Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Multiphase SPH for surface tension: Resolving zero-surface-energy modes and achieving high Reynolds number simulations","authors":"Shuaihao Zhang ,&nbsp;Sérgio D.N. Lourenço ,&nbsp;Xiangyu Hu","doi":"10.1016/j.cma.2025.118147","DOIUrl":"10.1016/j.cma.2025.118147","url":null,"abstract":"<div><div>This study introduces a Riemann-based Smoothed Particle Hydrodynamics (SPH) framework for the stable and accurate simulation of surface tension in multiphase flows, with density and viscosity ratios as high as 1000 and 100, respectively. The methodology begins with the computation of surface stress, from which the surface tension force is derived, ensuring the conservation of momentum. For the first time, this study identifies the root cause of particle disorder at fluid–fluid interfaces, attributed to a numerical instability defined herein as <em>zero-surface-energy modes</em>. To address this, we propose a novel penalty force method, which eliminates zero-surface-energy modes and significantly enhances the overall stability of the simulation. Importantly, the penalty force correction term is designed to maintain momentum conservation. The stability and accuracy of the proposed framework are validated through several benchmark cases with analytical solutions, performed under both two-dimensional and three-dimensional conditions. Furthermore, the robustness of the method is demonstrated in a three-dimensional high-velocity droplet impact scenario, achieving stable performance at high Reynolds numbers (<span><math><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>10000</mn></mrow></math></span>) and Weber numbers (<span><math><mrow><mi>W</mi><mi>e</mi><mo>=</mo><mn>25000</mn></mrow></math></span>). To the best of our knowledge, this represents the first successful demonstration of a mesh-free method achieving stable multiphase flow simulations under such extreme <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> and <span><math><mrow><mi>W</mi><mi>e</mi></mrow></math></span> conditions. A qualitative comparison with previous experimental results is also conducted, confirming the reliability of the simulation outcomes. An open-source code is provided for further in-depth study.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118147"},"PeriodicalIF":6.9,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144335662","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}

{"title":"FFV-PINN: A fast physics-informed neural network with simplified finite volume discretization and residual correction","authors":"Chang Wei ,&nbsp;Yuchen Fan ,&nbsp;Jian Cheng Wong ,&nbsp;Chin Chun Ooi ,&nbsp;Heyang Wang ,&nbsp;Pao-Hsiung Chiu","doi":"10.1016/j.cma.2025.118139","DOIUrl":"10.1016/j.cma.2025.118139","url":null,"abstract":"<div><div>With the growing application of deep learning techniques in computational physics, physics-informed neural networks (PINNs) have emerged as a major research focus. However, today’s PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often neglect information from neighboring points, which hinders their ability to enforce physical constraints and diminishes their accuracy. Furthermore, issues such as instability and poor convergence persist during PINN training, limiting their applicability to complex fluid dynamics problems. To address these challenges, this paper proposes a fast physics-informed neural network framework that integrates a simplified finite volume method (FVM) and residual correction loss term, referred to as Fast Finite Volume PINN (FFV-PINN). FFV-PINN utilizes a simplified FVM discretization for the convection term, which is one of the main sources of instability, with an accompanying improvement in the dispersion and dissipation behavior. Unlike traditional FVM, which requires careful selection of an appropriate discretization scheme based on the specific physics of the problem such as the sign of the convection term and relative magnitudes of convection and diffusion, the FFV-PINN outputs can be simply and directly harnessed to approximate values on control surfaces, thereby simplifying the discretization process. Moreover, a residual correction loss term is introduced in this study that significantly accelerates convergence and improves training efficiency. To validate the performance of FFV-PINN, we solve a series of challenging problems — including flow in the two-dimensional steady and unsteady lid-driven cavity, three-dimensional steady lid-driven cavity, backward-facing step scenarios, and natural convection at previously unsurpassed Reynolds (<span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>) number and Rayleigh (<span><math><mrow><mi>R</mi><mi>a</mi></mrow></math></span>) number, respectively — that are typically difficult for PINNs. Notably, the FFV-PINN can achieve data-free solutions for the lid-driven cavity flow at <span><math><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>10000</mn></mrow></math></span> and natural convection at <span><math><mrow><mi>R</mi><mi>a</mi><mo>=</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn></mrow></msup></mrow></math></span> for the first time in PINN literature, even while requiring only 680s and 231s respectively. These results further highlight the effectiveness of FFV-PINN in improving both speed and accuracy, marking another step forward in the progression of PINNs as competitive neural PDE solvers.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118139"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330532","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}

{"title":"Homogenization in hyperelasticity using Empirically Corrected Cluster Cubature (E3C) hyper-reduction","authors":"Stephan Wulfinghoff","doi":"10.1016/j.cma.2025.118137","DOIUrl":"10.1016/j.cma.2025.118137","url":null,"abstract":"<div><div>Computational homogenization methods open the possibility to simulate engineering structures on two scales simultaneously and to accurately describe complex macroscopic material behavior. Their intrinsically high computational cost can be alleviated through model order reduction methods in combination with hyper-reduction. The recently proposed E3C hyper-reduction method is applied to plane-strain hyperelasticity in this work. It is found that errors in the order of 1% are obtained for reinforced composites with phase contrasts of 10–100 and for porous microstructures with compressible and nearly incompressible material behavior using 10–30 integration points, depending on the application.</div><div>A second topic of the paper is concerned with the remedy of objectivity issues in geometrically nonlinear Galerkin projection applications and the related macroscopic tangent. The resulting simulation tool is provided online and enables the solution of simple two-dimensional two-scale boundary value problems with CPU times in the order of seconds to minutes with training efforts also typically in the minute range.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118137"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321935","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}

{"title":"Development and validation of an offline multiscale topology optimization framework using interpolated constraint functions","authors":"Brent Bielefeldt ,&nbsp;Richard Beblo ,&nbsp;Kevin Lawson ,&nbsp;Edward Meixner ,&nbsp;Robert Lowe","doi":"10.1016/j.cma.2025.118120","DOIUrl":"10.1016/j.cma.2025.118120","url":null,"abstract":"<div><div>Multiscale structural design is an emerging field within the aerospace community driven by the need for innovative structural concepts capable of fulfilling ever-expanding performance requirements. However, exploring novel material systems or architectures at the preliminary design stage can be inefficient due to potential changes in objectives, boundary conditions, and constraints. Such changes often necessitate a complete redesign at both the material and system levels, and can thus rapidly become intractable. To address this challenge, this paper presents a novel computational framework that seeks to reduce the barrier to entry for multiscale structural design by optimizing the structure sequentially across length scales. Specifically, a precomputed database of potential material-level responses is developed and subsequently passed to a system-level optimization process via a series of constraints. This database can be reused if the system-level problem changes, making it more suitable for the preliminary design stage. An optimized solution to a benchmark structural design problem is presented in the context of both the predicted mechanics of the problem as well as a solution obtained using a traditional structural design tool. A simplified design is then generated and compared against both an experimentally characterized 3D printed structure as well as high-fidelity finite element models, where it is shown that the proposed framework is capable of generating high-performance solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118120"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321937","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}

{"title":"AK-UL: An active learning kriging method based on uniform sampling and local refinement for efficient reliability analysis with small failure probability","authors":"Yong Pang ,&nbsp;Xiwang He ,&nbsp;Pengwei Liang ,&nbsp;Xueguan Song ,&nbsp;Ziyun Kan","doi":"10.1016/j.cma.2025.118163","DOIUrl":"10.1016/j.cma.2025.118163","url":null,"abstract":"<div><div>This paper introduces a novel active learning kriging-based reliability analysis method that uses uniform sampling and local refinement, termed AK-UL, with a focus on problems involving small failure probabilities. Traditional methods, such as AK-MCS, struggle to identify failure regions efficiently because of the irregular distribution of candidate points and the high computational cost of generating many samples. The AK-UL method overcomes these challenges by introducing a uniform sampling employed in active learning, which is separated from the random samples used for failure probability calculation. This separation ensures a more uniform distribution of training data around the limit state function, thereby enhancing the efficiency of failure region identification. Additionally, a small uniform sample set dramatically reduces the computational cost of the evaluation by the surrogate model in a small failure probability problem. Additionally, a local search process is incorporated to refine candidate points, guiding them closer to the limit state function along the gradient direction of the performance function and overcoming the sparse problem of the small uniform set that is not able to infill the design space. Numerical examples and an engineering case study demonstrate that AK-UL reduces the computational time and improves the accuracy compared with traditional methods. The results highlight that AK-UL is particularly effective for complex reliability analysis problems with small failure probabilities, offering significant computational cost savings while maintaining high accuracy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118163"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321934","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}

{"title":"Transitional active learning of small probabilities","authors":"Pengfei Wei","doi":"10.1016/j.cma.2025.118144","DOIUrl":"10.1016/j.cma.2025.118144","url":null,"abstract":"<div><div>Efficient estimation of small failure probability subjected to multiple failure domains is one of the central and challenging issues in structural reliability analysis and other rare event analysis tasks, especially in case where the computational resource is quite limited but high accuracy is required. A new active learning scheme, named as Transitional Bayesian Quadrature (TBQ), is proposed to fill this gap. Leveraging two types of smooth Artificial Intermediate Distributions (AIDs) for sequentially approaching the optimal importance sampling density, a Bayesian quadrature technique equipped with two novel acquisition functions is proposed for adaptive specification of the tempering parameters of the AIDs and active learning of the ratios of successive intermediate probabilities, with desired accuracy. Of special contribution is the presentation of closed-form formulations for facilitating the numerical computations concerning both acquisition functions and quadrature rules, making the TBQ algorithms numerically efficient and robust. A bridging scheme is also introduced for improving the stability. Two benchmark studies and two engineering applications are ultimately presented for demonstrating the effectiveness and relative merits of the two TBQ algorithms.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118144"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321936","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}

{"title":"An adaptive phase-field model integrated with multi-patch isogeometric analysis and adaptive cycle jump scheme for thermo-electro-mechanical fatigue fracture in flexoelectric solids","authors":"Haozhi Li ,&nbsp;Tiantang Yu ,&nbsp;Zhaowei Liu ,&nbsp;Jia-Nan He ,&nbsp;Leilei Chen","doi":"10.1016/j.cma.2025.118140","DOIUrl":"10.1016/j.cma.2025.118140","url":null,"abstract":"<div><div>Predicting the thermal fatigue life of flexoelectric components is of great engineering significance. In this study, an effective adaptive phase-field model combined with the cycle jump scheme is proposed to simulate thermo-electro-mechanical fatigue fracture in flexoelectric solids. To provide <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> continuity due to the presence of strain gradients, the phase-field model is implemented in the multi-patch isogeometric analysis framework based on polynomial splines over hierarchical T-meshes (PHT-splines). Multiple PHT-spline patches are employed to exactly model the geometry of the complex structure. Nitsche’s method is used to couple two adjacent patches and ensure the continuity of field variables such as displacement, electric potential, temperature, and phase field at the coupling edges. In order to reduce computational burden, an adaptive refinement strategy is adopted using the phase field as the refinement indicator. Additionally, the adaptive cycle jump method is used to improve computational efficiency further. The accuracy, reliability, and robustness of the proposed method are validated through several fatigue fracture simulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118140"},"PeriodicalIF":6.9,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144312744","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}

{"title":"Manufacturability-aware topology and toolpath co-design for continuous fiber-reinforced composites additive manufacturing","authors":"Huilin Ren ,&nbsp;Ziwen Chen ,&nbsp;Xiaoxiao Shen ,&nbsp;Yi Xiong","doi":"10.1016/j.cma.2025.118162","DOIUrl":"10.1016/j.cma.2025.118162","url":null,"abstract":"<div><div>Design for continuous fiber-reinforced polymer additive manufacturing (CFRP-AM) has evolved from sequential approaches to concurrent design methods, enabling the simultaneous optimization of structural topology and fiber toolpaths. However, existing studies fails to consider the manufacturing constraints inherent to CFRP-AM, such as toolpath width consistency and fiber continuity, which are critical to achieving both performance and manufacturability. To address these challenges, this study proposes an extended integrated structure and toolpath optimization (ISTO) method for CFRP-AM that embeds manufacturing constraints directly into the optimization problem formulation. Specifically, the toolpath width consistency constraint is modeled as a function of the scalar field gradient, with deviations minimized through standard deviation control to ensure uniform fiber deposition. The fiber continuity constraint is quantified through a penalty term derived from the logical interplay between structural and toolpath variables, ensuring smooth and uninterrupted fiber toolpaths. The method enables the concurrent optimization of structural topology and fiber toolpaths, generating designs that are both structurally robust and practically manufacturable. Case studies, including a Messerschmitt-Bölkow-Blohm (MBB) benchmark and applications in lightweight robotic systems, demonstrate the effectiveness of the proposed approach in improving manufacturability and structural performance. This method not only bridges the gap between theoretical structural design and practical manufacturing implementation but also provides a novel design paradigm for structural components in lightweight robotic systems, highlighting its potential for broader engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118162"},"PeriodicalIF":6.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144312743","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}

{"title":"A regular-vine copula-based evidence theory model for structural reliability analysis involving multidimensional parameter correlation","authors":"Dequan Zhang ,&nbsp;Xinjue Xie ,&nbsp;Zhijie Hao ,&nbsp;Weipeng Liu ,&nbsp;Xu Han ,&nbsp;Qing Li","doi":"10.1016/j.cma.2025.118152","DOIUrl":"10.1016/j.cma.2025.118152","url":null,"abstract":"<div><div>The structural reliability analysis subject to epistemic uncertainty and multidimensional correlations among input variables signifies a crucial and demanding task. To address this challenge, a new evidence theory model capable of quantifying complex multidimensional correlations is proposed in this study; and further, an efficient reliability analysis method is developed. To start with, the multidimensional correlations are investigated through the proposed regular-vine copula-based evidence theory (VCET) model by leveraging finite number of samples and the marginal distributions of evidence variables. A joint basic probability assignment reconstruction method is then developed which integrates the copula function with multidimensional correlated evidence variables using a full-factorial numerical integration approach, thereby addressing parameter correlations. Further, the proposed model is employed in reliability analysis, and an enhanced focus element reduction (EFER) technique is developed. EFER synchronously constructs multiple auxiliary regions within the frame of discernment, where the classes of joint focus elements are directly determined, bypassing the high-cost extreme value analysis. Finally, the probability interval consisting of belief and plausibility measures is derived for structures affected by parameter correlations. In this study, three numerical benchmark problems and an engineering case study on the reliability analysis of the array antenna’s maximum gain are presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118152"},"PeriodicalIF":6.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307150","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}

{"title":"Two-scale concurrent topology optimization of multiple lattice materials with non-uniform thickness interfaces","authors":"Chao Li ,&nbsp;Qihan Wang ,&nbsp;Minghui Zhang ,&nbsp;Wei Gao ,&nbsp;Zhen Luo","doi":"10.1016/j.cma.2025.118108","DOIUrl":"10.1016/j.cma.2025.118108","url":null,"abstract":"<div><div>Structures composed of multiple lattice materials have exceptional mechanical properties due to their rationally designed macrostructures and microstructures, which have enabled diverse engineering applications. However, existing topology optimization approaches for such structures often face challenges in achieving generality and flexibility, particularly in designing the thickness of interfacial regions. Hence, this paper proposes a two-scale concurrent topology optimization method for designing multiple lattice materials with non-uniform thickness interfaces, including solid shell and interface lattice materials. The method improves the existing two-step filtering/projection approach by optimizing the length scale parameter of the Helmholtz-type partial differential equation filter to control interface thickness. Additional variables associated with the filtering process are introduced to optimize the filtering strength spatially, enabling density gradients that vary across different regions. This expands the feasible design space, enhancing the potential for superior optimization outcomes. Interfaces are represented using variables derived from the spatial density gradient and a projection approach, effectively capturing non-uniform thickness characteristics. A material interpolation scheme is incorporated into the two-scale framework to handle multiple lattice materials with solid shell and interface lattice material. Numerical examples are provided to demonstrate the effectiveness and versatility of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118108"},"PeriodicalIF":6.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307152","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}