Computer Methods in Applied Mechanics and Engineering最新文献_第8页

An univariate method for multi-material topology optimization and its application to engineering structures with unstructured meshes

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-22 DOI: 10.1016/j.cma.2025.117749

Haitao Liao, Wenhao Yuan, Shigang Ai, Xujin Yuan

Multi-material topology optimization as a research hotspot has been widely investigated and all the reported multi-material interpolation models add m or m-1 design variables/level set equations to handle m levels or phases and the number of design variables is proportional to the number of material type. The current single variable interpolation model as an attractive alternative selection often leads to the emergence of interphase enclosed within the adjacent materials which excessively restricts the design space, resulting in a suboptimal solution and consequently placing limitations on the potential realistic application. To tackle the aforementioned challenges, a pioneering framework by incorporating the univariate characteristic function into the Discrete Material Optimization (DMO) scheme for the first time is proposed for both structured grids and unstructured meshes. Firstly, the univariate characteristic function is devised to transform the original single design variable field into a set of topology density functions, each independently controlling single material topology. The smoothing mechanism using the Helmholtz Partial Differential Equation (PDE) filter is applied for each topology density function field to ensure spatial correlation and continuity of single material distribution. Each filtered topology density field is in turn passed to a regularized Heaviside projection function that generates physical density field for a continuous representation of non-existence or existence for each material. All the resulting physical topology density fields ranging from 0 to 1 are then subsequently integrated to construct a composite interpolation model by virtue of the DMO scheme, preventing material overlaps due to the Helmholtz PDE filtering. The design variables allotted to nodes are updated using the method of moving asymptotes. An adaptive continuation strategy is introduced to adjust the projection slope and penalization parameters, enhancing optimization efficiency and accelerating optimization simulation. Finally, extensive numerical experiments including two practical real-world engineering examples are conducted to validate the performance of the proposed scheme. Numerical results show that the proposed method works well for both structured and unstructured meshes, while inheriting the benefits and favourable properties of both the univariate characteristic function and the DMO scheme, effectively addressing material envelope bottlenecks and reducing excessive design variables. The proposed approach offers a well-founded and flexible platform for solving multi-material topology optimization problems, making the approach practical for real-world engineering scenarios.

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引用次数: 0

Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2024.117725

Karl A. Kalina , Jörg Brummund , WaiChing Sun , Markus Kästner

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. By using a set of invariants as input, an energy-type output and by adding several correction terms to the overall energy density functional, the model fulfills multiple physical principles by construction. The invariants are formed from the right Cauchy–Green deformation tensor and fully symmetric 2nd, 4th or 6th order structure tensors which enables to describe a wide range of symmetry groups. Besides the network parameters, the structure tensors are simultaneously calibrated during training so that the underlying anisotropy of the material is reproduced most accurately. In addition, sparsity of the model with respect to the number of invariants is enforced by adding a trainable gate layer and using

ℓ_{p}

regularization. Our approach works for data containing tuples of deformation, stress and material tangent, but also for data consisting only of tuples of deformation and stress, as is the case in real experiments. The developed approach is exemplarily applied to several representative examples, where necessary data for the training of the PANN surrogate model are collected via computational homogenization. We show that the proposed model achieves excellent interpolation and extrapolation behaviors. In addition, the approach is benchmarked against an NN model based on the components of the right Cauchy–Green deformation tensor.

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引用次数: 0

Data-driven multifidelity topology design with multi-channel variational auto-encoder for concurrent optimization of multiple design variable fields

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117772

Hiroki Kawabe , Kentaro Yaji , Yuichiro Aoki

Topology optimization can generate high-performance structures with a high degree of freedom. Regardless, it generally confronts entrapment in undesirable local optima especially in problems characterized by strong non-linearity. This study aims to establish a gradient-free topology optimization framework that facilitates more global solution searches to avoid the entrapment. The framework utilizes a data-driven multifidelity topology design (MFTD), where solution candidates initially generated by solving low-fidelity (LF) optimization problems are iteratively updated by a variational auto-encoder (VAE) and high-fidelity (HF) evaluation. A key procedure of the solution update is to construct HF models by extruding material distributions obtained by the VAE to thickness distribution, which is spcatially constant across all solution candidates in the conventional data-driven MFTD. This constant assignment leads to no exploration of the thickness space, which necessitates extensive parametric studies outside the optimization loop. To enable a more comprehensive optimization in a single run, we propose a multi-channel image data architecture that stores material distributions in the first channel and other design variable fields like thickness distribution in the second or subsequent channels. This significant shift enables a thorough exploration of the additional design variable fields space with no necessity of parametric studies afterwards, by simultaneously optimizing both material distributions and those variable fields. We apply the framework to a maximum stress minimization problem, where the LF optimization problem is formulated with approximation techniques, whereas the HF evaluation is conducted by accurately analyzing the stress field, bypassing any approximation techniques. We first validate that the framework can successfully identify high-performance solutions superior to the reference solutions by effectively exploring both material and thickness distributions in a fundamental stiffness maximization. Then we demonstrate the framework can identify promising solutions for the original maximum stress minimization problems.

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引用次数: 0

On the use of physics-based constraints and validation KPI for data-driven elastoplastic constitutive modelling

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117743

Rúben Lourenço , Aiman Tariq , Petia Georgieva , A. Andrade-Campos , Babür Deliktaş

Constitutive modelling based on machine learning (ML) approaches has surged in the last couple of decades due to novel and more robust model architectures and computational power. The dependency of these models on large amounts of training data can be mitigated by imposing some phenomenological knowledge as constraints, which also helps maintain the quality of learning. This paper highlights the importance of physics-based constraints in elastoplastic data-driven constitutive modelling and focuses on model validation methods. Specifically, seven constraints applied to elastoplastic behaviour are identified that can be used during the model training process. To study the effects of these constraints, a set of recurrent neural network (RNN) models is trained using data from virtual mechanical experiments, based on a biaxial cruciform specimen. The models’ ability to accurately learn and predict the fundamental constitutive behaviour is then assessed using the different validation checkpoints, which include (i) statistical metrics, (ii) tests on previously unseen data, from virtual experiments based on different heterogeneous mechanical specimens, (iii) external key performance indicators (KPI) and (iv) single-element finite element analysis (FEA) tests. It was observed that the benefits of adding constraints to the training process were three-fold, resulting in (i) improved model predictive capacity, as well as (ii) enhanced extrapolation capabilities when tested on different mechanical specimens and (iii) overall improved training speed and stability. The use of independent validation KPI for data-driven constitutive modelling is highlighted and suggested as standard practice in future researches in the field.

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引用次数: 0

Tree–cotree-based tearing and interconnecting for 3D magnetostatics: A dual–primal approach

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117737

Mario Mally , Bernard Kapidani , Melina Merkel , Sebastian Schöps , Rafael Vázquez

The simulation of electromagnetic devices with complex geometries and large-scale discrete systems benefits from advanced computational methods like IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both concepts in an Isogeometric Tearing and Interconnecting method to enable the use of parallel computations for magnetostatic problems. We address the underlying non-uniqueness by using a graph-theoretic approach, the tree–cotree decomposition. The classical tree–cotree gauging is adapted to be feasible for parallelization, which requires that all local subsystems are uniquely solvable. Our contribution consists of an explicit algorithm for constructing compatible trees and combining it with a dual–primal approach to enable parallelization. The correctness of the proposed approach is proved and verified by numerical experiments, showing its accuracy, scalability and optimal convergence.

引用次数: 0

Phase-field hydraulic fracturing operator network based on En-DeepONet with integrated physics-informed mechanisms

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-21 DOI: 10.1016/j.cma.2025.117750

Xiaoqiang Wang , Peichao Li , Detang Lu

Hydraulic fracturing in porous media, driven by fluid injection, presents a formidable computational challenge due to the intricate interplay of fluid flow and fracture mechanics. The phase-field method offers a powerful approach for modeling such complex phenomena, but its high computational demands limit its practical application in large-scale scenarios. This work introduces a phase-field hydraulic fracturing operator network aimed at efficiently predicting fracture propagation and facilitating in the design of fracturing strategies. We develop a multi-input, multi-physics operator network based on the Enriched-DeepONet framework, incorporating multiple root networks to simultaneously handle diverse physics fields while integrating physical laws into the training process. The governing physical equations are formulated using the widely recognized phase-field hydraulic fracturing model, with Darcy’s law describing fluid flow in both fractures and the surrounding porous media. The hydraulic response across different computational domains is captured through interpolation of Darcy’s parameters using an indicator function derived from the phase-field variable. This methodology allows for the comprehensive representation of hydraulic fracturing processes through coupled partial differential equations, enabling the solution within the operator network framework. By embedding physical constraints into the loss function, the proposed model achieves enhanced convergence and accuracy during training. The effectiveness of the proposed approach is demonstrated through three numerical experiments varying in permeability, in-situ stress, critical energy release rate, and Young’s modulus. The results underscore the critical importance of integrating physical constraints to improve the accuracy of the training process. Our findings indicate that the developed phase-field hydraulic fracturing operator network is a promising advancement for enhancing the simulation capabilities of hydraulic fracturing processes.

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引用次数: 0

A transient dynamic topology optimization method with approximate dynamic response sensitivity using equivalent static loads

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-20 DOI: 10.1016/j.cma.2025.117760

Delin Cao , Yan Zeng , Zeng Meng , Gang Li

Transient dynamic response topology optimization methods always face the challenge of high computational costs due to the need for repeated time-domain discrete structural response calculations. To address this issue, the Equivalent Static Loads Method (ESLM) calculates structural responses with Equivalent Static Loads (ESLs), and solves a sequence of static response optimization problems to approximate the original dynamic problem. However, it has been noted that ESLM may not always identify a Karush–Kuhn–Tucker (KKT) point, and ESLM may produce nonnegligible errors due to using the static response sensitivity to approximate the dynamic response sensitivity, unless the dynamic characteristics of problems are weak enough. In this paper, we proposed a dynamic topology optimization method with the approximate dynamic response sensitivity by the Adjoint Variable Method (AVM) using ESLs, to replace the static response sensitivity used in ESLM. After conducting the dynamic structural analysis, the approximate sensitivity is equivalent to the dynamic sensitivity obtained by AVM. Nevertheless, the errors between them may occur and increase with increasing iterations of the static structural analysis, as the differential relationships between displacement, velocity and acceleration are relaxed. Thus, the similarity assessment criteria using necessary and sufficient conditions were proposed, which control the errors of sensitivities within an acceptable range and simplify the double-loop algorithm of ESLM into a single-loop. And the approximate structural responses can also be calculated in parallel using ESLs. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed method. It is shown that the proposed method exhibits similar capabilities to AVM in achieving optimized objectives and convergence rates. The proposed method also benefits from the efficiency of parallel computing, and the numerical example demonstrates that the overall optimization process can achieve a maximum speedup of up to around 4, with a structural response speedup of 12.7. The formula for estimating the upper limit of the overall speedup based on the structural response speedup is provided at the end.

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引用次数: 0

A deep learning framework to predict microstructurally small fatigue crack growth in three-dimensional polycrystals

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-20 DOI: 10.1016/j.cma.2024.117689

Vignesh Babu Rao, Ashley D. Spear

Accurately predicting the growth of microstructurally small cracks (MSCs) is vital for materials design and structural prognosis. Traditional physics-based simulations involving crystal plasticity, though precise, are computationally intensive and impractical for applications requiring high-throughput or real-time predictions, such as digital twins. This study introduces a deep learning framework using bidirectional long short-term memory (BiLSTM) networks to significantly expedite MSC growth predictions. Trained on comprehensive physics-based simulation data, these models leverage a novel data processing strategy to encode microstructure-dependent behavior through microstructural and micromechanical features. Notably, the input features used to predict incremental MSC growth are obtained from a physics-based simulation containing only the initial crack state, thereby obviating the need to continually update the crack state in the physics-based representation. Results demonstrate that the BiLSTM models can rapidly and accurately predict MSC growth parameters, including local crack growth rate and propagation direction, in microstructures statistically similar to the training set. The framework’s predictions on unseen scenarios, which deviate substantially from the training data, further highlight its generalizability. This accelerated prediction framework holds significant promise for future applications in identifying fracture-resistant microstructures, accurately estimating residual life in digital twin technologies, and enabling proactive structural maintenance.

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引用次数: 0

Learning the physics-consistent material behavior from measurable data via PDE-constrained optimization

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-20 DOI: 10.1016/j.cma.2025.117748

Xinxin Wu, Yin Zhang, Sheng Mao

Constitutive models play a crucial role in materials science as they describe the behavior of the materials in mathematical forms. Over the last few decades, the rapid development of manufacturing technologies has led to the discovery of many advanced materials with complex and novel behavior, which in the meantime, has also posed great challenges for constructing accurate and reliable constitutive models of these materials. In this work, we propose a data-driven approach to construct physics-consistent constitutive models for hyperelastic materials from measurable data, with the help of PDE-constrained optimization methods. Specifically, our constitutive models are based on the physically augmented neural networks (PANNs), which has been shown to ensure that the models are both physically consistent but also mathematically well-posed by construction. Specimens with deliberately introduced inhomogeneity are used to generate the data, i.e., the full-field displacement data and the total external load, for training the model. Using such approach, a considerably diverse pairs of stress–strain states can be explored with a limited number of simple tests, such as uniaxial tension. A loss function is defined to measure the difference between the data and the model prediction, which is obtained by numerically solving the governing PDEs under the same geometry and loading conditions. With the help of adjoint method, we can iteratively optimize the parameters of our NN-based constitutive models through gradient descent. We test our method for a wide range of hyperelastic materials and in all cases, our methods are able to capture the constitutive model efficiently and accurately. The trained models are also tested against unseen geometry and unseen loading conditions, exhibiting good interpolation and extrapolation capabilities.

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引用次数: 0

A novel design update framework for topology optimization with quantum annealing: Application to truss and continuum structures

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-20 DOI: 10.1016/j.cma.2025.117746

Naruethep Sukulthanasorn , Junsen Xiao , Koya Wagatsuma , Reika Nomura , Shuji Moriguchi , Kenjiro Terada

This paper presents a novel design update strategy for topology optimization, as an iterative optimization. The key contribution lies in incorporating a design updater concept with quantum annealing, applicable to both truss and continuum structures. To align with density-based approaches in topology optimization, these updaters are formulated through a multiplicative relationship to represent the design material and serve as design variables. Specifically, structural analysis is conducted on a classical computer using the finite element method, while quantum annealing is utilized for topology updates. The primary objective of the framework is to minimize compliance under a volume constraint. An encoding formulation for the design variables is derived, and the penalty method along with a slack variable is employed to transform the inequality volume constraint. Subsequently, the optimization problem for determining the updater is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. To demonstrate its performance, the developed design framework is tested on different computing platforms to perform design optimization for truss structures, as well as 2D and 3D continuum structures. Numerical results indicate that the proposed framework successfully finds optimal topologies similar to benchmark results. Furthermore, the results show the advantage of reduced time in finding an optimal design using quantum annealing compared to simulated annealing.

{"title":"A novel design update framework for topology optimization with quantum annealing: Application to truss and continuum structures","authors":"Naruethep Sukulthanasorn , Junsen Xiao , Koya Wagatsuma , Reika Nomura , Shuji Moriguchi , Kenjiro Terada","doi":"10.1016/j.cma.2025.117746","DOIUrl":"10.1016/j.cma.2025.117746","url":null,"abstract":"<div><div>This paper presents a novel design update strategy for topology optimization, as an iterative optimization. The key contribution lies in incorporating a design updater concept with quantum annealing, applicable to both truss and continuum structures. To align with density-based approaches in topology optimization, these updaters are formulated through a multiplicative relationship to represent the design material and serve as design variables. Specifically, structural analysis is conducted on a classical computer using the finite element method, while quantum annealing is utilized for topology updates. The primary objective of the framework is to minimize compliance under a volume constraint. An encoding formulation for the design variables is derived, and the penalty method along with a slack variable is employed to transform the inequality volume constraint. Subsequently, the optimization problem for determining the updater is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. To demonstrate its performance, the developed design framework is tested on different computing platforms to perform design optimization for truss structures, as well as 2D and 3D continuum structures. Numerical results indicate that the proposed framework successfully finds optimal topologies similar to benchmark results. Furthermore, the results show the advantage of reduced time in finding an optimal design using quantum annealing compared to simulated annealing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117746"},"PeriodicalIF":6.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0