{"title":"Learning Dynamics of Nonlinear Field-Circuit Coupled Problems With a Physics-Data Combined Model","authors":"Shiqi Wu, Gérard Meunier, Olivier Chadebec, Qianxiao Li, Ludovic Chamoin","doi":"10.1002/nme.70015","DOIUrl":"https://doi.org/10.1002/nme.70015","url":null,"abstract":"<p>This work introduces a combined model that integrates a linear state-space model with a Koopman-type machine-learning model to efficiently predict the dynamics of nonlinear, high-dimensional, and field-circuit coupled systems, as encountered in areas such as electromagnetic compatibility, power electronics, and electric machines. Using an extended nonintrusive model combination algorithm, the proposed model achieves high accuracy with an error of approximately 1%, outperforming baselines: a state-space model and a purely data-driven model. Moreover, it delivers a computational speed-up of three orders of magnitude compared with the traditional time-stepping volume integral method on the same mesh in the online prediction stage, at the cost of a one-time training effort and previously mentioned error, making it highly effective for real-time and repeated predictions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Giuliano Pretti, Robert E. Bird, Nathan D. Gavin, William M. Coombs, Charles E. Augarde
{"title":"A Stable Poro-Mechanical Formulation for Material Point Methods Leveraging Overlapping Meshes and Multi-Field Ghost Penalisation","authors":"Giuliano Pretti, Robert E. Bird, Nathan D. Gavin, William M. Coombs, Charles E. Augarde","doi":"10.1002/nme.7630","DOIUrl":"https://doi.org/10.1002/nme.7630","url":null,"abstract":"<p>The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formulations for poromechanics can be affected by two major sources of instability. Firstly, inf-sup condition violation can arise when the spaces for the displacement and pressure fields are not chosen correctly, resulting in an unstable pressure field when the equations are monolithically solved. Secondly, the intrinsic nature of particle-based discretisation makes the MPM an unfitted mesh-based method, which can affect the system's condition number and solvability, particularly when background mesh elements are poorly populated. This work proposes a solution to both problems. The inf-sup condition is avoided using two overlapping meshes, a coarser one for the pressure and a finer one for the displacement. This approach does not require stabilisation of the primary equations since it is stable by design and is particularly valuable for low-order shape functions. As for the system's poor condition number, a face ghost penalisation method is added to both the primary equations, which constitutes a novelty in the context of MPM mixed formulations. This study frequently makes use of the theories of functional analysis or the unfitted Finite Element Method (FEM). Although these theories may not directly apply to the MPM, they provide a robust and logical basis for the research. These rationales are further supported by four numerical examples, which encompass both elastic and elasto-plastic cases and drained and undrained conditions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7630","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-Phase-Field Method for Dynamic Fracture in Composite Materials Based on Reduced-Order-Homogenization","authors":"Nianqi Liu, Zifeng Yuan","doi":"10.1002/nme.70012","DOIUrl":"https://doi.org/10.1002/nme.70012","url":null,"abstract":"<div>\u0000 \u0000 <p>In this manuscript, we extend the quasi-static multi-phase-field method for composite materials to the dynamic case. In the dynamic multi-phase-field method, each phase of the composites has its individual phase field, and the degradation of each phase is governed by its respective phase field. The macroscopic response is then obtained by averaging and homogenization approaches through the reduced-order-homogenization (ROH) framework. Through the ROH and the <span>Francfort-Marigo</span> variational principle, we can obtain the equations that govern the motion of the composites and the evolution of each phase field. This method is capable of capturing the characteristics of dynamic fracture, such as crack branching, without the need for any additional bifurcation criterion. Moreover, it can capture dynamic fracture patterns in composite materials, including matrix cracking, fiber breakage, and delamination. The corresponding numerical algorithm that includes spatial and temporal discretization is developed. An implicit, staggered <span>Newton-Raphson</span> iterative scheme is implemented to solve the nonlinear coupled equations. Finally, this method is tested with several sets of dynamic fracture benchmarks, which demonstrates good agreement with the experiments and other numerical methods.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Masayoshi Matsui, Hiroya Hoshiba, Koji Nishiguchi, Hiroki Ogura, Junji Kato
{"title":"Multiscale Topology Optimization Applying FFT-Based Homogenization","authors":"Masayoshi Matsui, Hiroya Hoshiba, Koji Nishiguchi, Hiroki Ogura, Junji Kato","doi":"10.1002/nme.70009","DOIUrl":"https://doi.org/10.1002/nme.70009","url":null,"abstract":"<div>\u0000 \u0000 <p>Advances in 3D-printing technology have enabled the fabrication of periodic microstructures that exhibit characteristic mechanical performances. In response, multiscale topology optimization, which finds the optimal design of microstructure for the macrostructure geometry and performance requirements, has become a hot topic in the field of structural optimization. While the basic optimization framework based on the homogenization theory spanning macro and microscales is available, it is computationally expensive and not easily applicable in practical scenarios such as high-resolution design for precision modeling and reliable design considering non-linearities. To address this issue, we focus on a homogenization analysis using a fast Fourier transform as an alternative approach to conventional finite element analysis and develop an optimization method with fast computing speed and low memory requirements. In this paper, we define a simple stiffness maximization problem with linear elastic materials and conduct two and three-dimensional optimization analyses to evaluate the validity and performance of the proposed method. We discuss the advantages of computational cost, the influence of the filtering process, and the appropriate setting of material contrast.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143447026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of a \u0000 \u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 \u0000 $$ {C}^1 $$\u0000 Polygonal Spline Element Based on the Scaled Boundary Coordinates","authors":"Zhen-Yi Liu, Chong-Jun Li","doi":"10.1002/nme.7671","DOIUrl":"https://doi.org/10.1002/nme.7671","url":null,"abstract":"<div>\u0000 \u0000 <p>We construct a new polygonal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> spline finite element method based on the scaled boundary coordinates to address the plate bending problems in the Kirchhoff-love formulation. The Bernstein interpolations are utilized in both radial and circumferential directions in the scaled boundary coordinates. Firstly, the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> continuity conditions inside an S-domain and normal derivatives constraining conditions are imposed by a simple linear system on the S-net coefficients. Secondly, to satisfy the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> connection between different polygonal elements, we construct the Hermite interpolation by equivalently transforming part of the S-net coefficients to proper boundary degrees of freedom, namely, three degrees of freedom at each vertex and a normal derivative at the midpoint of each edge. Moreover, we discuss the convergence analysis of the proposed element over convex meshes by finding the necessary and sufficient geometric conditions, where the corresponding unisolvency theorem is proved by studying the dimension of the spline space <span></span><math>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mo>∗</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>𝒯</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </msub>\u0000 <","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143447203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}