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Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification
Tadej Dobravec, Boštjan Mavrič, Božidar Šarler, 2023, objavljeni znanstveni prispevek na konferenci

Povzetek: We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based approach decomposes the computational domain into quadtree sub-domains of different sizes. The algorithm generates uniformly-distributed computational nodes in each quadtree sub-domain. We apply the meshless radial basis function generated finite difference method and the forward Euler scheme to discretise governing equations in each computational node. The fixed ratio between the characteristic size and the node spacing of a quadtree sub-domain ensures space adaptivity. The adaptive time-stepping accelerates the calculations further. In the framework of previous research studies, we used the approach to solve quantitative phase-field models for single dendrite growth in pure melts and dilute binary alloys. In the present study, we upgrade the solution procedure for the modelling growth of multiple differently oriented dendrites. Along with the space-time adaptive approach, we apply non-linear preconditioning of the phase-field equation to increase computational efficiency. We investigate a novel numerical approach's accuracy and computational efficiency by simulating the equiaxed dendrite growth from a dilute binary alloy.
Ključne besede: dendritic growth, phase-field method, meshless methods, polycrystalline solidification
Objavljeno v DiRROS: 21.03.2024; Ogledov: 98; Prenosov: 54
.pdf Celotno besedilo (2,77 MB)
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3.
A meshless numerical solution of thermo-mechanics of hot-rolled steel bars on a cooling bed
Gašper Vuga, Boštjan Mavrič, Umut Hanoglu, Božidar Šarler, 2023, objavljeni znanstveni prispevek na konferenci

Povzetek: After the continuous hot-rolling process, steel bars are immediately placed on the cooling bed. At the beginning of the cooling, the material is at high temperatures, and the yield strength is low. Due to thermal load, yield strength can be exceeded, and permanent plastic strains start accumulating, resulting in possible unwanted shape changes and residual stresses. The present paper aims to develop a thermo-mechanical model for studying and eliminating undesirable phenomena before the products leave the cooling bed. The governing equations are solved for the two-dimensional slice in a strong form, and a modified version of the radial basis function generated finite difference (RBF-FD) method [1]. The initial bar geometry is obtained from the existing meshless hot-rolling simulation system [2]. The thermal and mechanical models are one-way coupled, i.e. the temperature solution represents a driving force for the stress and strain solution. The temperature field is obtained with explicit propagation in time. The convective and radiative heat fluxes on the boundary are updated at each time step using the ray tracing procedure to determine the radiative heat flux. The mechanical part is solved by considering the small strain elasto-plasticity, where the isotropic von Mises temperature-dependent hardening is employed. The global system of nonlinear equations of the mechanical part is solved by the Newton-Raphson method. The closest point projection method is used to solve the constitutive relations. A sensitivity study is performed on the influence of cooling intensity on a rectangular steel bar’s temperature, stress and strain field. We defined the most influential factors for defect formation. For the first time, a novel meshless RBF-FD method is successfully used for solving such a complex industrial problem. The model will be perspectively upgraded from the slice to the three-dimensional model to enable also bending.
Ključne besede: cooling bed, steel bars, thermo-mechanics, strong form, meshless method
Objavljeno v DiRROS: 21.03.2024; Ogledov: 81; Prenosov: 45
.pdf Celotno besedilo (1,62 MB)
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A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity : Application to cooling of hot-rolled steel bars on a cooling bed
Gašper Vuga, Boštjan Mavrič, Umut Hanoglu, Božidar Šarler, 2024, izvirni znanstveni članek

Povzetek: This paper represents Part 2 of the parallel paper Part 1, where the strong form hybrid RBF-FD method was developed for solving thermo-elasto-plastic problems. It addresses the industrial application of this novel meshless method to steel bars cooling on a cooling bed (CB) where the formation of residual stress is of primary interest. The study investigates the impact of the distance between the bars and the distance to the heat shield above the CB on radiative heat fluxes and, consequently, on thermo-mechanical response. The thermal model is solved on bars cross-section with a RBF-FD method where augmented polyharmonic splines are used for the local approximation. View factors, computed with a Monte-Carlo method, are included in radiative heat fluxes. The thermal solution is incrementally applied on a mechanical model that assumes a generalised plane strain state and captures bars bending. The study employs a hybrid RBF-FD method to resolve a nonlinear discontinuous mechanical problem successfully. The simulation of the process shows how different process parameters influence the thermo-mechanical response of the bars.
Ključne besede: steel bars, cooling bed, thermo-mechanical modelling, hybrid radial basis function, generated finite differences, residual stresses
Objavljeno v DiRROS: 28.02.2024; Ogledov: 99; Prenosov: 62
.pdf Celotno besedilo (8,55 MB)
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A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 1 : method formulation and testing
Gašper Vuga, Boštjan Mavrič, Božidar Šarler, 2024, izvirni znanstveni članek

Povzetek: A hybrid version of the strong form meshless Radial Basis Function-Finite Difference (RBF-FD) method is introduced for solving thermo-mechanics. The thermal model is spatially discretised with RBF-FD, where trial functions are polyharmonic splines augmented with polynomials. For time discretisation, the explicit Euler method is employed. An extension of RBF-FD, the hybrid RBF-FD, is introduced for solving mechanical problems. The model is one-way coupled, where temperature affects displacements. The thermo-elastoplastic material response is considered where the stress field is generally non-smooth. The hybrid RBF-FD, where the finite difference method is used to discretise the divergence operator from the balance equation, is shown to be successful when dealing with such problems. The mechanical model is introduced in a plane strain and in a generalised plane strain (GPS) assumption. For the first time, this work presents a strong form RBF-FD for GPS problems subjected to integral form constraints. The proposed method is assessed regarding h-convergence and accuracy on the benchmark with heating an elastoplastic square. It is proven to be successful at solving one-way coupled thermo-elastoplastic problems. The proposed novel meshless approach is efficient, accurate, and robust. Its use in an industrial situation is provided in Part 2 of this paper.
Ključne besede: thermo-mechanical modelling, von Mises small strain plasticity, hybrid radial basis function generated finite differences, polyharmonic splines
Objavljeno v DiRROS: 28.02.2024; Ogledov: 107; Prenosov: 59
.pdf Celotno besedilo (2,69 MB)
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An improved local radial basis function method for solving small-strain elasto-plasticity
Gašper Vuga, Boštjan Mavrič, Božidar Šarler, 2024, izvirni znanstveni članek

Povzetek: Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be elusive because of often non-smooth constitutive relations between stress and strain. The novelty in tackling them is the introduction of virtual finite difference stencils to formulate a hybrid radial basis function generated finite difference (RBF-FD) method, which is used to solve small-strain von Mises elasto-plasticity for the first time by this original approach. The paper further contrasts the new method to two alternative legacy RBF-FD approaches, which fail when applied to this class of problems. The three approaches differ in the discretization of the divergence operator found in the balance equation that acts on the non-smooth stress field. Additionally, an innovative stabilization technique is employed to stabilize boundary conditions and is shown to be essential for any of the approaches to converge successfully. Approaches are assessed on elastic and elasto-plastic benchmarks where admissible ranges of newly introduced free parameters are studied regarding stability, accuracy, and convergence rate.
Ključne besede: Von Mises elasto-plasticity, radial basis function, finite differences, polyharmonic splines, two dimensions, hybrid discretization
Objavljeno v DiRROS: 28.02.2024; Ogledov: 104; Prenosov: 55
.pdf Celotno besedilo (5,24 MB)
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A coupled domain–boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow
Tadej Dobravec, Boštjan Mavrič, Rizwan Zahoor, Božidar Šarler, 2023, izvirni znanstveni članek

Povzetek: Purpose - This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method. Design/methodology/approach - A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case. Findings - The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented. Originality/value - A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.
Ključne besede: dendritic solidification, Stokes flow, phase-field method, space-time adaptivity, meshless methods, RBF-FD, modified method of regularised sources
Objavljeno v DiRROS: 07.02.2024; Ogledov: 144; Prenosov: 62
.pdf Celotno besedilo (1,07 MB)
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