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Abstract: Abstract This paper introduces a continuous finite element model to simulate fluid flow-bedform interaction problems. The approach utilizes a non-oscillatory finite element algorithm to compute the fluid dynamics by solving the complete Navier–Stokes equations. Additionally, it addresses the evolution of the fluid–bedform interface as a consequence of spatially non-balanced sediment fluxes through the solution of a conservation equation for the erodible layer thickness. A sign preservation algorithm is particularly relevant for landform tracking because a positive definite thickness of the erodible sediment layer is essential to model the interaction between evolving cohesionless sediment layers and rigid beds. The fluid/terrain interface is explicitly captured through a surface tracking methodology. First, new nodes fitting the interface are incorporated into the finite element mesh; then, elements beneath this interface are deactivated, while intersected elements are restructured to get a mesh composed exclusively of tetrahedral elements. Numerical experiments demonstrate capabilities of the method by exploring relevant problems related with civil engineering, such as the evolution of trenches and the scour of a submerged pile. PubDate: 2024-03-02

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Abstract: Abstract Stress reconstruction based on experimentally acquired full-field strain measurements is computationally expensive when using conventional implicit stress integration algorithms. The computational burden associated with repetitive stress reconstruction is particularly relevant when inversely characterizing plastic material behaviour via inverse methods, like the nonlinear Virtual Fields Method (VFM). Spatial and temporal down-sampling of the available full-field strain data is often used to mitigate the computational effort. However, for metals subjected to non-linear strain paths, temporal down-sampling of the strain fields leads to erroneous stress states biasing the identification accuracy of the inverse method. Hence, a significant speedup factor of the stress integration algorithm is required to fully exploit the experimental data acquired by Digital Image Correlation (DIC). To this end, we propose an explicit stress integration algorithm that is independent on the number of images (i.e. strain fields) taken into account in the stress reconstruction. Theoretically, the proposed method eliminates the need for spatial and temporal down-sampling of the experimental full-field data used in the nonlinear VFM. Finally, the proposed algorithm is also beneficial in the emerging field of real-time DIC applications. PubDate: 2024-03-02

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Abstract: Abstract We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes which accounts for a coupling of the fiber-length and the fiber-orientation. For prescribed fiber-length distribution and fiber-orientation tensor of second order, a maximum-entropy estimate is used to produce a fiber-length-orientation distribution which mimics real injection molded specimens, where longer fibers show a stronger alignment than shorter fibers. We derive the length-orientation closure from scratch, discuss its integration into the sequential addition and migration algorithm for generating fiber-filled microstructures for industrial volume fractions and investigate the resulting effective elastic properties. We demonstrate that accounting for the length-orientation coupling permits to match the measured Young’s moduli in principal fiber direction and transverse to it more accurately than for closure approximations ignoring the length-orientation coupling. PubDate: 2024-02-24

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Abstract: Abstract A new crack-tip finite element able to improve the accuracy of Finite Element Method (FEM) solutions for cracks growing along the Winkler-type spring interfaces between linear elastic adherents is proposed. The spring model for interface fracture, sometimes called Linear-Elastic (perfectly) Brittle Interface Model (LEBIM), can be used, e.g., to analyse fracture of adhesive joints with a thin adhesive layer. Recently an analytical expression for the asymptotic elastic solution with logarithmic stress-singularity at the interface crack tip considering spring-like interface behaviour under fracture Mode III was deduced by some of the authors. Based on this asymptotic solution, a special 5-node triangular crack-tip finite element is developed. The generated special singular shape functions reproduce the radial behaviour of the first main term and shadow terms of the asymptotic solution. This special element implemented in a FEM code written in Matlab has successfully passed various patch tests with spring boundary conditions. The new element allows to model cracks in spring interfaces without the need of using excessively refined FEM meshes, which is one of the current disadvantages in the use of LEBIM when stiff spring interfaces are considered. Numerical tests carried out by h-refinement of uniform meshes show that the new singular element consistently provides significantly more accurate results than the standard finite elements, especially for stiff interfaces, which could be relevant for practical applications minimizing computational costs. The new element can also be used to solve other problems with logarithmic stress-singularities. PubDate: 2024-02-24

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Abstract: Abstract This paper introduces a metamodelling technique that employs gradient-enhanced Gaussian process regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor \(\varvec{F}\) and electric displacement field \(\varvec{D}_0\) . The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indifference and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the first Piola-Kirchhoff stress tensor and material electric field. The method ensures stress and electric field-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric field \(\varvec{E}_0\) , is inappropriate. The saddle point nature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of \(\varvec{F}\) and \(\varvec{E}_0\) (free energy-based GPR), compared to those involving \(\varvec{F}\) and \(\varvec{D}_0\) (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate model accuracy across challenging scenarios, comparing displacement and stress fields with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach. PubDate: 2024-02-20

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Abstract: Abstract A curved non-isoparametric Reissner–Mindlin shell element is developed for analyzing thin-walled structures. The standard kinematic description of the element requires the calculation of the director vector. To address this demand accurately, similar to isogeometric analysis (IGA), the geometry is defined by utilization of the non-uniform rational B-splines (NURBS) imported directly from computer-aided design (CAD) files. Then, shape functions of the Legendre spectral element method (SEM) are used to interpolate the displacements. Consequently, the shell director vector and Jacobian of the transformation are calculated properly according to the presented formulation. On the other hand, in Legendre SEM combined with Gauss–Lobatto–Legendre quadrature, the integration points and the element nodes coincide. Thus, the easily computable local coordinate systems at the integration points can be used directly as nodal basis systems. A separate calculation of nodal basis systems at control points, which is the source of either complexity or error in IGA shells, is not required. Given the condition number of the stiffness matrix in the developed method, super high-order elements can also be used. Very high order p-refined elements are used in addition to h-refinement of the mesh to show the capability of higher order elements to analyze problems without mesh refinement. The validity and convergence rate of the method are investigated and verified through various cases of h- and p-refinement in challenging obstacle course problems. PubDate: 2024-02-20

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Abstract: Abstract The aim of this work is the derivation and examination of a material model, accounting for large elastic deformations, coupled with species diffusion and thermal effects. This chemo-thermo-mechanical material model shows three key aspects regarding its numerical formulation. Firstly, a multiplicative split of the deformation gradient into a mechanical, a swelling and a thermal part. Secondly, temperature-scaled gradients for a numerical design comprising symmetric tangents and, thirdly, dissipation potentials for the modelling of dissipative effects. Additionally, the derived general material model is specialised to thermoresponsive hydrogels to study its predictive capabilities for a relevant example material class. An appropriate finite element formulation is established and its implementation discussed. Numerical examples are investigated, including phase transition and stability phenomena, to verify the ability of the derived chemo-thermo-mechanical material model to predict relevant physical effects properly. We compare our results to established models in the literature and discuss emerging deviations. PubDate: 2024-02-16

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Abstract: Abstract The Smoothed Particle Finite Element Method (SPFEM) has gained popularity as an effective numerical method for modelling geotechnical problems involving large deformations. To promote the research and application of SPFEM in geotechnical engineering, we present ESPFEM2D, an open-source two-dimensional SPFEM solver developed using MATLAB. ESPFEM2D discretizes the problem domain into computable particle clouds and generates the finite element mesh using Delaunay triangulation and the \( \alpha \) -shape technique to resolve mesh distortion issues. Additionally, it incorporates a nodal integration technique based on strain smoothing, effectively eliminating defects associated with the state variable mapping after remeshing. Furthermore, the solver adopts a simple yet robust approach to prevent the rank-deficiency problem due to under-integration by using only nodes as integration points. The Drucker-Prager model is adopted to describe the soil’s constitutive behavior as a demonstration. Implemented in MATLAB, this open-source solver ensures easy accessibility and readability for researchers interested in utilizing SPFEM. ESPFEM2D can be easily extended and effectively coupled with other existing codes, enabling its application to simulate a wide range of large geomechanical deformation problems. Through rigorous validation using four numerical examples, namely the oscillation of an elastic cantilever beam, non-cohesive soil collapse, cohesive soil collapse, and slope stability analysis, the accuracy, effectiveness and stability of this open-source solver have been thoroughly confirmed. PubDate: 2024-02-15

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Abstract: Abstract The Carrier-Domain Method was introduced for high-resolution computation of time-periodic long-wake flows. The cost-effectiveness of the method makes such computations practical in 3D. A short segment of the wake domain, the carrier domain, moves in the free-stream direction, from the beginning of the long wake domain to the end. The data at the moving inflow plane comes from the time-periodic data computed at an earlier position of the carrier domain. With the high mesh resolution that can easily be afforded over the short domain segment, the wake flow patterns can be carried, with superior accuracy, far downstream. Computing the long-wake flow with a high-resolution moving mesh that covers a short segment of the wake domain at any instant during the computation would certainly be far more cost-effective than computing it with a high-resolution fixed mesh that covers the entire length. We present high-resolution 3D computation of time-periodic long-wake flow for a cylinder and a wind turbine, both computed with isogeometric discretization and the Space–Time Variational Multiscale method. In the isogeometric discretization, the basis functions are quadratic NURBS in space and linear in time. The cylinder flow is at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding period. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. In the wind turbine long-wake flow computation, the velocity data at the inflow boundary of the wake domain comes from an earlier wind turbine computation, with the turbine rotor having a diameter of \({126}\,\hbox {m}\) , extracted by projection from a plane located \({10}\,\hbox {m}\) downstream of the turbine. The wake flow is computed up to \({482}\,\hbox {m}\) downstream of the wind turbine. In both the cylinder and wind turbine wake flow computations, the flow patterns obtained with the full domain and carrier domain show a near-perfect match, clearly demonstrating the effectiveness and practicality of the Carrier-Domain Method in high-resolution 3D computation of time-periodic long-wake flows. PubDate: 2024-02-12

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Abstract: Abstract In the field of materials engineering, the accurate prediction of material behavior under various loading conditions is crucial. Machine Learning (ML) methods have emerged as promising tools for generating constitutive models straight from data, capable of describing complex material behavior in a more flexible way than classical constitutive models. Yield functions, which serve as foundation of constitutive models for plasticity, can be properly described in a data-oriented manner using ML methods. However, the quality of these descriptions heavily relies on the availability of sufficient high-quality and representative training data that needs to be generated by fundamental numerical simulations, experiments, or a combination of both. The present paper addresses the issue of data selection, by introducing an active learning approach for Support Vector Classification (SVC) and its application in training an ML yield function with suitable data. In this regard, the Query-By-Committee (QBC) algorithm was employed, guiding the selection of new training data points in regions of the feature space where a committee of models shows significant disagreement. This approach resulted in a marked reduction in the variance of model predictions throughout the active learning process. It was also shown that the rate of decrease in the variance went along with an increase in the quality of the trained model, quantified by the Matthews Correlation Coefficient (MCC). This demonstrated the effectiveness of the approach and offered us the possibility to define a dynamic stopping criterion based on the variance in the committee results. PubDate: 2024-02-12

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Abstract: Abstract Standard non-local gradient damage methodology for fatigue analysis has an intrinsic drawback of unusual widening of the damage zone. This causes a rapid growth of crack in the simulations which often violate experimental evidences. In order to tackle this undesirable behaviour, the localizing gradient damage methodology has been formulated for high cycle fatigue crack growth simulations. The framework comprises of coupling damage and elasticity through continuum mechanics, a fatigue damage law and an interaction function which reduces the influence of damaged regions on the surrounding locality. The present scheme prevents the spurious widening of the damage-band around the critically damaged area and therefore the non-physical growth of fatigue crack in the simulations is successfully countered. The developed framework is tested on various standard specimens under mode-I and mixed-mode high cycle fatigue loads. Nonlinear finite element analysis is used for this purpose. The discretized form of solver equations for the localizing framework is mathematically derived. Numerical examples show that the simulated crack-growth curves using proposed localizing framework agree closely with the experimental data and has a higher accuracy than the standard non-local framework. PubDate: 2024-02-12

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Abstract: Abstract ELDIRK methods are defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge-Kutta methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes, e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability. PubDate: 2024-02-05

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Abstract: Abstract A recent mixed formulation of the Virtual Element Method in 2D elastostatics, based on the Hu-Washizu variational principle, is here extended to 2D elastodynamics. The independent modeling of the strain field, allowed by the mixed formulation, is exploited to derive first order quadrilateral Virtual Elements (VEs) not requiring a stabilization (namely, self-stabilized VEs), in contrast to the standard VEs, where an artificial stabilization is always required for first order quads. Lumped mass matrices are derived using a novel approach, based on an integration scheme that makes use of nodal values only, preserving the correct mass in the case of rigid-body modes. In the case of implicit time integration, it is shown how the combination of a self-stabilized stiffness matrix with a self-stabilized lumped mass matrix can produce excellent performances both in the compressible and quasi-incompressible regimes with almost negligible sensitivity to element distortion. Finally, in the case of explicit dynamics, the performances of the different types of derived VEs are analyzed in terms of their critical time-step size. PubDate: 2024-02-04

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Abstract: Abstract In this study, a novel approach is proposed by integrating the finite element tearing and interconnecting (FETI) method into the B-differentiable equations (BDEs) method for the analysis of 3D elastic frictional contact problem with small deformations. The contact blocks are divided into several nonoverlapping substructures with nonconforming meshes on the contact surface and the interface between two adjacent substructures. The enforcement of contact conditions and interface continuity conditions is achieved by using dual Lagrange multipliers discretized on the slave surface, typically defined with fine meshes. The modified Boolean transformation matrix is utilized to convert the contact stress into the equivalent nodal force. For large-scale elastic contact problems, the equilibrium equations for substructures and the relationship between the relative displacements and contact stresses on the contact surfaces and interfaces (i.e., the contact flexibility matrix) are efficiently computed using the FETI method. Subsequently, the governing equations consisting of the contact equations, interface continuity equations, and equilibrium equations for each floating substructure are uniformly formulated as the BDEs. These BDEs can be solved using the B-differentiable damped Newton method (BDNM). The proposed method harnesses the parallel scalability of the FETI method and extends the applicability of the BDEs algorithm, benefiting from its ability to precisely satisfy the contact constraints and theoretically ensure convergence when solving large-scale contact problems. The Hilber/Hughes/Taylor (HHT) time integration scheme is employed to investigate elastic dynamic contact problems. Numerical examples demonstrate the accuracy, convergence rate, and parallel scalability of the proposed algorithm. PubDate: 2024-02-03

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Abstract: Abstract The inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required \(C^1\) -continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated. PubDate: 2024-02-01

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Abstract: Abstract The paper deals with numerical analysis of the effect of stress state and loading direction with respect to the rolling direction on damage and fracture behavior of anisotropic metals. The continuum damage model has been enhanced to take into account the influence of production-induced anisotropies and loading direction on damage criteria and on evolution equations of damage strains. Constitutive parameters are determined using experimental results taken from tests with uni- and biaxially loaded specimens. The focus of the paper is on three-dimensional micro-mechanical numerical analyses of micro-defect-containing representative volume elements covering a wide range of stress states. These calculations lead to more insight in the different damage and failure processes on the micro-scale and their influence on the macroscopic damage laws. With the obtained numerical results it is possible to detect general trends, to propose governing equations for the damage criteria, to develop evolution equations for the damage strains, and to identify constitutive parameters of the anisotropic material model. It is shown that the anisotropic behavior and the loading direction with respect to the principal axes of anisotropy affect the evolution of damage mechanisms on the micro-level as well as the corresponding damage strains. PubDate: 2024-02-01

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Abstract: Abstract Recently, Murthy et al. (Commun Comput Phys 2:23, 2017. http://dx.doi.org/10.4208/cicp.OA-2016-0259 ) and Escande et al. (Lattice Boltzmann method for wave propagation in elastic solids with a regular lattice: theoretical analysis and validation, 2020. arXiv.doi:1048550/ARXIV.2009.06404. arXiv:2009.06404) adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be parallelised readily and lends itself to finely discretised simulations of dynamic effects in continua, allowing transient phenomena such as wave propagation to be modeled efficiently. This work proposes simple local boundary rules which approximate the behaviour of Dirichlet and Neumann boundary conditions with an LBM for elastic solids. The boundary rules are shown to be consistent with the target boundary values in the first order. An empirical convergence study is performed for the transient tension loading of a rectangular plate, with a Finite Element (FE) simulation being used as a reference. Additionally, we compare results produced by the LBM for the sudden loading of a stationary crack with an analytical solution from Freund (Dynamic fracture mechanics. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge, 1990. https://doi.org/10.1017/CBO9780511546761). PubDate: 2024-02-01

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Abstract: Abstract We formulate variational material modeling in a space-time context. The starting point is the description of the space-time cylinder and the definition of a thermodynamically consistent Hamilton functional which accounts for all boundary conditions on the cylinder surface. From the mechanical perspective, the Hamilton principle then yields thermo-mechanically coupled models by evaluation of the stationarity conditions for all thermodynamic state variables which are displacements, internal variables, and temperature. Exemplary, we investigate in this contribution elastic wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage. Therein, one key novel aspect are initial and end time velocity conditions for the wave equation, replacing classical initial conditions for the displacements and the velocities. The motivation is intensively discussed and illustrated with the help of a prototype numerical simulation. From the mathematical perspective, the space-time formulations are formulated within suitable function spaces and convex sets. The unified presentation merges engineering and applied mathematics due to their mutual interactions. Specifically, the chosen models are of high interest in many state-of-the art developments in modeling and we show the impact of this holistic physical description on space-time Galerkin finite element discretization schemes. Finally, we study a specific discrete realization and show that the resulting system using initial and end time conditions is well-posed. PubDate: 2024-02-01

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Abstract: Abstract 3D Concrete Printing (3DCP) is a rapidly evolving technology that allows for the efficient and accurate construction of complex concrete objects. In this paper, a numerical modelling approach is presented for the simulation of the printing process of cementitious materials, based on the homogeneous fluid assumption. To cope with the large deformations of the domain and the nonlinearity resulting from the use of a non-Newtonian rheological law, the Navier–Stokes equations are solved in the framework of the Particle Finite Element Method (PFEM). Furthermore, tailored solutions have been formulated and implemented for the time-dependent moving boundary conditions at the nozzle outlet and for the efficient handling of the inter-layer contact in the same PFEM framework. The overall computational cost is decreased by the implementation of an adaptive de-refinement technique, which drastically reduces the number of degrees of freedom in time. The proposed modelling approach is finally validated by simulating the printing process of six rectilinear layers and one multi-layer “wall”. The results show good agreement with the experimental data and provide valuable insights into the printing process, paving the way for the use of numerical modelling tools for the optimization of materials and processes in the field of 3D Concrete Printing. PubDate: 2024-02-01

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Abstract: Abstract A multigrid coupling approach of the extended isogeometric–meshfree (XIMF) method and bond-based peridynamics (PD) is developed for static and dynamic fracture problems. The coupling approach exploits the advantages of the XIMF method and PD, including the computational efficiency of the XIMF method and the generality of the PD in dealing with fracture problems. To couple the two methods, a problem domain is divided into the peridynamic and isogeometric–meshfree subdomains. The former subdomain aims to model both the crack-tip and potential cracking zone and is discretized by fine peridynamic points, while the latter corresponds to the remaining zone and is discretized by coarse isogeometric–meshfree meshes. The two subdomains are connected with the interface meshes, at which the ghost peridynamic particles are embedded and the displacement constraints are enforced. In this way, fracture patterns can be captured without requiring the crack-tip enrichment functions which are complicated in three dimensions while obtaining the comparable efficiency of the XIMF method. Furthermore, an adaptive switching strategy is proposed to convert the isogeometric–meshfree meshes into peridynamic particles. Finally, several representative benchmark problems including the two-dimensional static crack propagation in a double cantilever beam and dynamic crack branching, and the three-dimensional mixed-mode fracture in a skew-notched structure are attempted to validate the proposed approach. PubDate: 2024-02-01