Documents published in Scipedia

• Understanding the solidification and heat treatment characteristics in the CoCrNiSix medium-entropy alloy by experimentally verifiable multiscale thermodynamic and kinetic computational techniques

  T. Su, H. Huang, J. Chen

  WCCM2024.

  
  

  Abstract

  CoCrNi medium-entropy alloy (MEA) possesses an FCC crystal structure with multiple slip systems and low stacking fault energy [1]; a substantial amount of nanoscale deformation twins can be generated under low-temperature and high-speed deformation. Adding a proper amount of Si can not only reduce the manufacturing cost and mass density but also enhance ballistic resistance by further lowering the stacking fault energy. Previous studies [2] utilized small-scale vacuum arc remelting techniques to investigate the solid solution or secondary phase strengthening of CoCrNi-based MEAs with Al or Si additions. However, to extend the application of lightweight, high-entropy alloys to industrial-grade impact-resistant plate manufacturing, especially for low-temperature environments, it is necessary to study the solidification and heat treatment characteristics of CoCrNiSix castings. This study employs finite element analysis at the macroscopic scale to investigate the solidification phase transformation and heat transfer characteristics of CoCrNiSix under precision-cast conditions. Additionally, at the mesoscopic scale, the phase-field method [3] is used to simulate the dendritic solidification microstructure and element segregation of CoCrNiSix. Thermodynamic parameters required for simulations are calculated using Thermo-Calc high-entropy alloy databases TCHEA6 and MOBHEA2. This research also utilizes electron microscopy to analyze the microstructures of chemically complex CoCrNiSix ingots, focusing on measuring the secondary dendrite arm spacing and elemental segregation profiles. Collecting these microstructure-related features allows us to reasonably infer the cooling rate corresponding to the investment casting process of CoCrNiSix and design rational parameter combinations for homogenization heat treatment of the cast ingots in terms of temperature and isothermal holding time. By validating macroscopic and mesoscopic simulation results through CoCrNiSix microstructure analysis experiments, the multiscale kinetic computational techniques included in this study can be further applied to cost-saving and process optimization practices in the manufacturing of various lightweight high-entropy alloys

  Abstract
  CoCrNi medium-entropy alloy (MEA) possesses an FCC crystal structure with multiple slip systems and low stacking fault energy [1]; a substantial amount of nanoscale deformation [...]

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• Space-time Galerkin finite element discretization and error control for coupled problems

  T. Wick, P. Junker, J. Thiele, J. Roth

  WCCM2024.

  
  

  Abstract

  In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only

  Abstract
  In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically [...]

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• Goal oriented error estimation for space-time adaptivity in phase-field fracture

  V. Kosin, A. Fau, F. Hild, T. Wick

  WCCM2024.

  
  

  Abstract

  This work focuses on temporal adaptivity for phase-field fracture problems. The methodology requires a space-time formulation and utilizes a space-time Galerkin finite element discretization for the governing phase-field equations. Then, goal functionals (i.e., quantities of interest) are introduced. The computational implementation of goal-oriented error control employs the dual-weighted residual method in which an adjoint problem must be solved. As the analysis is quasi-static, without a temporal derivative, the adjoint problem of the quasistatic primal problem decouples in time. Nonetheless, time-averaged goal functionals can also be considered. The temporal errors are localized using a partition of unity, which allows one to adaptively refine and coarsen the time intervals in the space-time cylinder. Numerical tests are performed on a single edge notched tensile test to investigate the quality of the proposed error estimator.

  Abstract
  This work focuses on temporal adaptivity for phase-field fracture problems. The methodology requires a space-time formulation and utilizes a space-time Galerkin finite element [...]

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• Assessment of flow-induced stresses in spiral weld pipes with bends

  S. Ahmadizade, S. Verma, A. Hemmati

  WCCM2024.

  
  

  Abstract

  This study numerically investigates flow-induced stresses and displacements in bent pipes at varying angles (20◦ ≤ θb ≤ 80◦ ) using Solids4Foam at Reynolds number of 20,000. The results indicate that increasing θb enhances the formation of symmetric vortex structures, which coincide with enhanced non-uniformity in pressure distribution and wall shear stresses. Additionally, maximum equivalent stresses (σeq) for the solid shell occur near the inlet. The pipes with higher θb also depict a reduced displacement magnitude(D), which hints at the strong role of fixed displacement boundary condition assigned at the pipe inlet and outlet. These findings provide essential insights for performing numerical investigation of pipeline reliability and structural integrity in oil transportation.

  Abstract
  This study numerically investigates flow-induced stresses and displacements in bent pipes at varying angles (20◦ ≤ θb ≤ 80◦ ) using Solids4Foam at Reynolds number [...]

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• Computational interpretation of shape memory epoxy: processing and its operation

  Y. Kim, H. Kim, J. Choi

  WCCM2024.

  
  

  Abstract

  The shape forming and restoration mechanisms of shape memory epoxy originate from the molecular-scale dynamics that epoxy molecules undergo during thermomechanical processes. In this study, the microstructural changes that occur at the molecular scale caused by heat and load during the programming and operation of the epoxy network were investigated using molecular dynamics simulations. The mechanical behaviors of each molecule were analyzed by classifying it into translation, rotation, and deformation based on the classical kinematic framework. Specifically, depending on its structural properties, each molecular component was rearranged to different levels, forming local residual stresses. The principle leading to shape recovery as the subsequent thermal load breaks the equilibrium of residual stresses and resulting changes in the mechanical anisotropy of entire epoxy network were also analyzed through a subcontinuum perspective. This study has the potential to be extended to a method for designing epoxy resins that satisfy desired physical properties and shape recovery performance

  Abstract
  The shape forming and restoration mechanisms of shape memory epoxy originate from the molecular-scale dynamics that epoxy molecules undergo during thermomechanical processes. [...]

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• An improved flux vector splitting method for characteristic-wise WENO schemes of the Euler equations

  J. Kim, Y. Shen

  WCCM2024.

  
  

  Abstract

  Steger-Warming (SW) [1] and Lax-Friedrich-type (LF) [2] flux vector splitting methods are used extensively by shock capturing WENO schemes in varieties of compressible flow simulations. Due to the less dissipation, the SW method is preferred in flow calculations that require fine scale structures such as direct numerical simulation of turbulence. However, this paper shows that, even if the characteristic-wise WENO scheme is used, the SW method may still exhibit some oscillations near contact discontinuities, while the LF method does not. Analysis similar to the reference [3] shows that, using the SW method may make the characteristic-wise WENO scheme become close the component-wise WENO scheme near subsonic contact discontinuities. Based on that, an improved flux vector splitting method, which adjusts the eigenvalues of the flux vector splitting in the characteristic-wise WENO procedure, is proposed to obtain the low-dissipation property and prevent contact discontinuity oscillations at the same time. Numerical experiments are performed to validate and evaluate the new method. Numerical results show that the proposed method keeps the non-oscillatory flow field near discontinuities as LF method and also avoids smearing out other flow regions, similar to the SW method.

  Abstract
  Steger-Warming (SW) [1] and Lax-Friedrich-type (LF) [2] flux vector splitting methods are used extensively by shock capturing WENO schemes in varieties of compressible flow [...]

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• Modeling the enhanced geothermal systems using the extended–FEM and an equivalent continuum model

  A. Khoei, S. Mortazavi, O. Rezaie Beydokhti, P. Pirmoradi

  WCCM2024.

  
  

  Abstract

  . In this paper, a computational technique is presented for Thermo-Hydro-Mechanical (THM) simulation of Enhanced Geothermal Systems (EGS) based on the eXtended Finite Element Method (XFEM) and Equivalent Continuum Method (ECM) in the framework of Local Thermal Non-Equilibrium (LTNE). Heat extraction from Enhanced Geothermal Systems involves several multi-physics coupling processes, including the seepage through the fractured porous media, the thermal exchange between the working fluid and the matrix, and the deformation of fractured porous media that play essential roles in exploiting the geothermal energy contained in hot dry rocks. The ECM provides the equivalent tensors for the fluid permeability and solid compliance, which is an essential feature for the coupled Thermo-Hydro Mechanical simulation of fracture networks. In the model, the XFEM is employed for large scale fractures to capture the mass and heat transfer between the fracture and matrix more accurately, while the ECM is applied on the network of small-scale fractures. Hence, the proposed model benefits from the advantages of both methods, and it allows for managing between accuracy and cost. The set of THM equations is solved with both Local Thermal Equilibrium (LTE) and Local Thermal Non-Equilibrium (LTNE) assumptions to find out the impact of each method on the production temperature. The capability of the proposed computational model is demonstrated for the diagonal arrangement of the injection and production wells with different fracture orientations in-between. The simultaneous effects of fracture connectivity and inclination are investigated between the two injection and production wells. It is observed that the temperature difference between the two cases is higher in the middle of the domain by comparing the results of LTE and LTNE assumptions. Moreover, it is concluded that the LTE model overestimates the fluid temperature in comparison to the LTNE model in cold water injection problems. The results show the proposed computational model is a promising tool for estimation of the heat mining performance of EGS

  Abstract
  . In this paper, a computational technique is presented for Thermo-Hydro-Mechanical (THM) simulation of Enhanced Geothermal Systems (EGS) based on the eXtended Finite Element [...]

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• Stabilization of mixed displacement-pressure finite elements at finite strains using polyhedral formulations and Voronoi meshing

  B. Sauren, E. Oheim, S. Klinkel

  WCCM2024.

  
  

  Abstract

  The hexahedral mixed displacement-pressure finite element of the lowest order (H1/P0) has shown to be simple and effective during both linear and nonlinear analysis of incompressible solids. While the discrete displacement field is generally considered to be sufficiently accurate, the discrete pressure field can sometimes be heavily polluted by spurious pressure modes. This results from the fact that the element does not fulfill the inf-sup condition. While postprocessing techniques, such as pressure filtering or smoothing, exist to remove the spurious pressure modes from the solution, this contribution aims on the exclusion of spurious pressure modes from the solution a priori due to the element geometry. By employing polyhedral finite element formulations on Voronoi tessellations in three dimensions, we show that the discrete kernel of the linearized mixed bilinear form only consists of the hydrostatic pressure mode. A spurious pressure mode is automatically suppressed due to the vertex-to-volume ratio in the finite element mesh. These considerations hold for any arbitrary physically admissible displacement state that can occur within a Newton-Raphson framework. A nonlinear numerical example shows that spurious pressure modes are indeed suppressed if the type of tessellation is changed from hexahedral to Voronoi.

  Abstract
  The hexahedral mixed displacement-pressure finite element of the lowest order (H1/P0) has shown to be simple and effective during both linear and nonlinear analysis of incompressible [...]

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• A coupled SPH-FDM method for simulations of unsteady flows

  C. Huang, H. Jiang, F. He, A. Shakibaeinia

  WCCM2024.

  
  

  Abstract

  The fluid-flexible-structure interaction (FFSI) is characterized by the large deformation, the thin structure, and the complex of the flow field. Accurately simulating FFSI poses three challenges, which are the reproduction of thin structure, the capture of moving interface, and the numerical stability of multi-physics field coupling, respectively. In this study, the FFSI is simulated by the smoothed particle hydrodynamics (SPH) because of its natural advantage in dealing with the moving interface. The shell model with single-layer particles[1] is introduced into SPH to simulate the thin flexible structure. The truncation error caused by the single-layer boundary is modified by the normal flux approach[2]. κ-ε turbulence model is introduced into SPH to enhance the numerical stability and capture complex flow details. In addition, other techniques or models that ensure the efficiency and stability of the calculation are used in this study, including PST (particle shifting technique), δ-SPH method, and GPU (graphics processing unit). The flows around the single filament are simulated to verify the accuracy and stability of the current FFSI algorithm based on the SPH method.

  Abstract
  The fluid-flexible-structure interaction (FFSI) is characterized by the large deformation, the thin structure, and the complex of the flow field. Accurately simulating FFSI [...]

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• A computationally efficient method for considering a large number of nonlinear multi-point constraints within the finite element method

  J. Wackerfuβ, J. Boungard

  WCCM2024.

  
  

  Abstract

  Nonlinear constraints are crucial in modeling various problems in computational mechanics. Among other things, they can be used for the subsequent consideration of rigid inclusions in a body originally modeled as deformable, without requiring a remeshing of the considered domain and thus contributing to a rapid modeling building. Unlike Lagrange multipliers and the penalty method, the master-slave elimination reduces the problem dimension but is limited to linear constraints. We introduce a new master-slave elimination method for arbitrary nonlinear multi-point constraints. It is compared to existing methods through analysis of the resulting equations and numerical examples. Results indicate that the method is as accurate, robust, and flexible as Lagrange multipliers, with improved efficiency due to reduced degrees of freedom, which is particularly advantageous when a large number of constraints have to be considered.

  Abstract
  Nonlinear constraints are crucial in modeling various problems in computational mechanics. Among other things, they can be used for the subsequent consideration of rigid inclusions [...]

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