Pub Date : 2023-10-11DOI: 10.1177/10812865231199460
Daniel J Arrigo, Travis C Chism
The governing equations for plane deformations of isotropic incompressible hyperelastic materials are highly nonlinear, and consequently, very few exact solutions are known. As far as we are aware, the Varga material is the only material in which results of any generality are known. In this paper, we show that for the Varga material, the full governing equations are in fact linearizable.
{"title":"Plane deformations of the Varga material","authors":"Daniel J Arrigo, Travis C Chism","doi":"10.1177/10812865231199460","DOIUrl":"https://doi.org/10.1177/10812865231199460","url":null,"abstract":"The governing equations for plane deformations of isotropic incompressible hyperelastic materials are highly nonlinear, and consequently, very few exact solutions are known. As far as we are aware, the Varga material is the only material in which results of any generality are known. In this paper, we show that for the Varga material, the full governing equations are in fact linearizable.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210853","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 : 2023-10-11DOI: 10.1177/10812865231193735
L Angela Mihai
Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor.
{"title":"A theoretical model for power generation via liquid crystal elastomers","authors":"L Angela Mihai","doi":"10.1177/10812865231193735","DOIUrl":"https://doi.org/10.1177/10812865231193735","url":null,"abstract":"Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"244 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063817","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 : 2023-10-09DOI: 10.1177/10812865231190845
Soheil Moradalizadeh, Heiko Topol, Hasan Demirkoparan, Andrey Melnikov, Bernd Markert, José Merodio
We consider a tubular membrane whose mechanical behavior is defined by a strain energy density function that combines the neo-Hookean model with the Demiray model. Both, the neo-Hookean and the Demiray models are isotropic material models, which found their application in the modeling of the mechanical behavior of biological soft tissue. This tubular membrane is subjected to an inner pressure, an axial stretch, and a change in the material volume due to swelling or deswelling. The interplay between the cylinder geometry and the loading conditions and different instability modes, namely, bulging bifurcation, bending bifurcation, and prismatic bifurcation, are studied. It is shown that a change in the material volume has a strong effect on the occurrence of these bifurcation modes because a change in the material volume may stabilize the cylinder against a particular bifurcation mode and may trigger another bifurcation mode at the same time. Despite the restriction to isotropic material behavior, this article shows that the material response to pressure, axial stretch, and material volume change is quite complex.
{"title":"Remarks on bifurcation of an inflated and extended swellable isotropic tube","authors":"Soheil Moradalizadeh, Heiko Topol, Hasan Demirkoparan, Andrey Melnikov, Bernd Markert, José Merodio","doi":"10.1177/10812865231190845","DOIUrl":"https://doi.org/10.1177/10812865231190845","url":null,"abstract":"We consider a tubular membrane whose mechanical behavior is defined by a strain energy density function that combines the neo-Hookean model with the Demiray model. Both, the neo-Hookean and the Demiray models are isotropic material models, which found their application in the modeling of the mechanical behavior of biological soft tissue. This tubular membrane is subjected to an inner pressure, an axial stretch, and a change in the material volume due to swelling or deswelling. The interplay between the cylinder geometry and the loading conditions and different instability modes, namely, bulging bifurcation, bending bifurcation, and prismatic bifurcation, are studied. It is shown that a change in the material volume has a strong effect on the occurrence of these bifurcation modes because a change in the material volume may stabilize the cylinder against a particular bifurcation mode and may trigger another bifurcation mode at the same time. Despite the restriction to isotropic material behavior, this article shows that the material response to pressure, axial stretch, and material volume change is quite complex.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135094260","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 : 2023-10-08DOI: 10.1177/10812865231193697
Liyuan Wang, Hongmei Wu, Zhiying Ou
In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.
{"title":"Contact behaviors involving a nanobeam with surface effect by a rigid indenter","authors":"Liyuan Wang, Hongmei Wu, Zhiying Ou","doi":"10.1177/10812865231193697","DOIUrl":"https://doi.org/10.1177/10812865231193697","url":null,"abstract":"In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135199987","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 : 2023-10-07DOI: 10.1177/10812865231189807
Soumya Mukherjee, Parag Ravindran
A model for residually stressed viscoelastic bodies undergoing finite deformations is developed and applied to the study of time-dependent responses of spheres and cylinders to various stress and strain controlled tests. An approach based on the notion of natural configurations is employed. An appropriate free energy function is used, and a suitable dissipation function is adopted to obtain a constitutive model. This constitutive model is applied to the study of different boundary value problems of thick spheres and cylinders. The responses to various strain controlled tests are investigated, which includes the stress-relaxation test and a test for a time-dependent inflation–deflation cycle. Also, the response to creep test and step-stress test in thick viscoelastic spheres is investigated. Furthermore, the stretch-controlled responses of residually stressed viscoelastic cylinders to pure torsion and axial stretch are studied. Pure torsion involves an axial extension or compression known as the Poynting effect. The Poynting effect in residually stressed viscoelastic bodies, which does not appear to be studied in the literature, is investigated in detail here. It is noted that the magnitude of the angle of twist has a significant influence (sometimes involving a change of sign) on the observed Poynting effect.
{"title":"A model for residually stressed viscoelastic bodies and its application to some boundary value problems","authors":"Soumya Mukherjee, Parag Ravindran","doi":"10.1177/10812865231189807","DOIUrl":"https://doi.org/10.1177/10812865231189807","url":null,"abstract":"A model for residually stressed viscoelastic bodies undergoing finite deformations is developed and applied to the study of time-dependent responses of spheres and cylinders to various stress and strain controlled tests. An approach based on the notion of natural configurations is employed. An appropriate free energy function is used, and a suitable dissipation function is adopted to obtain a constitutive model. This constitutive model is applied to the study of different boundary value problems of thick spheres and cylinders. The responses to various strain controlled tests are investigated, which includes the stress-relaxation test and a test for a time-dependent inflation–deflation cycle. Also, the response to creep test and step-stress test in thick viscoelastic spheres is investigated. Furthermore, the stretch-controlled responses of residually stressed viscoelastic cylinders to pure torsion and axial stretch are studied. Pure torsion involves an axial extension or compression known as the Poynting effect. The Poynting effect in residually stressed viscoelastic bodies, which does not appear to be studied in the literature, is investigated in detail here. It is noted that the magnitude of the angle of twist has a significant influence (sometimes involving a change of sign) on the observed Poynting effect.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135253560","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 : 2023-10-06DOI: 10.1177/10812865231196512
Xinze Guo, Kemin Zhou, Shunyi Shi
The traditional structural performance may be seriously degraded due to applied indeterministic cases. A novel framework for robust topology optimization of truss-like continuum considering uncertain loads is presented. The robust optimization formula is constructed as minimizing the weighted sum of expectancy and standard variance of structural compliance with volume constraints. In this framework, both the magnitude and direction of applied loads are uncertain and independent. Truss-like continuum provides the topology optimal structure theoretically. Based on the classic truss-like optimization method, the statistical moments of compliance are accurately evaluated utilizing a bivariate cloud model tool. An effective strategy based on linear decoupling is reported to largely reduce the total number of finite element analysis. The optimization is achieved with gradient-based mathematic programming. Several numerical examples demonstrate a better structural robust performance obtained by the proposed algorithm than the traditional one.
{"title":"Robust topology optimization of truss-like continuum structures under uncertain loads based on cloud model","authors":"Xinze Guo, Kemin Zhou, Shunyi Shi","doi":"10.1177/10812865231196512","DOIUrl":"https://doi.org/10.1177/10812865231196512","url":null,"abstract":"The traditional structural performance may be seriously degraded due to applied indeterministic cases. A novel framework for robust topology optimization of truss-like continuum considering uncertain loads is presented. The robust optimization formula is constructed as minimizing the weighted sum of expectancy and standard variance of structural compliance with volume constraints. In this framework, both the magnitude and direction of applied loads are uncertain and independent. Truss-like continuum provides the topology optimal structure theoretically. Based on the classic truss-like optimization method, the statistical moments of compliance are accurately evaluated utilizing a bivariate cloud model tool. An effective strategy based on linear decoupling is reported to largely reduce the total number of finite element analysis. The optimization is achieved with gradient-based mathematic programming. Several numerical examples demonstrate a better structural robust performance obtained by the proposed algorithm than the traditional one.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350938","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 : 2023-10-04DOI: 10.1177/10812865231193703
Ni An, Yu Chen, Jing Zhang, Tian-shu Song
In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.
{"title":"Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials","authors":"Ni An, Yu Chen, Jing Zhang, Tian-shu Song","doi":"10.1177/10812865231193703","DOIUrl":"https://doi.org/10.1177/10812865231193703","url":null,"abstract":"In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135591802","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 : 2023-10-04DOI: 10.1177/10812865231191733
Yoanh Espinosa-Almeyda, David Guinovart-Sanjuán, Reinaldo Rodríguez-Ramos, Héctor Camacho-Montes, Panters Rodríguez-Bermúdez
In this work, the two-scale asymptotic homogenization method (AHM) is developed to describe the effective behavior of multi-laminated elastic micropolar composites with Fibonacci and random structure under perfect contact conditions at the interfaces. The local problem statements over the periodic cell [Formula: see text] are presented, and the corresponding effective stiffness and torque properties are reported. The transversal cross-section of the periodic cell [Formula: see text] is characterized by a laminated structure where the pattern for the layers follows two distinct configurations: (a) a Fibonacci arrangement, and (b) a random sequence focused on the probabilistic binomial function. The non-null effective properties of multi-laminated Cosserat elastic composites with isotropic centro-symmetric constituents are listed. Numerical results for multi-laminated elastic micropolar composites with both types of structures and centro-symmetric isotropic constituents are illustrated and discussed. The overall effective behavior for both cases converges to specific effective values of periodic structures as the number of layers increases.
{"title":"Effective properties of multi-laminated micropolar composites with Fibonacci and random structures","authors":"Yoanh Espinosa-Almeyda, David Guinovart-Sanjuán, Reinaldo Rodríguez-Ramos, Héctor Camacho-Montes, Panters Rodríguez-Bermúdez","doi":"10.1177/10812865231191733","DOIUrl":"https://doi.org/10.1177/10812865231191733","url":null,"abstract":"In this work, the two-scale asymptotic homogenization method (AHM) is developed to describe the effective behavior of multi-laminated elastic micropolar composites with Fibonacci and random structure under perfect contact conditions at the interfaces. The local problem statements over the periodic cell [Formula: see text] are presented, and the corresponding effective stiffness and torque properties are reported. The transversal cross-section of the periodic cell [Formula: see text] is characterized by a laminated structure where the pattern for the layers follows two distinct configurations: (a) a Fibonacci arrangement, and (b) a random sequence focused on the probabilistic binomial function. The non-null effective properties of multi-laminated Cosserat elastic composites with isotropic centro-symmetric constituents are listed. Numerical results for multi-laminated elastic micropolar composites with both types of structures and centro-symmetric isotropic constituents are illustrated and discussed. The overall effective behavior for both cases converges to specific effective values of periodic structures as the number of layers increases.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135645069","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 : 2023-09-30DOI: 10.1177/10812865231196796
András A Sipos
The collapse of masonry arches under static loads mainly occurs because some voussoir interfaces open and form hinges and eventually transform the structure into a mechanism. There is an interest in the maximum number of concurrent hinges at a given arch geometry and stereotomy, which latter refers to the cutting pattern of the voussoirs. This paper applies the governing equations of a geometrically exact rod to thrust line analysis while it adopts the Heymanian assumptions. With the new model, the number of concurrent hinges can be investigated in an organized and predictive manner generalizing the numerical and analytical results of the literature. Specifically, this paper proves that the number of hinges for a symmetric, circular pointed arch loaded by self-weight cannot exceed seven in the cases of vertical stereotomy and constant thickness in the vertical or normal directions. The maximum number of hinges is also seven for an arch with constant thickness and radial stereotomy.
{"title":"About the number of hinges at failure of semicircular and pointed masonry arches","authors":"András A Sipos","doi":"10.1177/10812865231196796","DOIUrl":"https://doi.org/10.1177/10812865231196796","url":null,"abstract":"The collapse of masonry arches under static loads mainly occurs because some voussoir interfaces open and form hinges and eventually transform the structure into a mechanism. There is an interest in the maximum number of concurrent hinges at a given arch geometry and stereotomy, which latter refers to the cutting pattern of the voussoirs. This paper applies the governing equations of a geometrically exact rod to thrust line analysis while it adopts the Heymanian assumptions. With the new model, the number of concurrent hinges can be investigated in an organized and predictive manner generalizing the numerical and analytical results of the literature. Specifically, this paper proves that the number of hinges for a symmetric, circular pointed arch loaded by self-weight cannot exceed seven in the cases of vertical stereotomy and constant thickness in the vertical or normal directions. The maximum number of hinges is also seven for an arch with constant thickness and radial stereotomy.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136279785","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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