Pub Date : 2024-12-07DOI: 10.1016/j.euromechsol.2024.105527
David Lindblom, Carl F.O. Dahlberg
This paper presents a finite element implementation of strain gradient plasticity (SGP) and coupled hydrogen diffusion. The model encompasses stress-assisted diffusion, solute swelling, and multiple trap sites. The primary achievement of this paper is that a new transport term, that is driven by plastic strain gradients, has been developed and implemented with the finite element method (FEM). The model is applied to the problem of biaxial loading of a solid, under plane strain conditions, featuring a circular hole to investigate the extended transport equation. The results show that the hydrogen concentration increases significantly compared to conventional stress-assisted diffusion. In addition, the localization of hydrogen occurs in regions where there is a restriction on the plastic strain state, such as is often the case around microstructural sites. Together with other mechanisms at play during hydrogen embrittlement this preferential segregation could be used to explain the intergranular fracture mode often observed in experiments.
{"title":"A strain gradient plasticity model to investigate diffusion and dynamic segregation of hydrogen","authors":"David Lindblom, Carl F.O. Dahlberg","doi":"10.1016/j.euromechsol.2024.105527","DOIUrl":"10.1016/j.euromechsol.2024.105527","url":null,"abstract":"<div><div>This paper presents a finite element implementation of strain gradient plasticity (SGP) and coupled hydrogen diffusion. The model encompasses stress-assisted diffusion, solute swelling, and multiple trap sites. The primary achievement of this paper is that a new transport term, that is driven by plastic strain gradients, has been developed and implemented with the finite element method (FEM). The model is applied to the problem of biaxial loading of a solid, under plane strain conditions, featuring a circular hole to investigate the extended transport equation. The results show that the hydrogen concentration increases significantly compared to conventional stress-assisted diffusion. In addition, the localization of hydrogen occurs in regions where there is a restriction on the plastic strain state, such as is often the case around microstructural sites. Together with other mechanisms at play during hydrogen embrittlement this preferential segregation could be used to explain the intergranular fracture mode often observed in experiments.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105527"},"PeriodicalIF":4.4,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-05DOI: 10.1016/j.euromechsol.2024.105532
Gary F. Dargush
A boundary element formulation for three-dimensional size-dependent couple stress elastostatic analysis is developed for the first time in the present work. The resulting computational method can play an important role in evaluating the mechanical response of a wide variety of components and systems at the micro- and nano-scale within a continuum framework. Initially, the infinite space fundamental solution is obtained by following the systematic Kupradze method and the remaining kernel functions due to point forces and point couples are derived. Via the reciprocal theorem, the boundary integral representation is then developed, and details of the numerical implementation are provided. In this process, regularization techniques are introduced, along with a novel five-node hybrid displacement-rotation boundary element, to eliminate the need for Cauchy principal value and Hadamard finite part integrals despite the deeply singular nature of the couple stress kernels. Several prototype computational examples are studied to explore the convergence of this new boundary element method and to elucidate some interesting behavior of couple stress theory, including the importance of three-dimensional analysis.
{"title":"Boundary element method for three-dimensional couple stress elastostatic analysis","authors":"Gary F. Dargush","doi":"10.1016/j.euromechsol.2024.105532","DOIUrl":"10.1016/j.euromechsol.2024.105532","url":null,"abstract":"<div><div>A boundary element formulation for three-dimensional size-dependent couple stress elastostatic analysis is developed for the first time in the present work. The resulting computational method can play an important role in evaluating the mechanical response of a wide variety of components and systems at the micro- and nano-scale within a continuum framework. Initially, the infinite space fundamental solution is obtained by following the systematic Kupradze method and the remaining kernel functions due to point forces and point couples are derived. Via the reciprocal theorem, the boundary integral representation is then developed, and details of the numerical implementation are provided. In this process, regularization techniques are introduced, along with a novel five-node hybrid displacement-rotation boundary element, to eliminate the need for Cauchy principal value and Hadamard finite part integrals despite the deeply singular nature of the couple stress kernels. Several prototype computational examples are studied to explore the convergence of this new boundary element method and to elucidate some interesting behavior of couple stress theory, including the importance of three-dimensional analysis.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105532"},"PeriodicalIF":4.4,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136228","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}
Isothermal fatigue (IF) and thermo-mechanical fatigue (TMF) tests are conducted on type 316L austenitic stainless steel within a temperature range of 475 °C–625 °C under symmetric strain-controlled condition. The results indicate that 316L exhibits significant cyclic hardening, strain range memory effect (SRME), temperature history effect (THE), and phase angle effect (PAE). An improved damage-coupled unified viscoplastic constitutive model (DCUVCM) is accordingly developed based on the framework of Chaboche model and a widely-utilized creep-fatigue interaction damage model. In which, cycle- and maximum inelastic strain amplitude-dependent scalar functions are coupled into nonlinear kinematic hardening rules (KHRs) and isotropic hardening rules (IHRs) to describe cyclic hardening and SRME. THE is explained by introducing temperature rate terms into both the KHR and IHR. Moreover, a novel phasing coefficient is incorporated into the damage variable to describe the PAE. Eventually, the excellent agreement between experimental and simulated results under both IF and TMF loadings demonstrates the robustness of the proposed DCUVCM in predicting the whole-life cyclic response and fatigue life of 316L.
{"title":"A damage-coupled unified constitutive modelling for predicting the deformation behaviour of 316L under isothermal fatigue and thermo-mechanical fatigue loading conditions","authors":"Qiaofa Yang, Wei Zhang, Peng Niu, Xinghui Chen, Peng Yin, Le Chang, Changyu Zhou","doi":"10.1016/j.euromechsol.2024.105529","DOIUrl":"10.1016/j.euromechsol.2024.105529","url":null,"abstract":"<div><div>Isothermal fatigue (IF) and thermo-mechanical fatigue (TMF) tests are conducted on type 316L austenitic stainless steel within a temperature range of 475 °C–625 °C under symmetric strain-controlled condition. The results indicate that 316L exhibits significant cyclic hardening, strain range memory effect (SRME), temperature history effect (THE), and phase angle effect (PAE). An improved damage-coupled unified viscoplastic constitutive model (DCUVCM) is accordingly developed based on the framework of Chaboche model and a widely-utilized creep-fatigue interaction damage model. In which, cycle- and maximum inelastic strain amplitude-dependent scalar functions are coupled into nonlinear kinematic hardening rules (KHRs) and isotropic hardening rules (IHRs) to describe cyclic hardening and SRME. THE is explained by introducing temperature rate terms into both the KHR and IHR. Moreover, a novel phasing coefficient is incorporated into the damage variable to describe the PAE. Eventually, the excellent agreement between experimental and simulated results under both IF and TMF loadings demonstrates the robustness of the proposed DCUVCM in predicting the whole-life cyclic response and fatigue life of 316L.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105529"},"PeriodicalIF":4.4,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136212","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}
Pub Date : 2024-12-03DOI: 10.1016/j.euromechsol.2024.105530
Jiayu Tian , Chenzhe Li , Guohua Nie , Xingwei Zhao , Ying Zhao
Soft materials are widely employed in wearable electronics, soft robotics and biomedicine due to high deformability and superior flexibility. However, large deformability and flexibility in general come with highly nonlinear viscoelastic behavior, which poses great challenges for traditional polymer processing methods to manufacture these materials into three-dimensional (3D) structures with high precision. Converting flat soft materials into 3D forms through prestress is an effective solution for fabrication of complex 3D morphologies. However, the 3D shapes cannot be customized due to the limit of existent manufacturing strategy, which hinders further application. In this paper, we report a 3D-assembly strategy of customizable shape. It utilizes the spontaneous spring-back of pre-stretched elastomer film upon release as the driving force for shape transformation, creating 3D structure from flat two-dimensional (2D) configuration. Furthermore, the use of digital light processing technology ensures 3D morphologies to be constructed from programmable 2D configurations with high precision. Spiral band and double-curvature surfaces are created from designed 2D patterns as demonstration. In addition, we created a wearable luminous band that spontaneously wrap around fingers under stress relaxation. This work offers a straightforward, controllable, and transferable technique that is efficient for the creation of 3D soft structures.
{"title":"Prestress-induced 3D assembly of soft material with programmable shape","authors":"Jiayu Tian , Chenzhe Li , Guohua Nie , Xingwei Zhao , Ying Zhao","doi":"10.1016/j.euromechsol.2024.105530","DOIUrl":"10.1016/j.euromechsol.2024.105530","url":null,"abstract":"<div><div>Soft materials are widely employed in wearable electronics, soft robotics and biomedicine due to high deformability and superior flexibility. However, large deformability and flexibility in general come with highly nonlinear viscoelastic behavior, which poses great challenges for traditional polymer processing methods to manufacture these materials into three-dimensional (3D) structures with high precision. Converting flat soft materials into 3D forms through prestress is an effective solution for fabrication of complex 3D morphologies. However, the 3D shapes cannot be customized due to the limit of existent manufacturing strategy, which hinders further application. In this paper, we report a 3D-assembly strategy of customizable shape. It utilizes the spontaneous spring-back of pre-stretched elastomer film upon release as the driving force for shape transformation, creating 3D structure from flat two-dimensional (2D) configuration. Furthermore, the use of digital light processing technology ensures 3D morphologies to be constructed from programmable 2D configurations with high precision. Spiral band and double-curvature surfaces are created from designed 2D patterns as demonstration. In addition, we created a wearable luminous band that spontaneously wrap around fingers under stress relaxation. This work offers a straightforward, controllable, and transferable technique that is efficient for the creation of 3D soft structures.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105530"},"PeriodicalIF":4.4,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136213","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}
Pub Date : 2024-12-03DOI: 10.1016/j.euromechsol.2024.105514
Giorgio Previati, Federico Ballo, Pietro Stabile
Beams on elastic foundations are applied to a vast number of engineering problems. Several elastic foundation models are available, from the simplest Winkler element with one parameter to complex models with more parameters and nonlinear characteristics. Analytical and numerical approaches have been developed in the literature for the solution of this problem, often specialized for a particular application. In this paper, a novel numerical approach that can be applied to any combination of beam and foundation models is presented. The method is based on independent meshes for the beam and for the foundation. The independent discretization of the foundation opens the possibility to model any kind of foundation behaviour, including nonlinearities, discontinuities and space-dependent properties. The two meshes are then connected by a variable reduction approach, formulated by standard finite element procedures. Such an approach allows to refine the discretization of the foundation without affecting the dimension of the solving system, i.e. with a limited effect on the computational time. Additionally, a relevant advantage of the presented method is that, contrary to most approaches described in the literature, gaps between the beam and the foundation can be straightforwardly included by an energy-based formulation. Examples of applications to linear, nonlinear, and foundation with gaps are reported in the paper. This innovative approach not only simplifies the modelling process but also offers significant computational advantages, making it a versatile and efficient tool for a wide range of engineering applications involving beam–foundation interactions.
{"title":"Beams on elastic foundation: A variable reduction approach for nonlinear contact problems","authors":"Giorgio Previati, Federico Ballo, Pietro Stabile","doi":"10.1016/j.euromechsol.2024.105514","DOIUrl":"10.1016/j.euromechsol.2024.105514","url":null,"abstract":"<div><div>Beams on elastic foundations are applied to a vast number of engineering problems. Several elastic foundation models are available, from the simplest Winkler element with one parameter to complex models with more parameters and nonlinear characteristics. Analytical and numerical approaches have been developed in the literature for the solution of this problem, often specialized for a particular application. In this paper, a novel numerical approach that can be applied to any combination of beam and foundation models is presented. The method is based on independent meshes for the beam and for the foundation. The independent discretization of the foundation opens the possibility to model any kind of foundation behaviour, including nonlinearities, discontinuities and space-dependent properties. The two meshes are then connected by a variable reduction approach, formulated by standard finite element procedures. Such an approach allows to refine the discretization of the foundation without affecting the dimension of the solving system, i.e. with a limited effect on the computational time. Additionally, a relevant advantage of the presented method is that, contrary to most approaches described in the literature, gaps between the beam and the foundation can be straightforwardly included by an energy-based formulation. Examples of applications to linear, nonlinear, and foundation with gaps are reported in the paper. This innovative approach not only simplifies the modelling process but also offers significant computational advantages, making it a versatile and efficient tool for a wide range of engineering applications involving beam–foundation interactions.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105514"},"PeriodicalIF":4.4,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-02DOI: 10.1016/j.euromechsol.2024.105501
Bruno Musil, Philipp Höfer
The advent of additive manufacturing has profoundly transformed component production. However, anisotropic structural behaviour is frequently observed in additively manufactured components, despite the isotropic nature of the constituent materials. This behaviour can be attributed to the manufacturing process, which involves the extrusion and deposition of individual material paths or the powder-based melting of such paths. For example, fused deposition modelling is a common technique employed in the production of polymer components. Technological advancements have enabled the use of fibre reinforcement, which can further amplify anisotropic material behaviour.
Several computational models and approaches have been proposed for simulating and optimising additively manufactured components treated as an anisotropic continuum. Current methods rely on a finite element discretisation of the continuum, where the print paths are assumed to be linear within a finite element. However, since the print paths are essentially arbitrary curves, a fine discretisation is necessary to achieve realistic simulations.
In this work, we propose a curvilinear local approach, where the print paths at the element level are considered to be curvilinear. The fineness of the mesh used in this concept depends solely on the stress gradients that need to be resolved. Furthermore, curvilinear print paths represent the coordinate lines used to describe anisotropy. As a result, the solution to the balance of linear momentum occurs within the local curvilinear coordinate system. This paper presents the implementation of this approach within the finite element method, using an exemplary boundary value problem.
{"title":"Simulation of anisotropic behaviour in additively manufactured structures using a curvilinear coordinate based finite element formulation","authors":"Bruno Musil, Philipp Höfer","doi":"10.1016/j.euromechsol.2024.105501","DOIUrl":"10.1016/j.euromechsol.2024.105501","url":null,"abstract":"<div><div>The advent of additive manufacturing has profoundly transformed component production. However, anisotropic structural behaviour is frequently observed in additively manufactured components, despite the isotropic nature of the constituent materials. This behaviour can be attributed to the manufacturing process, which involves the extrusion and deposition of individual material paths or the powder-based melting of such paths. For example, fused deposition modelling is a common technique employed in the production of polymer components. Technological advancements have enabled the use of fibre reinforcement, which can further amplify anisotropic material behaviour.</div><div>Several computational models and approaches have been proposed for simulating and optimising additively manufactured components treated as an anisotropic continuum. Current methods rely on a finite element discretisation of the continuum, where the print paths are assumed to be linear within a finite element. However, since the print paths are essentially arbitrary curves, a fine discretisation is necessary to achieve realistic simulations.</div><div>In this work, we propose a curvilinear local approach, where the print paths at the element level are considered to be curvilinear. The fineness of the mesh used in this concept depends solely on the stress gradients that need to be resolved. Furthermore, curvilinear print paths represent the coordinate lines used to describe anisotropy. As a result, the solution to the balance of linear momentum occurs within the local curvilinear coordinate system. This paper presents the implementation of this approach within the finite element method, using an exemplary boundary value problem.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105501"},"PeriodicalIF":4.4,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1016/j.euromechsol.2024.105515
Changzhi Hu , Zhishuai Wan , Zonghan Li , Ximing Tan , Lichen Wang , Mingji Chen
The quasi-zero stiffness (QZS) vibration isolator is considered to be an effective way to address the contradiction between high load-bearing capacity and low-frequency vibration isolation. However, the design of traditional QZS isolators with multiple components, brings about complexity in structure integration, while designing a structure that is compact and lightweight is required for many engineering applications, especially for aerospace engineering. In this study, inverse design was employed to achieve QZS characteristics of the curved beam system. The trajectory of the cross-section center of a curved beam was optimized by using the genetic algorithm. The present design strategy has the advantage of achieving customizable stiffness and load-bearing capability, as well as constructing multiple QZS regions. The harmonic balance method was employed to analyze the dynamic response of the metatructure, and a parameter analysis was conducted to assess its isolation performance. Numerical simulations were also used to validate the theoretical model in the time and frequency domains, respectively. It is demonstrated by experiment that the proposed metastructure can effectively isolate vibrations above 4.67 Hz, with a mass of only 3.2% of the its load-bearing capacity. The presented design strategy provides a feasible solution for the compact and lightweight low-frequency vibration isolators, particularly benefiting miniature devices, precision instruments, and aerospace applications where space and weight constraints are critical.
{"title":"Inverse-designed metastructures with customizable low dynamic stiffness characteristics for low-frequency vibration isolation","authors":"Changzhi Hu , Zhishuai Wan , Zonghan Li , Ximing Tan , Lichen Wang , Mingji Chen","doi":"10.1016/j.euromechsol.2024.105515","DOIUrl":"10.1016/j.euromechsol.2024.105515","url":null,"abstract":"<div><div>The quasi-zero stiffness (QZS) vibration isolator is considered to be an effective way to address the contradiction between high load-bearing capacity and low-frequency vibration isolation. However, the design of traditional QZS isolators with multiple components, brings about complexity in structure integration, while designing a structure that is compact and lightweight is required for many engineering applications, especially for aerospace engineering. In this study, inverse design was employed to achieve QZS characteristics of the curved beam system. The trajectory of the cross-section center of a curved beam was optimized by using the genetic algorithm. The present design strategy has the advantage of achieving customizable stiffness and load-bearing capability, as well as constructing multiple QZS regions. The harmonic balance method was employed to analyze the dynamic response of the metatructure, and a parameter analysis was conducted to assess its isolation performance. Numerical simulations were also used to validate the theoretical model in the time and frequency domains, respectively. It is demonstrated by experiment that the proposed metastructure can effectively isolate vibrations above 4.67 Hz, with a mass of only 3.2% of the its load-bearing capacity. The presented design strategy provides a feasible solution for the compact and lightweight low-frequency vibration isolators, particularly benefiting miniature devices, precision instruments, and aerospace applications where space and weight constraints are critical.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"110 ","pages":"Article 105515"},"PeriodicalIF":4.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756940","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}
Pub Date : 2024-11-26DOI: 10.1016/j.euromechsol.2024.105504
Shanhong Lin, Qiang Han, Chunlei Li
With the miniaturization of devices, the size effect of structures becomes increasingly apparent and it becomes crucial to consider flexoelectricity in MEMS/NEMS. Given that functionally graded materials (FGMs) can generate strain gradients that enhance flexoelectricity, it is both novel and crucial to investigate the synergistic effects of FGMs and flexoelectricity on bandgap characteristics. Understanding these interactions is essential for advancing materials science and could lead to significant innovations in nanotechnology. In this work, a theorectical model for the periodic flexoelectric doubly-curved nanoshells with bi-directional functionally graded (BDFG) and porosity considered are constructed. As the governing equations for longitudinal FG problems are more difficult to be solved analytically, their precise analysis is more challenging. Thus, an improved transfer matrix method based on state-space is proposed innovatively to obtain the complex band structures for longitudinal FG problems. Subsequently, the influences of the flexoelectric effect, strain gradient effect, BDFG indices, and porosity distributions on bandgaps are systematically discussed. The results indicate that the flexoelectric effect is non-negligible at small scales, which generally widens the bandgaps, with higher frequency ranges and larger attenuation capacity. Bandgaps are sensitive to the variation of functionally graded indices. Particularly, flexoelectricity brings about the appearance and disappearance of some bandgaps during the variation of FG index in the thickness direction , and complicates the bandgaps variation. Besides, the porosity distribution patterns and porosity coefficients enrich the regulation of bandgaps. Our investigation offers valuable insights into the application of flexoelectric electrical components combined with BDFG in MEMS/NEMS to the wave propagation domain.
{"title":"Flexoelectric effect on bandgap properties of periodic bi-directional-graded curved nanoshells","authors":"Shanhong Lin, Qiang Han, Chunlei Li","doi":"10.1016/j.euromechsol.2024.105504","DOIUrl":"10.1016/j.euromechsol.2024.105504","url":null,"abstract":"<div><div>With the miniaturization of devices, the size effect of structures becomes increasingly apparent and it becomes crucial to consider flexoelectricity in MEMS/NEMS. Given that functionally graded materials (FGMs) can generate strain gradients that enhance flexoelectricity, it is both novel and crucial to investigate the synergistic effects of FGMs and flexoelectricity on bandgap characteristics. Understanding these interactions is essential for advancing materials science and could lead to significant innovations in nanotechnology. In this work, a theorectical model for the periodic flexoelectric doubly-curved nanoshells with bi-directional functionally graded (BDFG) and porosity considered are constructed. As the governing equations for longitudinal FG problems are more difficult to be solved analytically, their precise analysis is more challenging. Thus, an improved transfer matrix method based on state-space is proposed innovatively to obtain the complex band structures for longitudinal FG problems. Subsequently, the influences of the flexoelectric effect, strain gradient effect, BDFG indices, and porosity distributions on bandgaps are systematically discussed. The results indicate that the flexoelectric effect is non-negligible at small scales, which generally widens the bandgaps, with higher frequency ranges and larger attenuation capacity. Bandgaps are sensitive to the variation of functionally graded indices. Particularly, flexoelectricity brings about the appearance and disappearance of some bandgaps during the variation of FG index in the thickness direction <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, and complicates the bandgaps variation. Besides, the porosity distribution patterns and porosity coefficients enrich the regulation of bandgaps. Our investigation offers valuable insights into the application of flexoelectric electrical components combined with BDFG in MEMS/NEMS to the wave propagation domain.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"110 ","pages":"Article 105504"},"PeriodicalIF":4.4,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744999","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}
Pub Date : 2024-11-26DOI: 10.1016/j.euromechsol.2024.105506
Qiang Chen , Wenqiong Tu , Jiajun Wu , Zhelong He , George Chatzigeorgiou , Fodil Meraghni , Zhibo Yang , Xuefeng Chen
We present a novel elasticity-inspired data-driven Fourier homogenization network (FHN) theory for periodic heterogeneous microstructures with square or hexagonal arrays of cylindrical fibers. Towards this end, two custom-tailored networks are harnessed to construct microscopic displacement functions in each phase of composite materials, based on the exact Fourier series solutions of Navier's displacement differential equations. The fiber and matrix networks are seamlessly connected through a common loss function by enforcing the continuity conditions, in conjunction with periodicity boundary conditions, of both tractions and displacements. These conditions are evaluated on a set of weighted collocation points located on the fiber/matrix interface and the exterior faces of the unit cell, respectively. The partial derivatives of displacements are computed effortlessly through the automatic differentiation functionality. During the training of the FHN model, the total loss function is minimized with respect to the Fourier series parameters using gradient descent and concurrently maximized with respect to the adaptive weights using gradient ascent. The transfer learning technique is employed to speed up the training of new geometries by leveraging a pre-trained model. Comparison with finite-element/volume-based unit cell solutions under various loading scenarios showcases the computational capability of the proposed method. The utility of the proposed technique is further demonstrated by capturing the interfacial debonding in unidirectional composites via a cohesive interface model.
{"title":"Elasticity-inspired data-driven micromechanics theory for unidirectional composites with interfacial damage","authors":"Qiang Chen , Wenqiong Tu , Jiajun Wu , Zhelong He , George Chatzigeorgiou , Fodil Meraghni , Zhibo Yang , Xuefeng Chen","doi":"10.1016/j.euromechsol.2024.105506","DOIUrl":"10.1016/j.euromechsol.2024.105506","url":null,"abstract":"<div><div>We present a novel elasticity-inspired data-driven Fourier homogenization network (FHN) theory for periodic heterogeneous microstructures with square or hexagonal arrays of cylindrical fibers. Towards this end, two custom-tailored networks are harnessed to construct microscopic displacement functions in each phase of composite materials, based on the exact Fourier series solutions of Navier's displacement differential equations. The fiber and matrix networks are seamlessly connected through a common loss function by enforcing the continuity conditions, in conjunction with periodicity boundary conditions, of both tractions and displacements. These conditions are evaluated on a set of weighted collocation points located on the fiber/matrix interface and the exterior faces of the unit cell, respectively. The partial derivatives of displacements are computed effortlessly through the automatic differentiation functionality. During the training of the FHN model, the total loss function is minimized with respect to the Fourier series parameters using gradient descent and concurrently maximized with respect to the adaptive weights using gradient ascent. The transfer learning technique is employed to speed up the training of new geometries by leveraging a pre-trained model. Comparison with finite-element/volume-based unit cell solutions under various loading scenarios showcases the computational capability of the proposed method. The utility of the proposed technique is further demonstrated by capturing the interfacial debonding in unidirectional composites via a cohesive interface model.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105506"},"PeriodicalIF":4.4,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136210","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}
Pub Date : 2024-11-22DOI: 10.1016/j.euromechsol.2024.105505
Hongwei Luo, Ke Li, Yuwu Zhang, Minzu Liang, Xiangcheng Li, Yuliang Lin
Rigid polyurethane foam (RPUF) is a porous material with good energy absorption characteristics, but it may suffer from the destructive effects of impact and cutting when used as a protective structure. Herein, the mechanical response characteristics of RPUF under combined cutting and compression loads is analysed. A cutting tool with a certain width is used to apply a load to the polyurethane foam under quasi-static conditions. The force and displacement are measured, and the influence of the geometric parameters of the cutting tool and the density of RPUF on the force are analysed. In addition, a theoretical model of the total force on RPUF under the combined action of cutting and compressive loads is established. Based on this model, the proportion of component force in the total force is calculated and the influence of size effect on the deformation mechanism of RPUF is analysed. Experimental results indicate that when the density of the RPUF is high, the amplitude of the increase in the total force improved after the increased cutting depth and tear length. Theoretical analysis results indicate that the proportion of crushing force increases with the increase of the foam's pore size, whereas the proportion of tearing force and friction decreases with the increase of the foam's pore size. When the width of the cutting tool is 0.5–20 times the pore size, the proportion of the crushing force decreased from 86.01% to 34.19%, and the proportion of tearing force is 0%–60.25%.
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