manufactured microlattice structures ranging from low- to high-cycle regimes. It is also shown that the model can be applied to technologically relevant microlattices with mathematically-created complex microstructure topologies. PubDate: 2022-11-10

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