Pub Date : 2026-05-01Epub Date: 2026-02-11DOI: 10.1016/j.cma.2026.118805
Won Seok Song , Haram Park , Jeonghyun Park , Seungjae Min
The Heaviside projection method is widely used to obtain binary solutions in topology optimization, and the projection steepness parameter beta is typically increased by doubling at fixed update intervals. However, such interval-based schemes often lead to excessive iterations and numerical oscillations during the optimization process. In this study, we propose an adaptive beta update strategy that extends the role of the gray-level indicator, a measure of non-discreteness, to an adaptive parameter governing the progression of beta throughout the optimization. The proposed method consists of two phases: a stability-based Phase 1 that guides a gradual reduction of intermediate densities, and a prediction-based Phase 2 that adjusts beta when beta-update congestion is detected to ensure continuous and stable projection progression. Numerical experiments across various physical problems and parameter settings demonstrate that the proposed approach significantly reduces the number of iterations required to reach convergence while maintaining or improving the final objective performance. These results indicate that the adaptive beta update strategy can serve as a consistent and effective beta update framework for the Heaviside projection in topology optimization.
{"title":"Adaptive beta update scheme in heaviside projection method of topology optimization","authors":"Won Seok Song , Haram Park , Jeonghyun Park , Seungjae Min","doi":"10.1016/j.cma.2026.118805","DOIUrl":"10.1016/j.cma.2026.118805","url":null,"abstract":"<div><div>The Heaviside projection method is widely used to obtain binary solutions in topology optimization, and the projection steepness parameter beta is typically increased by doubling at fixed update intervals. However, such interval-based schemes often lead to excessive iterations and numerical oscillations during the optimization process. In this study, we propose an adaptive beta update strategy that extends the role of the gray-level indicator, a measure of non-discreteness, to an adaptive parameter governing the progression of beta throughout the optimization. The proposed method consists of two phases: a stability-based Phase 1 that guides a gradual reduction of intermediate densities, and a prediction-based Phase 2 that adjusts beta when beta-update congestion is detected to ensure continuous and stable projection progression. Numerical experiments across various physical problems and parameter settings demonstrate that the proposed approach significantly reduces the number of iterations required to reach convergence while maintaining or improving the final objective performance. These results indicate that the adaptive beta update strategy can serve as a consistent and effective beta update framework for the Heaviside projection in topology optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118805"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-13DOI: 10.1016/j.cma.2026.118798
Jongmin Rim , Jinhui Yan , Yuri Bazilevs
The level set method is widely employed in two-phase flow simulations due to its robustness in handling complex interface topological changes. However, it suffers from two main limitations. First, the method is not inherently mass conservative. Second, the signed-distance property of the level set field can deteriorate under strong convection, particularly in high Reynolds-number flows. Consequently, conventional level set methods often require auxiliary procedures such as sharpening (or re-distancing) and mass correction, which rely on and are sensitive to user-defined parameters and also increase implementation complexity and computational cost. Here, we present a naturally sharpened level-set formulation for incompressible air-water flows that is mass conservative and eliminates the need for these additional algorithmic steps. The resulting free-surface flow modeling and simulation framework is more efficient and robust as demonstrated through several challenging numerical test cases.
{"title":"A naturally sharpened level-set formulation for incompressible free-surface flows","authors":"Jongmin Rim , Jinhui Yan , Yuri Bazilevs","doi":"10.1016/j.cma.2026.118798","DOIUrl":"10.1016/j.cma.2026.118798","url":null,"abstract":"<div><div>The level set method is widely employed in two-phase flow simulations due to its robustness in handling complex interface topological changes. However, it suffers from two main limitations. First, the method is not inherently mass conservative. Second, the signed-distance property of the level set field can deteriorate under strong convection, particularly in high Reynolds-number flows. Consequently, conventional level set methods often require auxiliary procedures such as sharpening (or re-distancing) and mass correction, which rely on and are sensitive to user-defined parameters and also increase implementation complexity and computational cost. Here, we present a naturally sharpened level-set formulation for incompressible air-water flows that is mass conservative and eliminates the need for these additional algorithmic steps. The resulting free-surface flow modeling and simulation framework is more efficient and robust as demonstrated through several challenging numerical test cases.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118798"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-13DOI: 10.1016/j.cma.2026.118807
Lei Zhang , Jiachen Guo , Shaoqiang Tang , Thomas J.R. Hughes , Wing Kam Liu
In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) as the approximation basis, which enables fine-grained control over the trade-off between computational efficiency and interpolation accuracy. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Crucially, our method departs from existing VMS-based multilevel approaches by approximating the fine-scale solution directly using the fine-scale basis functions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order p, patch size s) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 1010 spatial degrees of freedom (DoFs), our three-level ML-VMS C-HiDeNN-TD demonstrates a promising speedup of approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM. We further validate the generality of ML-VMS through a 3D elasticity case study. Compared to the linear FEM-TD ROM, our approach achieves theoretical convergence rates and provides significant speedups with higher precision.
{"title":"MultiLevel variational MultiScale (ML-VMS) framework for large-scale simulation","authors":"Lei Zhang , Jiachen Guo , Shaoqiang Tang , Thomas J.R. Hughes , Wing Kam Liu","doi":"10.1016/j.cma.2026.118807","DOIUrl":"10.1016/j.cma.2026.118807","url":null,"abstract":"<div><div>In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) as the approximation basis, which enables fine-grained control over the trade-off between computational efficiency and interpolation accuracy. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Crucially, our method departs from existing VMS-based multilevel approaches by approximating the fine-scale solution directly using the fine-scale basis functions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order <em>p</em>, patch size <em>s</em>) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10<sup>10</sup> spatial degrees of freedom (DoFs), our three-level ML-VMS C-HiDeNN-TD demonstrates a promising speedup of approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM. We further validate the generality of ML-VMS through a 3D elasticity case study. Compared to the linear FEM-TD ROM, our approach achieves theoretical convergence rates and provides significant speedups with higher precision.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118807"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-13DOI: 10.1016/j.cma.2026.118804
Rylan Spence , Troy Butler , Clint Dawson
This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware regularization term. The first method formulated is referred to as Data-Consistent 4D-Var (DC-4DVar), which is then enhanced using a Weighted Mean Error (WME) quantity-of-interest map to construct the DC-WME 4D-Var method. While the DC and DC-WME cost functions both involve a predictability-aware regularization term, the DC-WME function includes a modification to the model-data misfit, thereby improving estimation accuracy, robustness, and theoretical consistency in nonlinear and partially observed dynamical systems. Proofs are provided that establish the existence and uniqueness of the minimizer and analyze how a predictability assumption that is common within the DCI framework helps to promote solution stability. Numerical experiments are presented on benchmark dynamical systems (Lorenz-63 and Lorenz-96) as well as for the shallow water equations (SWE). In the benchmark dynamical systems, the DC-WME 4D-Var formulation is shown to consistently outperform standard 4D-Var in reducing both error and bias while maintaining robustness under high observation noise and short assimilation windows. Despite introducing modest computational overhead, DC-WME 4D-Var delivers improvements in estimation performance and forecast skill, demonstrating its potential practicality and scalability for high-dimensional data assimilation problems.
{"title":"Variational data-consistent assimilation","authors":"Rylan Spence , Troy Butler , Clint Dawson","doi":"10.1016/j.cma.2026.118804","DOIUrl":"10.1016/j.cma.2026.118804","url":null,"abstract":"<div><div>This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware regularization term. The first method formulated is referred to as Data-Consistent 4D-Var (DC-4DVar), which is then enhanced using a Weighted Mean Error (WME) quantity-of-interest map to construct the DC-WME 4D-Var method. While the DC and DC-WME cost functions both involve a predictability-aware regularization term, the DC-WME function includes a modification to the model-data misfit, thereby improving estimation accuracy, robustness, and theoretical consistency in nonlinear and partially observed dynamical systems. Proofs are provided that establish the existence and uniqueness of the minimizer and analyze how a predictability assumption that is common within the DCI framework helps to promote solution stability. Numerical experiments are presented on benchmark dynamical systems (Lorenz-63 and Lorenz-96) as well as for the shallow water equations (SWE). In the benchmark dynamical systems, the DC-WME 4D-Var formulation is shown to consistently outperform standard 4D-Var in reducing both error and bias while maintaining robustness under high observation noise and short assimilation windows. Despite introducing modest computational overhead, DC-WME 4D-Var delivers improvements in estimation performance and forecast skill, demonstrating its potential practicality and scalability for high-dimensional data assimilation problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118804"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-02-14DOI: 10.1016/j.cma.2026.118818
Xinyi Yu, Xiaoping Qian
This work introduces an interface filtering structural optimization (IFSO) method featuring parameter-free interface movement, which combines a nonuniform filter radius with a proposed dual-filtering strategy for two-fluid counter-flow heat exchangers (HXs). The approach supports seeding from different initial geometries and maintains their sharp material interfaces, enforces prescribed minimum thickness through dual filtering, and employs an interpolation scheme to represent the two fluids and the solid within one stepped density field. The method is demonstrated on a conventional straight-channel HX and high-performance Gyroid-based HXs. Post-optimization simulations confirm the improvements, including ∼ 50.96% higher heat transfer rate in straight pipes and over 123% enhancement in power density for Gyroid HXs, attributed to increased interfacial curvature and intensified mixing effects. These results establish the dual-filtering IFSO as a viable computational method for HX optimization.
{"title":"Interface filtering structural optimization for two-fluid heat exchanger","authors":"Xinyi Yu, Xiaoping Qian","doi":"10.1016/j.cma.2026.118818","DOIUrl":"10.1016/j.cma.2026.118818","url":null,"abstract":"<div><div>This work introduces an interface filtering structural optimization (IFSO) method featuring parameter-free interface movement, which combines a nonuniform filter radius with a proposed dual-filtering strategy for two-fluid counter-flow heat exchangers (HXs). The approach supports seeding from different initial geometries and maintains their sharp material interfaces, enforces prescribed minimum thickness through dual filtering, and employs an interpolation scheme to represent the two fluids and the solid within one stepped density field. The method is demonstrated on a conventional straight-channel HX and high-performance Gyroid-based HXs. Post-optimization simulations confirm the improvements, including ∼ 50.96% higher heat transfer rate in straight pipes and over 123% enhancement in power density for Gyroid HXs, attributed to increased interfacial curvature and intensified mixing effects. These results establish the dual-filtering IFSO as a viable computational method for HX optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118818"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-15Epub Date: 2026-01-07DOI: 10.1016/j.cma.2025.118724
Tao Xu , Yi Min Xie , Jie Yang
Achieving crisp, manufacturable black-and-white (0/1) designs from element-based topology optimization methods is a critical and long-standing challenge. This paper introduces a novel continuous framework, termed Explicit Binarization Topology Optimization (EBTO), that addresses this challenge by treating binarization not as an implicit byproduct but as a direct mathematical constraint. The proposed method achieves this by introducing an explicit constraint formulated using a tunable function that directly measures and controls the global “greyness” of the design. This approach fundamentally decouples the binarization mechanism from the material model, allowing for the use of a linear material interpolation scheme that simplifies sensitivity analysis and provides a clearer physical interpretation for optimization problems. The versatility and robustness of the EBTO framework are demonstrated through a comprehensive set of 2D and 3D numerical examples, including compliance minimization, compliant mechanism design, and challenging stress-based optimization problems. The results consistently show that the proposed method generates clear 0/1 solutions with excellent structural performance, demonstrating superior results in benchmark cases compared to established methods. Furthermore, a set of guiding principles for formulating such explicit constraints is established, providing a foundation for future advancements in this class of topology optimization methods.
{"title":"A continuous topology optimization framework using an explicit binarization constraint","authors":"Tao Xu , Yi Min Xie , Jie Yang","doi":"10.1016/j.cma.2025.118724","DOIUrl":"10.1016/j.cma.2025.118724","url":null,"abstract":"<div><div>Achieving crisp, manufacturable black-and-white (0/1) designs from element-based topology optimization methods is a critical and long-standing challenge. This paper introduces a novel continuous framework, termed Explicit Binarization Topology Optimization (EBTO), that addresses this challenge by treating binarization not as an implicit byproduct but as a direct mathematical constraint. The proposed method achieves this by introducing an explicit constraint formulated using a tunable function that directly measures and controls the global “greyness” of the design. This approach fundamentally decouples the binarization mechanism from the material model, allowing for the use of a linear material interpolation scheme that simplifies sensitivity analysis and provides a clearer physical interpretation for optimization problems. The versatility and robustness of the EBTO framework are demonstrated through a comprehensive set of 2D and 3D numerical examples, including compliance minimization, compliant mechanism design, and challenging stress-based optimization problems. The results consistently show that the proposed method generates clear 0/1 solutions with excellent structural performance, demonstrating superior results in benchmark cases compared to established methods. Furthermore, a set of guiding principles for formulating such explicit constraints is established, providing a foundation for future advancements in this class of topology optimization methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118724"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-15Epub Date: 2026-01-08DOI: 10.1016/j.cma.2025.118664
Christos Papagiannis , Guillaume Balarac , Pietro M. Congedo , Olivier P. Le Maître
In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.
{"title":"Autoregressive multiplier bootstrap for in-situ error estimation and quality monitoring of finite time averages in turbulent flow simulations","authors":"Christos Papagiannis , Guillaume Balarac , Pietro M. Congedo , Olivier P. Le Maître","doi":"10.1016/j.cma.2025.118664","DOIUrl":"10.1016/j.cma.2025.118664","url":null,"abstract":"<div><div>In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118664"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-15Epub Date: 2026-01-08DOI: 10.1016/j.cma.2025.118690
Maximilian Krause , Thomas Böhlke , Matti Schneider
We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a moment-matching, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group SO(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.
We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.
To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.
{"title":"Generating high-fidelity microstructures of polycrystalline materials with prescribed higher-order texture tensors","authors":"Maximilian Krause , Thomas Böhlke , Matti Schneider","doi":"10.1016/j.cma.2025.118690","DOIUrl":"10.1016/j.cma.2025.118690","url":null,"abstract":"<div><div>We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a <em>moment-matching</em>, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group <em>SO</em>(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.</div><div>We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.</div><div>To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118690"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-15Epub Date: 2026-01-08DOI: 10.1016/j.cma.2025.118700
Michał Ł. Mika , René R. Hiemstra , Stein K.F. Stoter , Dominik Schillinger
This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.
{"title":"A data-driven approach to cut-cell quadrature using spline interpolation","authors":"Michał Ł. Mika , René R. Hiemstra , Stein K.F. Stoter , Dominik Schillinger","doi":"10.1016/j.cma.2025.118700","DOIUrl":"10.1016/j.cma.2025.118700","url":null,"abstract":"<div><div>This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118700"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-15Epub Date: 2026-01-07DOI: 10.1016/j.cma.2025.118711
Shanwei Li , Zongliang Du , Zunyi Duan , Yibo Jia , Chang Liu , Zhifu Ge , Xuefeng Mu , Xu Guo
Aiming to optimize thin-walled composite structures commonly used in the aerospace industry, the concurrent optimization of stiffeners and layup angles in stiffened laminated composite structures is achieved by combining the Moving Morphable Component (MMC) method and the Shape Function with Penalization (SFP) method. Based on the proposed explicit topology optimization framework for stiffened laminate structures, optimization formulations for maximizing stiffness and maximizing fundamental natural frequency, considering additive manufacturing constraints, are proposed. An efficient numerical algorithm is established, with analytical sensitivity analysis results derived. The constraints considered include stiffener thickness limits and laminate layup requirements. In addition, by fully leveraging the larger design space of synergies between stiffeners and laminates, it is demonstrated that the design result obtained through concurrent optimization exhibits better structural performance than the stiffened laminate structures achieved through the sequential optimization of stiffener and laminate layup angles.
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