Documents published in Scipedia

• 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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• Geometric formulation of three-temperature radiation hydrodynamics

  B. Tran, B. Southworth, J. Burby, M. Leok

  WCCM2024.

  
  

  Abstract

  Three-temperature (3T) radiation hydrodynamics models high energy-density plasma of nonlinearly coupled electron, ion, and radiation fields, finding applications in astrophysics and inertial confinement fusion. We present a geometric formulation of three-temperature radiation hydrodynamics. This is done utilizing an irreverisble portHamiltonian framework in the entropy representation. This geometric formulation separates the advection, interaction, and diffusion processes occuring into separate operators and establishes the energy-preserving interconnections between them. Structural properties such as mass, momentum and energy conservation as well as entropy production arise naturally from the geometric formulation. As an application, we briefly discuss a framework for the energy control of the 3T system within the port-Hamiltonian framework.

  Abstract
  Three-temperature (3T) radiation hydrodynamics models high energy-density plasma of nonlinearly coupled electron, ion, and radiation fields, finding applications in astrophysics [...]

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• The Picard-Newton iteration for the Boussinesq equations

  L. Rebholz, E. Hawkins

  WCCM2024.

  
  

  Abstract

  We consider the Picard-Newton and Anderson accelerated Picard-Newton solvers applied to the Boussinesq equations, nonlinear Helmholtz equations and Liouville equation, for the purpose of accelerating convergence and improving robustness with respect to problem parameters. In all cases, we show the proposed solvers improve efficiency over the commonly used solvers and are able to find solutions for a much larger set of problem parameters.

  Abstract
  We consider the Picard-Newton and Anderson accelerated Picard-Newton solvers applied to the Boussinesq equations, nonlinear Helmholtz equations and Liouville equation, for [...]

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• A new concept for embedding sub-structures via level-sets

  T. Fries, J. Neumeyer, M. Kaiser

  WCCM2024.

  
  

  Abstract

  A framework is presented to continuously embed sub-structures such as fibres and membranes into otherwise homogeneous, isotropic bulk materials. The bulk material is modeled with classical finite strain theory. The sub-structures are geometrically defined via all level sets of a scalar function over the bulk domain. A mechanical model that is simultaneously applicable to all level sets is given and coupled to the bulk material. This results in a new concept for anisotropic materials with possible applications in biological tissues, layered rocks, composites, and textiles. For the numerical analysis, the bulk domain is discretized possibly using higher-order finite elements which do not conform to the level sets implying the shapes of the embedded sub-structures. Numerical results confirm the success of the proposed embedded sub-structure models in different contexts

  Abstract
  A framework is presented to continuously embed sub-structures such as fibres and membranes into otherwise homogeneous, isotropic bulk materials. The bulk material is modeled [...]

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• On triangular self-stabilized virtual elements for Kirchhoff-Love shells

  T. Park Wu, P. de Mattos Pimenta, P. Wriggers

  WCCM2024.

  
  

  Abstract

  This work presents a self-stabilized triangular virtual element for linear Kirchhoff–Love shells. The domain decomposition by flat triangles directly approximates the shell geometry without resorting to a curvilinear coordinate system or an initial mapping approach. The problem is discretized by the lowest-order conventional virtual element method for the membrane, in which stabilization is needless, and by a stabilization-free virtual element procedure for the plate. Numerical examples of static problems show the potential of the formulation as a prelude for the evolution of self-stabilized Kirchhoff–Love shell virtual elements.

  Abstract
  This work presents a self-stabilized triangular virtual element for linear Kirchhoff–Love shells. The domain decomposition by flat triangles directly approximates the shell [...]

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