Abstract The ball-on-ring test (BoR) is one of the standard tests for biaxial bending, suggested in ASTM F394-78. This test has been applied to determine the biaxial bending strength of silicon dies to avoid the die edge effect of the three-point bending tests. However, from the literature, when the relatively thin silicon dies are tested, this test suffers from a contact-nonlinearity effect, due to a maximum applied stress moving away from the loading pin center before the specimen failure, and thus results in overestimated maximum stress calculated by the theoretical linear solution. This study aims to investigate this mechanical issue experimentally, theoretically and numerically by taking into account the specimen material anisotropy and thickness effects on the maximum stresses and deflections, and then propose new correction factor equations to the theoretical linear solutions, based on the numerical fitting results of the geometric nonlinear finite element solutions. Those correction factor equations proposed in this study are material-property independent, but specimen thickness dependent, which can be estimated by an interpolation function. It has been proved that the BoR test using the conventional theory associated with the proposed correction factor equations can successfully determine the bending strength of the thin silicon dies on untreated surfaces, which mostly fails in the contact-nonlinear region.
{"title":"Correction Factors to Biaxial Bending Strength of Thin Silicon Die in the Ball-on-Ring Test by Considering Geometric Nonlinearity and Material Anisotropy","authors":"M Y Tsai, P J Hsieh, T C Kuo","doi":"10.1093/jom/ufad026","DOIUrl":"https://doi.org/10.1093/jom/ufad026","url":null,"abstract":"Abstract The ball-on-ring test (BoR) is one of the standard tests for biaxial bending, suggested in ASTM F394-78. This test has been applied to determine the biaxial bending strength of silicon dies to avoid the die edge effect of the three-point bending tests. However, from the literature, when the relatively thin silicon dies are tested, this test suffers from a contact-nonlinearity effect, due to a maximum applied stress moving away from the loading pin center before the specimen failure, and thus results in overestimated maximum stress calculated by the theoretical linear solution. This study aims to investigate this mechanical issue experimentally, theoretically and numerically by taking into account the specimen material anisotropy and thickness effects on the maximum stresses and deflections, and then propose new correction factor equations to the theoretical linear solutions, based on the numerical fitting results of the geometric nonlinear finite element solutions. Those correction factor equations proposed in this study are material-property independent, but specimen thickness dependent, which can be estimated by an interpolation function. It has been proved that the BoR test using the conventional theory associated with the proposed correction factor equations can successfully determine the bending strength of the thin silicon dies on untreated surfaces, which mostly fails in the contact-nonlinear region.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135839030","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}
Abstract Several parameters need to be monitored for turbocharger rotor faults and the overlap between different fault parameters as well as the redundancy of data, which leads to increased calculation time and reduced classification accuracy. To improve the recognition rate of turbocharger rotor faults, a recursive elimination method based on the support vector machine-recursive feature elimination (SVM-RFE) combined with improved Hu invariant moments is developed for the axial orbit feature extraction of turbocharger rotor with rotor fault. Firstly, improved Hu-invariant moments are extracted for different rotor fault axis orbits, and then the feature ranking and selection are performed by the SVM-RFE method to filter out the feature combinations with higher classification recognition rates. Then, the feature matrix of the Hu-SVM-RFE algorithm screening combination was identified for classification using each of the three diagnostic algorithms. The results show that the optimal feature subset obtained by the Hu-SVM-RFE method can ensure the richness of the fault information of the turbocharger rotor with small number of features. And, a high classification rate can be obtained with low time consumption in combination with the probabilistic neural network (PNN) algorithm. Therefore, Hu-SVM-RFE feature screening method combined with PNN fault diagnosis technology has high accuracy and efficiency, which is of great significance for online fault identification of the supercharger rotor.
{"title":"Research on fault diagnosis method of turbocharger rotor based on Hu-SVM-RFE","authors":"Chunyu Zhang, Xinyang Qiu, Haiyu Qian, Yun Liu, Junchao Zhu","doi":"10.1093/jom/ufad028","DOIUrl":"https://doi.org/10.1093/jom/ufad028","url":null,"abstract":"Abstract Several parameters need to be monitored for turbocharger rotor faults and the overlap between different fault parameters as well as the redundancy of data, which leads to increased calculation time and reduced classification accuracy. To improve the recognition rate of turbocharger rotor faults, a recursive elimination method based on the support vector machine-recursive feature elimination (SVM-RFE) combined with improved Hu invariant moments is developed for the axial orbit feature extraction of turbocharger rotor with rotor fault. Firstly, improved Hu-invariant moments are extracted for different rotor fault axis orbits, and then the feature ranking and selection are performed by the SVM-RFE method to filter out the feature combinations with higher classification recognition rates. Then, the feature matrix of the Hu-SVM-RFE algorithm screening combination was identified for classification using each of the three diagnostic algorithms. The results show that the optimal feature subset obtained by the Hu-SVM-RFE method can ensure the richness of the fault information of the turbocharger rotor with small number of features. And, a high classification rate can be obtained with low time consumption in combination with the probabilistic neural network (PNN) algorithm. Therefore, Hu-SVM-RFE feature screening method combined with PNN fault diagnosis technology has high accuracy and efficiency, which is of great significance for online fault identification of the supercharger rotor.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135008438","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}
Hydrodynamic herringbone-grooved journal bearings (HGJBs) are analyzed by solving Navier–Stokes and energy equations. It is well known that the load capacity of hydrodynamic bearings may be affected by high temperatures and low oil viscosity. Therefore, the main objective of this study is to understand the pressure distribution of hydrodynamic HGJBs under different oil viscosity and eccentricity ratios. In this paper, 3 different configurations are studied, namely, a HGJB, a combined HGJB and thrust bearing, and a combined HGJB and grooved thrust bearing. The bearing characteristics, such as load capacity and attitude angle that vary with different eccentricity ratios, are also discussed. The results show that the load capacity of the bearing decreases with increasing temperature. The pressure difference also increases as the eccentricity ratio increases. The high-pressure region is concentrated at the tip of the groove for the HGJB. In addition, the combined HGJB and grooved thrust bearing can be used to stabilize the journal because of the low attitude angle. These findings may help and facilitate the design of hydrodynamic bearings suitable for working in warm and hot environments in the future.
{"title":"Numerical study of hydrodynamic herringbone-grooved journal bearings combined with thrust bearings considering thermal effects","authors":"Chin-Cheng Wang, Jyun-Ting Lin","doi":"10.1093/jom/ufab036","DOIUrl":"https://doi.org/10.1093/jom/ufab036","url":null,"abstract":"Hydrodynamic herringbone-grooved journal bearings (HGJBs) are analyzed by solving Navier–Stokes and energy equations. It is well known that the load capacity of hydrodynamic bearings may be affected by high temperatures and low oil viscosity. Therefore, the main objective of this study is to understand the pressure distribution of hydrodynamic HGJBs under different oil viscosity and eccentricity ratios. In this paper, 3 different configurations are studied, namely, a HGJB, a combined HGJB and thrust bearing, and a combined HGJB and grooved thrust bearing. The bearing characteristics, such as load capacity and attitude angle that vary with different eccentricity ratios, are also discussed. The results show that the load capacity of the bearing decreases with increasing temperature. The pressure difference also increases as the eccentricity ratio increases. The high-pressure region is concentrated at the tip of the groove for the HGJB. In addition, the combined HGJB and grooved thrust bearing can be used to stabilize the journal because of the low attitude angle. These findings may help and facilitate the design of hydrodynamic bearings suitable for working in warm and hot environments in the future.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61538896","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}
An undulatory fin bionic underwater robot that is able to mimic the undulation motions of the median and/or the paired fin of fish is designed and analyzed. A simplified rays-membrane structure system has been developed in order to save computational cost in finite element analysis. The undulatory motion of the soft fins in the water is experimentally measured by using two cameras and the DLTdv system. The dynamic characteristics of the fin structure and the hydrodynamics of the fluid are analyzed by a fluid-structure interaction model developed by the commercial software ANSYS, and the results are compared to those of the experiment for validation. The fin motion of different fin amplitudes (ray swing angles), membrane dimensions and phase difference of adjacent rays are compared to realize the influence of robot design on the motion. It is found in the results that the displacements of the points on the fin membrane obtained by the finite element analysis have the same trend as those by the experiment; hence, the finite element model is verified. It is indicated by the finite element analysis results that the stress of the points on the fin membrane increases with the amplitude. The maximum velocity in one section plane is largest for the 40 mm width fin. The average stress on the fin with 45° phase difference is larger than that of 90° phase difference. Because of the complexity of the soft fin's material behavior and fluid-structure interaction analysis, the finite element analysis model developed in this study has a significant contribution for the soft-fin-based underwater robot design.
{"title":"Experimental and numerical investigations on undulatory motion of a soft-fin-based underwater robot","authors":"Yu-Chih Lin, Dai Zhang","doi":"10.1093/jom/ufac021","DOIUrl":"https://doi.org/10.1093/jom/ufac021","url":null,"abstract":"An undulatory fin bionic underwater robot that is able to mimic the undulation motions of the median and/or the paired fin of fish is designed and analyzed. A simplified rays-membrane structure system has been developed in order to save computational cost in finite element analysis. The undulatory motion of the soft fins in the water is experimentally measured by using two cameras and the DLTdv system. The dynamic characteristics of the fin structure and the hydrodynamics of the fluid are analyzed by a fluid-structure interaction model developed by the commercial software ANSYS, and the results are compared to those of the experiment for validation. The fin motion of different fin amplitudes (ray swing angles), membrane dimensions and phase difference of adjacent rays are compared to realize the influence of robot design on the motion. It is found in the results that the displacements of the points on the fin membrane obtained by the finite element analysis have the same trend as those by the experiment; hence, the finite element model is verified. It is indicated by the finite element analysis results that the stress of the points on the fin membrane increases with the amplitude. The maximum velocity in one section plane is largest for the 40 mm width fin. The average stress on the fin with 45° phase difference is larger than that of 90° phase difference. Because of the complexity of the soft fin's material behavior and fluid-structure interaction analysis, the finite element analysis model developed in this study has a significant contribution for the soft-fin-based underwater robot design.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61539938","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}
Tung-Huan Su, Szu-Jui Huang, J. Jean, Chuin-Shan Chen
Multiscale computational solid mechanics concurrently connects complex material physics and macroscopic structural analysis to accelerate the application of advanced materials in the industry rather than resorting to empirical constitutive models. The rise of data-driven multiscale material modeling opens a major paradigm shift in multiscale computational solid mechanics in the era of material big data. This paper reviews state-of-the-art data-driven methods for multiscale simulation, focusing on data-driven multiscale finite element method (data-driven FE2) and data-driven multiscale finite element-deep material network method (data-driven FE-DMN). Both types of data-driven multiscale methods aim to resolve the past challenge of concurrent multiscale simulation. Numerical examples are designed to demonstrate the effectiveness of data-driven multiscale simulation methods. Future research directions are discussed, including data sampling strategy and data generation technique for the data-driven FE2 method and generalization of data-driven FE-DMN method.
{"title":"Multiscale computational solid mechanics: data and machine learning","authors":"Tung-Huan Su, Szu-Jui Huang, J. Jean, Chuin-Shan Chen","doi":"10.1093/jom/ufac037","DOIUrl":"https://doi.org/10.1093/jom/ufac037","url":null,"abstract":"Multiscale computational solid mechanics concurrently connects complex material physics and macroscopic structural analysis to accelerate the application of advanced materials in the industry rather than resorting to empirical constitutive models. The rise of data-driven multiscale material modeling opens a major paradigm shift in multiscale computational solid mechanics in the era of material big data. This paper reviews state-of-the-art data-driven methods for multiscale simulation, focusing on data-driven multiscale finite element method (data-driven FE2) and data-driven multiscale finite element-deep material network method (data-driven FE-DMN). Both types of data-driven multiscale methods aim to resolve the past challenge of concurrent multiscale simulation. Numerical examples are designed to demonstrate the effectiveness of data-driven multiscale simulation methods. Future research directions are discussed, including data sampling strategy and data generation technique for the data-driven FE2 method and generalization of data-driven FE-DMN method.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61541162","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}
Developed herein is an analysis procedure based on closed-form solutions to elastoplastic bilinear model of building structures accounted for different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels due to the layout of buildings and the complexity of structural members. The seismic design often considers earthquake forces on multiple floor levels but usually only in a single direction. However, in reality, the direction of the earthquake is not limited to one particular direction. Therefore, studying the influence of a two-way, furthermore multi-dimensional, earthquake on buildings is of great value. To estimate the total seismic demand on inelastic building structures subjected to multi-dimensional loading, this paper aims to find closed-form solution responses to an input rectilinear force path for the elastoplastic bilinear model of Hong and Liu (1999) which already has available closed-form solution responses to an input rectilinear displacement path. In this paper the elastoplastic bilinear model of building structures and Minkowski spacetime are adapted to accommodate such situations as different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels.
{"title":"Building structure with elastoplastic bilinear model under multi-dimensional earthquake forces","authors":"H. Hong, Li-Wei Liu, Ya-Po Shiao, Cheng-Jih Chang","doi":"10.1093/jom/ufac045","DOIUrl":"https://doi.org/10.1093/jom/ufac045","url":null,"abstract":"Developed herein is an analysis procedure based on closed-form solutions to elastoplastic bilinear model of building structures accounted for different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels due to the layout of buildings and the complexity of structural members. The seismic design often considers earthquake forces on multiple floor levels but usually only in a single direction. However, in reality, the direction of the earthquake is not limited to one particular direction. Therefore, studying the influence of a two-way, furthermore multi-dimensional, earthquake on buildings is of great value. To estimate the total seismic demand on inelastic building structures subjected to multi-dimensional loading, this paper aims to find closed-form solution responses to an input rectilinear force path for the elastoplastic bilinear model of Hong and Liu (1999) which already has available closed-form solution responses to an input rectilinear displacement path. In this paper the elastoplastic bilinear model of building structures and Minkowski spacetime are adapted to accommodate such situations as different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61541949","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}
To explore the influence law of dry–wet cycles on the microstructure of expansive soil and the deterioration effect of macroscopic shear strength, the correlation between the change in the soil internal structure and the deterioration of the mechanical properties is analysed. The expansive soil in the test section of the slope support project in Hanzhong city, Shaanxi Province, China, is selected for sample preparation, three groups of different dry–wet cyclic water content variation paths are defined. The volume damage rate of the soil sample caused by dry–wet cycles is tested, and the microscopic evolution law of soil sample structure was analyzed. On the basis of the conclusion of microscopic analysis, the deterioration effect of macro shear strength of soil samples is further elaborated. The results show that expansive soil is rich in hydrophilic minerals such as illite and montmorillonite. The larger the amplitude of the dry–wet cycle, the more significant the volume change is. With the alternating dry–wet cycle treatment, the microscopic analysis shows that the water migration channels gradually become larger until a new balance is reached. The T2 spectra of the NMR test also show that the overall internal structure develops from stable to unstable. With dry–wet cycles, the unstable change in the soil internal structure leads to the attenuation of the macroscopic shear strength. These micro- and macroscopic research results show that the deterioration effect of drying and wetting on expansive soil cannot be ignored.
{"title":"Multiscale study on the microstructural evolution and macromechanical deterioration of expansive soil under dry–wet cycles","authors":"Zihao Zhou, Y. Bai, Yuntao Wu, Yiqian Chen, Zhuang Guo, Weikang Cheng","doi":"10.1093/jom/ufac048","DOIUrl":"https://doi.org/10.1093/jom/ufac048","url":null,"abstract":"To explore the influence law of dry–wet cycles on the microstructure of expansive soil and the deterioration effect of macroscopic shear strength, the correlation between the change in the soil internal structure and the deterioration of the mechanical properties is analysed. The expansive soil in the test section of the slope support project in Hanzhong city, Shaanxi Province, China, is selected for sample preparation, three groups of different dry–wet cyclic water content variation paths are defined. The volume damage rate of the soil sample caused by dry–wet cycles is tested, and the microscopic evolution law of soil sample structure was analyzed. On the basis of the conclusion of microscopic analysis, the deterioration effect of macro shear strength of soil samples is further elaborated. The results show that expansive soil is rich in hydrophilic minerals such as illite and montmorillonite. The larger the amplitude of the dry–wet cycle, the more significant the volume change is. With the alternating dry–wet cycle treatment, the microscopic analysis shows that the water migration channels gradually become larger until a new balance is reached. The T2 spectra of the NMR test also show that the overall internal structure develops from stable to unstable. With dry–wet cycles, the unstable change in the soil internal structure leads to the attenuation of the macroscopic shear strength. These micro- and macroscopic research results show that the deterioration effect of drying and wetting on expansive soil cannot be ignored.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61542221","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}
T. Kuraishi, Takuya Terahara, K. Takizawa, T. Tezduyar
In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and to represent the contact without leaving a mesh protection gap. The space-time topology change (ST-TC) method, introduced in 2013, makes moving-mesh computation possible even when we have contact between moving solid surfaces or other kinds of flow-domain TC. The contact is represented without giving up on high-resolution flow representation near the moving surfaces. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting this class of flow analysis in the presence of additional complexities such as geometric complexity, rotation or deformation of the solid surfaces and the multiscale nature of the flow. In this first part of a two-part article, we provide an overview of the methods that made all that possible. We also provide an overview of the computations performed for tire aerodynamics with challenges that include the complexity of a near-actual tire geometry with grooves, road contact, tire deformation and rotation, road roughness and fluid films.
{"title":"Computational flow analysis with boundary layer and contact representation: I. Tire aerodynamics with road contact","authors":"T. Kuraishi, Takuya Terahara, K. Takizawa, T. Tezduyar","doi":"10.1093/jom/ufac009","DOIUrl":"https://doi.org/10.1093/jom/ufac009","url":null,"abstract":"In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and to represent the contact without leaving a mesh protection gap. The space-time topology change (ST-TC) method, introduced in 2013, makes moving-mesh computation possible even when we have contact between moving solid surfaces or other kinds of flow-domain TC. The contact is represented without giving up on high-resolution flow representation near the moving surfaces. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting this class of flow analysis in the presence of additional complexities such as geometric complexity, rotation or deformation of the solid surfaces and the multiscale nature of the flow. In this first part of a two-part article, we provide an overview of the methods that made all that possible. We also provide an overview of the computations performed for tire aerodynamics with challenges that include the complexity of a near-actual tire geometry with grooves, road contact, tire deformation and rotation, road roughness and fluid films.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61539735","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}
Y. Leng, Tianyi Hu, Sthavishtha R. Bhopalam, Héctor Mauricio Serna-Gómez
In this work, we study numerical solutions of a gradient-elastic Kirchhoff plate model on convex and concave geometries. For a convex plate, we first show the well-posedness of the model. Then, we split the sixth-order partial differential equation (PDE) into a system of three second-order PDEs. The solution of the resulting system coincides with that of the original PDE. This is verified with convergence studies performed by solving the sixth-order PDE directly (direct method) using isogeometric analysis (IGA) and the system of second-order PDEs (split method) using both IGA and C0 finite elements. Next, we study a concave pie-shaped plate, which has one re-entrant point. The well-posedness of the model on the concave domain is proved. Numerical solutions obtained using the split method differ significantly from that of the direct method. The split method may even lead to nonphysical solutions. We conclude that for gradient-elastic Kirchhoff plates with concave corners, it is necessary to use the direct method with IGA.
{"title":"Numerical solutions of a gradient-elastic Kirchhoff plate model on convex and concave geometries using isogeometric analysis","authors":"Y. Leng, Tianyi Hu, Sthavishtha R. Bhopalam, Héctor Mauricio Serna-Gómez","doi":"10.1093/jom/ufac017","DOIUrl":"https://doi.org/10.1093/jom/ufac017","url":null,"abstract":"In this work, we study numerical solutions of a gradient-elastic Kirchhoff plate model on convex and concave geometries. For a convex plate, we first show the well-posedness of the model. Then, we split the sixth-order partial differential equation (PDE) into a system of three second-order PDEs. The solution of the resulting system coincides with that of the original PDE. This is verified with convergence studies performed by solving the sixth-order PDE directly (direct method) using isogeometric analysis (IGA) and the system of second-order PDEs (split method) using both IGA and C0 finite elements. Next, we study a concave pie-shaped plate, which has one re-entrant point. The well-posedness of the model on the concave domain is proved. Numerical solutions obtained using the split method differ significantly from that of the direct method. The split method may even lead to nonphysical solutions. We conclude that for gradient-elastic Kirchhoff plates with concave corners, it is necessary to use the direct method with IGA.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61539835","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}
This study characterized the interfacial fracture energy of stiff islands deposited on a thermoplastic polyurethane (TPU) film. The film can deform by >200%. The film was stretched using a designed fixture, and the fracture behaviors of the islands were observed using a microscope. The island–substrate interface debonding lengths associated with different levels of substrate strain were determined in the stretching tests. Because the stretchable film was a nonlinear material, the Ogden model was employed to characterize the nonlinear constitutive relation. Through the tensile tests, the material parameters in the Ogden model were determined using the reduced-gradient optimization method. On the basis of the measured debonding lengths, a finite element model was generated for the nonlinear properties of the film, and the energy release rates at the crack tip were calculated using the J-integral method. The energy release rates, representing the interfacial fracture energy, were calculated on the basis of the arrested crack associated with different crack lengths. Results reveal that the interfacial fracture energy increased from 0.14 to 0.91 kJ/m2 as the debonding length increased. The behavior is related to the rising resistance curve in TPU materials. In addition, the shearing-dominated mode slightly decreased as the debonded length increased in the stretching tests.
{"title":"Characterizing the interfacial fracture energy of stiff islands on stretchable films","authors":"J. Lin, J. Tsai","doi":"10.1093/jom/ufac023","DOIUrl":"https://doi.org/10.1093/jom/ufac023","url":null,"abstract":"This study characterized the interfacial fracture energy of stiff islands deposited on a thermoplastic polyurethane (TPU) film. The film can deform by >200%. The film was stretched using a designed fixture, and the fracture behaviors of the islands were observed using a microscope. The island–substrate interface debonding lengths associated with different levels of substrate strain were determined in the stretching tests. Because the stretchable film was a nonlinear material, the Ogden model was employed to characterize the nonlinear constitutive relation. Through the tensile tests, the material parameters in the Ogden model were determined using the reduced-gradient optimization method. On the basis of the measured debonding lengths, a finite element model was generated for the nonlinear properties of the film, and the energy release rates at the crack tip were calculated using the J-integral method. The energy release rates, representing the interfacial fracture energy, were calculated on the basis of the arrested crack associated with different crack lengths. Results reveal that the interfacial fracture energy increased from 0.14 to 0.91 kJ/m2 as the debonding length increased. The behavior is related to the rising resistance curve in TPU materials. In addition, the shearing-dominated mode slightly decreased as the debonded length increased in the stretching tests.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61540058","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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