Pub Date : 2024-03-13DOI: 10.1177/10812865241232463
Duy Vo, Zwe Yan Aung, Toan Minh Le, Pana Suttakul, Elena Atroshchenko, Jaroon Rungamornrat
As the first endeavor in the context of Mindlin’s strain gradient theory, this study contributes a systematic and rigorous derivation for governing equations and boundary conditions of planar arbitrarily curved microbeams. The Timoshenko–Ehrenfest beam model is incorporated into a simplified version of Mindlin’s strain gradient theory. Kinematic unknowns include displacement components of the beam axis in the local coordinate system and the rotation of cross-section. Since the derived governing equations and boundary conditions are extremely complex, analytical solutions are not achievable for microbeams having non-uniform curvature. To facilitate the numerical analysis, two isogeometric collocation formulations are proposed, that is, displacement-based and mixed formulations. Several tests are designed to evaluate the accuracy and reliability of the proposed isogeometric collocation formulations, especially with respect to the well-known locking pathology. It is found that the mixed formulation is more accurate and robust than the displacement-based one. Therefore, the mixed formulation is then used to numerically investigate the size-dependent behavior and stiffening effect. Furthermore, some informative tests are performed to delineate the significance of the curviness in the prediction of structural responses of planar arbitrarily curved microbeams, which appears to be still an unanswered issue.
{"title":"Analysis of planar arbitrarily curved microbeams with simplified strain gradient theory and Timoshenko–Ehrenfest beam model","authors":"Duy Vo, Zwe Yan Aung, Toan Minh Le, Pana Suttakul, Elena Atroshchenko, Jaroon Rungamornrat","doi":"10.1177/10812865241232463","DOIUrl":"https://doi.org/10.1177/10812865241232463","url":null,"abstract":"As the first endeavor in the context of Mindlin’s strain gradient theory, this study contributes a systematic and rigorous derivation for governing equations and boundary conditions of planar arbitrarily curved microbeams. The Timoshenko–Ehrenfest beam model is incorporated into a simplified version of Mindlin’s strain gradient theory. Kinematic unknowns include displacement components of the beam axis in the local coordinate system and the rotation of cross-section. Since the derived governing equations and boundary conditions are extremely complex, analytical solutions are not achievable for microbeams having non-uniform curvature. To facilitate the numerical analysis, two isogeometric collocation formulations are proposed, that is, displacement-based and mixed formulations. Several tests are designed to evaluate the accuracy and reliability of the proposed isogeometric collocation formulations, especially with respect to the well-known locking pathology. It is found that the mixed formulation is more accurate and robust than the displacement-based one. Therefore, the mixed formulation is then used to numerically investigate the size-dependent behavior and stiffening effect. Furthermore, some informative tests are performed to delineate the significance of the curviness in the prediction of structural responses of planar arbitrarily curved microbeams, which appears to be still an unanswered issue.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"15 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-12DOI: 10.1177/10812865241227972
James M Hill
Newton’s laws of motion and Newtonian conservation principles such as those for energy and momentum involve the assumption that the vanishing of a certain total time derivative, on integration, yields a fixed constant value as an immediate consequence. While this may ultimately be the case for additional reasons, it is possible to have a properly vanishing total time derivative and yet the individual partial derivates are non-zero. Here, for a particular problem and based only on the requirement that the total time derivative of the quantity vanishes, we investigate the particular mechanism leading to a conventional conservation principle. For the energy and angular momentum totals for planar steady orbiting motion, the partial differential conditions may be formally solved to obtain the general solutions. We determine the general structure for variable energy and angular momentum for which the total time derivatives vanish, and from which it is apparent that the standard expression for constant energy and angular momentum is recovered.
{"title":"Newtonian laws of motion and conservation principles","authors":"James M Hill","doi":"10.1177/10812865241227972","DOIUrl":"https://doi.org/10.1177/10812865241227972","url":null,"abstract":"Newton’s laws of motion and Newtonian conservation principles such as those for energy and momentum involve the assumption that the vanishing of a certain total time derivative, on integration, yields a fixed constant value as an immediate consequence. While this may ultimately be the case for additional reasons, it is possible to have a properly vanishing total time derivative and yet the individual partial derivates are non-zero. Here, for a particular problem and based only on the requirement that the total time derivative of the quantity vanishes, we investigate the particular mechanism leading to a conventional conservation principle. For the energy and angular momentum totals for planar steady orbiting motion, the partial differential conditions may be formally solved to obtain the general solutions. We determine the general structure for variable energy and angular momentum for which the total time derivatives vanish, and from which it is apparent that the standard expression for constant energy and angular momentum is recovered.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-12DOI: 10.1177/10812865241230274
Yi-Lun Liao, Chien-Ching Ma, Ching-Kong Chao
This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.
{"title":"Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material","authors":"Yi-Lun Liao, Chien-Ching Ma, Ching-Kong Chao","doi":"10.1177/10812865241230274","DOIUrl":"https://doi.org/10.1177/10812865241230274","url":null,"abstract":"This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"83 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-11DOI: 10.1177/10812865241233737
Hazel Yücel, Nihal Ege, Barış Erbaş, Julius Kaplunov
The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this case, numerical implementations would greatly benefit from preliminary asymptotic predictions. The normal incidence of an acoustic wave is studied for a circular cylindrical shell governed by plane strain equations in elasticity. A novel high-order asymptotic procedure is established considering for the first time all the peculiarities of the low-frequency behavior of a thin fluid-loaded cylinder. The obtained results are exposed in the form suggested by the Resonance Scattering Theory. It is shown that the pressure scattered by rigid cylinder is the best choice for a background component. Simple explicit formulae for resonant frequencies, amplitudes, and widths are presented. They support various important observations, including comparison between widths and the error of the asymptotic expansion for frequencies.
{"title":"A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell","authors":"Hazel Yücel, Nihal Ege, Barış Erbaş, Julius Kaplunov","doi":"10.1177/10812865241233737","DOIUrl":"https://doi.org/10.1177/10812865241233737","url":null,"abstract":"The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this case, numerical implementations would greatly benefit from preliminary asymptotic predictions. The normal incidence of an acoustic wave is studied for a circular cylindrical shell governed by plane strain equations in elasticity. A novel high-order asymptotic procedure is established considering for the first time all the peculiarities of the low-frequency behavior of a thin fluid-loaded cylinder. The obtained results are exposed in the form suggested by the Resonance Scattering Theory. It is shown that the pressure scattered by rigid cylinder is the best choice for a background component. Simple explicit formulae for resonant frequencies, amplitudes, and widths are presented. They support various important observations, including comparison between widths and the error of the asymptotic expansion for frequencies.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"73 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-11DOI: 10.1177/10812865241235117
Bowen Zhao, Jianmin Long
By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.
{"title":"In-plane surface waves propagating in a coated half-space based on the strain-gradient elasticity theory","authors":"Bowen Zhao, Jianmin Long","doi":"10.1177/10812865241235117","DOIUrl":"https://doi.org/10.1177/10812865241235117","url":null,"abstract":"By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"31 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-08DOI: 10.1177/10812865241236861
Kostas P Soldatos
This short communication rectifies an issue that may cause controversy in a recent publication and thus removes some doubt recorded in the same regarding its ability to determine the spherical part of the couple-stress in the case of large elastic deformations of isotropic polar materials.
{"title":"On the role of the invariant “I4” in conventional couple-stress hyperelasticity","authors":"Kostas P Soldatos","doi":"10.1177/10812865241236861","DOIUrl":"https://doi.org/10.1177/10812865241236861","url":null,"abstract":"This short communication rectifies an issue that may cause controversy in a recent publication and thus removes some doubt recorded in the same regarding its ability to determine the spherical part of the couple-stress in the case of large elastic deformations of isotropic polar materials.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-08DOI: 10.1177/10812865241233013
Jicheng Li, Hongling Ye, Nan Wei, Xingyu Zhang
Topology optimization is one of the most common methods for design of material distribution in mechanical metamaterials, but resulting in expensive computational cost due to iterative simulation of finite element method. In this work, a novel deep learning-based topology optimization method is proposed to design mechanical microstructure efficiently for metamaterials with extreme material properties, such as maximum bulk modulus, maximum shear modulus, or negative Poisson’s ratio. Large numbers of microstructures with various configurations are first simulated by modified solid isotropic material with penalization (SIMP), to construct the microstructure data set. Subsequently, the ResUNet involved generative and adversarial network (ResUNet-GAN) is developed for high-dimensional mapping between optimization parameters and corresponding microstructures to improve the design accuracy of ResUNet. By given optimization parameters, the well-trained ResUNet-GAN is successfully applied to the microstructure design of metamaterials with different optimization objectives under proper configurations. According to the simulation results, the proposed ResUNet-GAN-based topology optimization not only significantly reduces the computational duration for the optimization process, but also improves the structure precise and mechanical performance.
{"title":"ResUNet involved generative adversarial network-based topology optimization for design of 2D microstructure with extreme material properties","authors":"Jicheng Li, Hongling Ye, Nan Wei, Xingyu Zhang","doi":"10.1177/10812865241233013","DOIUrl":"https://doi.org/10.1177/10812865241233013","url":null,"abstract":"Topology optimization is one of the most common methods for design of material distribution in mechanical metamaterials, but resulting in expensive computational cost due to iterative simulation of finite element method. In this work, a novel deep learning-based topology optimization method is proposed to design mechanical microstructure efficiently for metamaterials with extreme material properties, such as maximum bulk modulus, maximum shear modulus, or negative Poisson’s ratio. Large numbers of microstructures with various configurations are first simulated by modified solid isotropic material with penalization (SIMP), to construct the microstructure data set. Subsequently, the ResUNet involved generative and adversarial network (ResUNet-GAN) is developed for high-dimensional mapping between optimization parameters and corresponding microstructures to improve the design accuracy of ResUNet. By given optimization parameters, the well-trained ResUNet-GAN is successfully applied to the microstructure design of metamaterials with different optimization objectives under proper configurations. According to the simulation results, the proposed ResUNet-GAN-based topology optimization not only significantly reduces the computational duration for the optimization process, but also improves the structure precise and mechanical performance.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140070912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-03-05DOI: 10.1177/10812865231225769
Gongye Zhang, Xin-Lin Gao, Ziwen Guo
A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.
{"title":"A new model for spatial rods incorporating surface energy effects","authors":"Gongye Zhang, Xin-Lin Gao, Ziwen Guo","doi":"10.1177/10812865231225769","DOIUrl":"https://doi.org/10.1177/10812865231225769","url":null,"abstract":"A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"270 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-02-28DOI: 10.1177/10812865241230269
Mariam Mubarak Almudarra, Ariel Ramírez-Torres
This study investigates the growth of an avascular tumour described through the interchange of mass among its constituents and the production of inelastic distortions induced by growth itself. A key contribution of this research examines the role of non-local diffusion arising from the complex and heterogeneous tumour micro-environment. In our context, the non-local diffusion is enhanced by a variable-order fractional operator that incorporates crucial information about regions of limited nutrient availability within the tissue. Our research also focuses on the identification of an evolution law for the growth-induced inelastic distortions recast through the identification of non-conventional forces dual to suitable kinematic descriptors associated with the growth tensor. The establishment of such evolution law stems from examining the dissipation inequality and subsequently determining a posteriori connections between the inelastic distortions and the source/sink terms in the mass balance laws. To gain insights into the dynamics of tumour growth and its response to the proposed modelling framework, we first study how the variables governing the tissue evolution are affected by the introduction of the new growth law. Second, we investigate how regions of limited diffusion within the tumour, encoded into a fractional operator of variable-order, influence its growth.
{"title":"Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective","authors":"Mariam Mubarak Almudarra, Ariel Ramírez-Torres","doi":"10.1177/10812865241230269","DOIUrl":"https://doi.org/10.1177/10812865241230269","url":null,"abstract":"This study investigates the growth of an avascular tumour described through the interchange of mass among its constituents and the production of inelastic distortions induced by growth itself. A key contribution of this research examines the role of non-local diffusion arising from the complex and heterogeneous tumour micro-environment. In our context, the non-local diffusion is enhanced by a variable-order fractional operator that incorporates crucial information about regions of limited nutrient availability within the tissue. Our research also focuses on the identification of an evolution law for the growth-induced inelastic distortions recast through the identification of non-conventional forces dual to suitable kinematic descriptors associated with the growth tensor. The establishment of such evolution law stems from examining the dissipation inequality and subsequently determining a posteriori connections between the inelastic distortions and the source/sink terms in the mass balance laws. To gain insights into the dynamics of tumour growth and its response to the proposed modelling framework, we first study how the variables governing the tissue evolution are affected by the introduction of the new growth law. Second, we investigate how regions of limited diffusion within the tumour, encoded into a fractional operator of variable-order, influence its growth.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"135 1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-02-26DOI: 10.1177/10812865241231208
Pietro Liguori, Massimiliano Gei
We study the nonlinear deformation of a soft dielectric tube subjected to an external electric field induced by two outer fixed electrodes. The tube follows an electro-elastic, ideal dielectric, neo-Hookean free energy and is longitudinally either constrained or free; in general, it deforms by shrinking and finding an equilibrium configuration closer to the inner electrode. The non-homogeneous system of governing equations is solved numerically with details given for each type of boundary conditions. The notion of contraction limit is introduced and emergence of electromechanical instability for both problems is noted with the relevant modes studied at some relevant points of the stretch–voltage actuation curve.
{"title":"Large deformation of soft dielectric cylindrical tubes under external radial electric field","authors":"Pietro Liguori, Massimiliano Gei","doi":"10.1177/10812865241231208","DOIUrl":"https://doi.org/10.1177/10812865241231208","url":null,"abstract":"We study the nonlinear deformation of a soft dielectric tube subjected to an external electric field induced by two outer fixed electrodes. The tube follows an electro-elastic, ideal dielectric, neo-Hookean free energy and is longitudinally either constrained or free; in general, it deforms by shrinking and finding an equilibrium configuration closer to the inner electrode. The non-homogeneous system of governing equations is solved numerically with details given for each type of boundary conditions. The notion of contraction limit is introduced and emergence of electromechanical instability for both problems is noted with the relevant modes studied at some relevant points of the stretch–voltage actuation curve.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"21 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139977256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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