European Journal of Mechanics A-Solids最新文献

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On the limitations of linear vibrations of membrane-like multi-layered graphene sheets carrying bi-directional electric currents: An insight into the nonlinear dynamical analyses 承载双向电流的膜状多层石墨烯片线性振动的局限性:对非线性动力学分析的洞察
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-08 DOI: 10.1016/j.euromechsol.2025.105819
Keivan Kiani, Hossein Pakdaman
{"title":"On the limitations of linear vibrations of membrane-like multi-layered graphene sheets carrying bi-directional electric currents: An insight into the nonlinear dynamical analyses","authors":"Keivan Kiani,&nbsp;Hossein Pakdaman","doi":"10.1016/j.euromechsol.2025.105819","DOIUrl":"10.1016/j.euromechsol.2025.105819","url":null,"abstract":"<div><div>This study aims to present an original comprehensive investigation into the linear and nonlinear free vibration behaviors of pre-stretched multi-layered graphene nanomembranes in the presence of bi-directional electric currents. Using the Biot–Savart law, the applied nonlinear electromagnetic forces on each layer are calculated. By adopting the von Kármán large deflection theory and Eringen’s nonlocal differential/integral models, the nonlinear partial differential/integral equations of motion are methodically derived via Hamilton’s principle for the first time. These governing equations are then converted into a set of nonlinear ordinary differential equations via the Galerkin formulation, which are subsequently solved by applying the incremental harmonic balance (IHB) approach. Through numerous numerical analyses, the impacts of crucial factors, such as electric current, pre-tensioning forces, aspect ratio, number of layers, and nonlocality, on both the linear and nonlinear frequencies are comprehensively examined, further revealing the limitations of the linear analysis in capturing the free dynamic response. Such vital investigations also lead to the determination of the critical pre-tensioning forces and the critical electric currents for a special case of linear analysis, which will be of grave significance in the design and analysis of these nano-electro-mechanical systems. The results indicate that bi-directional electric currents and pre-tensioning forces exert opposing effects on the nonlinear dynamics of the nanosystem. Specifically, increasing the applied electric currents reduces the nonlinear frequencies, while increasing the pre-tensioning forces increases the nonlinear frequencies.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105819"},"PeriodicalIF":4.2,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A geometrically inspired constitutive framework for damage and intrinsic self-healing of elastomers 弹性体损伤和内在自愈的几何启发本构框架
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-08 DOI: 10.1016/j.euromechsol.2025.105800
Sanhita Das, Nivedita Kumari
{"title":"A geometrically inspired constitutive framework for damage and intrinsic self-healing of elastomers","authors":"Sanhita Das,&nbsp;Nivedita Kumari","doi":"10.1016/j.euromechsol.2025.105800","DOIUrl":"10.1016/j.euromechsol.2025.105800","url":null,"abstract":"<div><div>Autonomic interfacial self-healing in elastomers enables their reprocessing and recycling, making them valuable for applications such as ballistic resistance, surface coatings, adhesives, and biomedical materials. This article prescribes a geometry-based damage-healing theory for autonomic healing in elastomers, built on a framework where damage induces an incompatibility in the Euclidean material manifold, transforming it into a Riemannian manifold. Healing restores the Euclidean state through a reversing damage variable or an evolving healing variable. The reversing damage variable models the rebonding mechanism while the healing variable accounts for healing by chain diffusion and entanglement. The model also predicts healing in cases where rebonding is preceded by chain diffusion. The microforce balance governs the evolution of the damage and healing variables, capturing rate-dependent damage and intrinsic temperature-independent healing. The model is validated through numerical simulations, including one-dimensional and two-dimensional simulations, demonstrating accurate predictions of coupling between damage and healing and post-healing mechanical response. The model also predicts the recovery of fracture toughness with healing time in supramolecular elastomers, aligning with experimental data. With minimal parameters, the model is versatile and can easily be used for material design and structural analysis, surpassing existing models in simplicity and predictive capability.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105800"},"PeriodicalIF":4.2,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep-learning-based low-frequency bandgap prediction and elastic wave propagation properties of two-dimensional locally resonant metamaterials 基于深度学习的二维局部共振超材料低频带隙预测和弹性波传播特性
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-07 DOI: 10.1016/j.euromechsol.2025.105823
Hong-yun Yang , Xiao-sun Wang , Lu Liu , Shi-jing Wu
{"title":"Deep-learning-based low-frequency bandgap prediction and elastic wave propagation properties of two-dimensional locally resonant metamaterials","authors":"Hong-yun Yang ,&nbsp;Xiao-sun Wang ,&nbsp;Lu Liu ,&nbsp;Shi-jing Wu","doi":"10.1016/j.euromechsol.2025.105823","DOIUrl":"10.1016/j.euromechsol.2025.105823","url":null,"abstract":"<div><div>Flexible design of bandgaps is a challenge in phononic crystals for vibration damping and noise reduction applications. In this study, based on novel 2D localized resonance (LR) metamaterials, the correlation between the spatial distribution of the materials and the bandgap properties is innovatively constructed, and the bandgap formation mechanism under the synergistic effect of microstructural parameters is revealed. An intelligent design framework integrating finite element method (FEM) and artificial neural networks (ANNs) is developed, which realizes the rapid generation of massive data sets through parametric modeling techniques, significantly shortens the traditional trial-and-error design cycle, and comparatively verifies the enhancement effect of different network architectures on the bandgap prediction accuracy. It is further found that the bandgap range can be synergistically regulated by the periodic array structure size and uni/biaxial compressive strain, which verifies that the low-frequency vibration suppression bandwidth can be effectively expanded by the combination of periodic array structure size optimization and dynamic compression control, and can be used as a strategy to realize the active design of the bandgap. This predictable bandgap design paradigm breaks through the limitations of the traditional trial-and-error method, and provides a new theoretical framework and technical path for the development of vibration- and noise-reducing metamaterials with adaptive adjustment capability, which shows important application value in the fields of intelligent vibration isolation equipment and precision instrument protection.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105823"},"PeriodicalIF":4.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144840800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elastic guided waves in a spiral wire rope: Theory and modeling 螺旋钢丝绳中的弹性导波:理论与模型
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-07 DOI: 10.1016/j.euromechsol.2025.105821
F. Treyssède
{"title":"Elastic guided waves in a spiral wire rope: Theory and modeling","authors":"F. Treyssède","doi":"10.1016/j.euromechsol.2025.105821","DOIUrl":"10.1016/j.euromechsol.2025.105821","url":null,"abstract":"<div><div>Elastic guided waves are of great interest for the non-destructive evaluation of cables. However, accurately modeling wave propagation in these structures requires complex numerical models that account for their helical, multi-wire geometry and the effects of prestress due to high tension loads. This paper provides a theoretical and computational framework for studying wave propagation in spiral ropes, also known as spiral strands, consisting of a central wire surrounded by two layers of helical wires. These layers are typically wound in opposite directions, breaking continuous symmetry and introducing both line and point interwire contacts. Using a non-trivial curvilinear coordinate system, termed bi-helical, this paper establishes the existence of wave modes in such structures, defines the three-dimensional repetitive unit cell of the spiral rope, and implements a specific Bloch–Floquet wave finite-element method to solve the wave propagation eigenproblem along bi-directional helical coordinates. Interwire contact areas and their dependence on tensile loads are approximated through geometric interpenetrations governed by Hertzian contact laws. The proposed method is validated through numerical experiments on reference test cases, including a cylinder, a seven-wire strand, and a special spiral strand exhibiting translational symmetry. Finally, dispersion curves are presented for various two-layered spiral strands, considering different helix angles and tensile loads. The results reveal complex wave behavior, characterized by multiple veerings strongly influenced by contact areas, paving the way for future experiments and practical applications in the non-destructive evaluation of cables.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105821"},"PeriodicalIF":4.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144840799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tunable second-order elastic topological insulator and multi-dimensional rainbow trapping in ferroelectric phononic crystal plates 可调谐二阶弹性拓扑绝缘体和铁电声子晶体板中的多维彩虹俘获
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105822
Shao-Yong Huo , Qiu-Shuang Yang , Zhi-Peng Jin , Shu-xin Zhang , Chun-Ming Fu , Jiu-Jiu Chen , Rong-hua Chen
{"title":"Tunable second-order elastic topological insulator and multi-dimensional rainbow trapping in ferroelectric phononic crystal plates","authors":"Shao-Yong Huo ,&nbsp;Qiu-Shuang Yang ,&nbsp;Zhi-Peng Jin ,&nbsp;Shu-xin Zhang ,&nbsp;Chun-Ming Fu ,&nbsp;Jiu-Jiu Chen ,&nbsp;Rong-hua Chen","doi":"10.1016/j.euromechsol.2025.105822","DOIUrl":"10.1016/j.euromechsol.2025.105822","url":null,"abstract":"<div><div>Manipulation of elastic waves to achieve rainbow trapping effect has attracted wide attention. However, most of the current researches achieve rainbow trapping effect by changing the structural parameters, which means that the structure and mechanical properties are always fixed. Realizing the actively tunable working frequency range in elastic topological systems and obtain multi-dimensional rainbow trapping is still a challenge. In this paper, we design a topologically protected second-order thermostatic phononic crystal (PC) plate by using ferroelectric ceramic materials. By adjusting the rotation angle of the T-shaped scatterer, we can realize the multi-dimensional topological phase transition between the bulk and edge bands of elastic wave. Then, a “trivial-nontrivial-trivial” (TNT) heterostructure is constructed to obtain the coupled topological edge states of elastic wave, and the influence of intermediate coupling layer number on the edge states is investigated, which exhibits a multi-mode interference effect. Furthermore, the tunable topological edge states and corner states of elastic wave are obtained based on the temperature control of the ferroelectric materials. In addition, by employing the active tunability of the coupled edge states and corner states, the multi-dimensional topological rainbow trapping of elastic wave in ferroelectric PC plates is demonstrated. The edge and corner states of different frequencies are well separated and captured in different spatial positions, and the working frequency range of the PC plate can be easily tuned by controlling the temperature. Our results further promote the practical integration application of tunable and multi-dimensional elastic wave devices.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105822"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical solution to the scattering of Rayleigh waves by spherical inclusions 球形夹杂物对瑞利波散射的解析解
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105827
Zeyu Cao, Pengyang Zhao
{"title":"Analytical solution to the scattering of Rayleigh waves by spherical inclusions","authors":"Zeyu Cao,&nbsp;Pengyang Zhao","doi":"10.1016/j.euromechsol.2025.105827","DOIUrl":"10.1016/j.euromechsol.2025.105827","url":null,"abstract":"<div><div>The scattering of Rayleigh waves by various types of inclusions is of great significance to analyzing many experimentally measured surface acoustic waves but still lacks any analytical solution so far. Here we succeed in expressing the Rayleigh wave as a linear combination of spherical harmonic functions with all the coefficients being given in closed-form. In the context of multiple reflections during the scattering of Rayleigh waves by spherical inclusions, the primary “first reflection” introduced by the boundary condition of inclusions is decoupled using spherical harmonic series. Using this framework, we present, for the first time, the near-field analytical solution for the scattered Rayleigh waves by spherical inclusions (in the absence of multiple reflections) of two fundamental types, i.e., a rigid inclusion and a void. The significant difference between scattering signals of the two types provides the possibility to characterize inclusions with different mechanical properties via scattering of Rayleigh wave.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105827"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simulating scatter in fragmentation of metal rings and tubes 模拟金属环和金属管碎片中的散射
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105806
J.D. Robson , D. Armstrong , J. Cordell
{"title":"Simulating scatter in fragmentation of metal rings and tubes","authors":"J.D. Robson ,&nbsp;D. Armstrong ,&nbsp;J. Cordell","doi":"10.1016/j.euromechsol.2025.105806","DOIUrl":"10.1016/j.euromechsol.2025.105806","url":null,"abstract":"<div><div>Understanding the break up of a metal component under high strain rate deformation by natural fragmentation is important in a range of industrial and military applications. In this work, natural fragmentation of metal rings and tubes has been simulated in a finite element model by assigning initial damage sampled from an empirical damage function. Different random sampling of this function leads to differences in behaviour, enabling both the average and scatter in fragmentation to be predicted. Once calibrated for one condition, the model provides a good prediction of the mean and scatter in the number of fragments from ring expansion experiments reported in the literature. The model has been extended to consider damage in aligned bands, replicating the spatially correlated defects expected from manufacturing processes such as extrusion or additive manufacture. Fragment formation is strongly affected by damage bands, which can lead to a much greater maximum fragment size and more consistent behaviour. However, not all high damage bands will lead to fracture, and a simple criterion for assessing this is presented.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105806"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mitigation of vertical vibrations in coupled meta-rods through internal interactions and boundary constraint 通过内部相互作用和边界约束减轻耦合棒的垂直振动
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105826
Haoran Lu , Jacopo M. De Ponti , Raffaele Ardito , Li Xiao , Yuanqiang Cai , Zhigang Cao
{"title":"Mitigation of vertical vibrations in coupled meta-rods through internal interactions and boundary constraint","authors":"Haoran Lu ,&nbsp;Jacopo M. De Ponti ,&nbsp;Raffaele Ardito ,&nbsp;Li Xiao ,&nbsp;Yuanqiang Cai ,&nbsp;Zhigang Cao","doi":"10.1016/j.euromechsol.2025.105826","DOIUrl":"10.1016/j.euromechsol.2025.105826","url":null,"abstract":"<div><div>Environmental vibrations caused by seismic waves and traffic loads pose increasing risks in urban areas due to their low attenuation and structural impact. To mitigate the in-plane bulk waves and vertical Raleigh wave component generated by ambient vibrations, we proposed a coupled meta-rod assembled from a local resonance (LR) bar and a negative-stiffness (NS) system. This meta-rod is designed in two forms to redistribute the wave energy, where the NS system is introduced as a boundary constraint. We develop analytical models based on the Bloch conditions and the transfer matrix method to solve and investigate dispersion relationship and transmission abilities. Complementarily, finite elements (FE) models are also established to validate the analytical results and further visualise the interaction between the LR bar and NS system during longitudinal wave propagation. The results indicate that most of long-wavelength waves propagate through the low-stiffness medium within the coupled system. As wave energy is redistributed across frequency, an additional attenuation region emerges beyond the LR bandgap due to the maximum in-phase motion between the LR bar and NS system. This internal interaction gradually dominates the attenuation mechanism as the LR bandgap shifts toward lower frequencies under boundary constraints, providing more effective suppression before the resonance frequency. This study offers a promising strategy for the design of efficient vertical vibration mitigation solutions.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105826"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Physics-informed Fourier neural operator for the bending analysis of bi-directional functionally graded beams with variable cross-sections 用于变截面双向功能梯度梁弯曲分析的傅立叶神经算子
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105798
Duy-Trung Vo, Jaehong Lee
{"title":"Physics-informed Fourier neural operator for the bending analysis of bi-directional functionally graded beams with variable cross-sections","authors":"Duy-Trung Vo,&nbsp;Jaehong Lee","doi":"10.1016/j.euromechsol.2025.105798","DOIUrl":"10.1016/j.euromechsol.2025.105798","url":null,"abstract":"<div><div>Neural operators have recently shown great potential for solving parametric partial differential equations (PDEs). However, their training process requires a large labeled input–output dataset, which is computationally expensive in engineering modeling. Consequently, physics-informed neural operators, which forego that requirement, have attracted significant attention. In this work, a physics-informed Fourier neural operator (PIFNO) is proposed for the bending analysis of bi-directional functionally graded (BDFG) beams with variable cross-sections. The problem is formulated as a boundary value problem with variable coefficients. These coefficients include the material and geometrical properties, while the beam response is measured in terms of transverse displacement and bending moment. PIFNO is designed to predict the beam’s response (output) given the coefficients (input). The input is characterized by the flexural stiffness, based on Euler–Bernoulli beam theory, and the output is approximated by a Fourier neural operator (FNO). In PIFNO, a non-dimensional form of the governing equations is introduced along with property scaling. Furthermore, the output is combined with boundary conditions to produce a new output that automatically satisfies these conditions. The loss function is defined using the finite difference method (FDM). Numerical examples examine various types of material distributions and different forms of variable cross-sections under multiple boundary conditions. The results show that PIFNO can accurately predict the displacement and bending moment for various boundary conditions without requiring a labeled input–output dataset.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105798"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random phase field method for quasi-static and dynamic fracture propagation: Strict phase field equations based on variational principle 准静态和动态断裂扩展的随机相场方法:基于变分原理的严格相场方程
IF 4.2 2区 工程技术
European Journal of Mechanics A-Solids Pub Date : 2025-08-05 DOI: 10.1016/j.euromechsol.2025.105815
Shuwei Zhou , Xiuhan He , Yingjun Xu , Caichu Xia , Xiaoying Zhuang , Timon Rabczuk
{"title":"Random phase field method for quasi-static and dynamic fracture propagation: Strict phase field equations based on variational principle","authors":"Shuwei Zhou ,&nbsp;Xiuhan He ,&nbsp;Yingjun Xu ,&nbsp;Caichu Xia ,&nbsp;Xiaoying Zhuang ,&nbsp;Timon Rabczuk","doi":"10.1016/j.euromechsol.2025.105815","DOIUrl":"10.1016/j.euromechsol.2025.105815","url":null,"abstract":"<div><div>Spatial variability in mechanical properties significantly affects fracture evolution in materials. A strict random phase field model suitable for spatially heterogeneous materials is developed, in which a gradient term of the critical energy release rate is introduced. Compared with the simple integration of traditional finite element models with random fields, which involves merely replacing deterministic mechanical properties in the governing equations, a more accurate coupling approach is adopted by incorporating a coordinate-dependent critical energy release rate into the energy functional, which is reformulated from existing models. The governing equation of the phase field is derived through variational principles. Unlike traditional random phase field models, the proposed model captures the spatial variation in the gradient of the critical energy release rate and effectively characterizes the directional rate of change in fracture toughness. The proposed model is implemented by using COMSOL Multiphysics and MATLAB, and validated through the rock fracture experiment. Quasi-static and dynamic fracture simulations reveal that in the presence of pronounced spatial heterogeneity, incorporating the critical energy release rate gradient can significantly alters fracture behavior in heterogeneous materials, often producing effects not captured by traditional random phase field models. Therefore, the rigorous random phase field model is indispensable for understanding and predicting the fracture behavior of spatially heterogeneous materials such as rocks.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"115 ","pages":"Article 105815"},"PeriodicalIF":4.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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