We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N -phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.
{"title":"Screw dislocations in piezoelectric laminates with four or more phases","authors":"X. Wang, L. Chen, P. Schiavone","doi":"10.24423/AOM.3218","DOIUrl":"https://doi.org/10.24423/AOM.3218","url":null,"abstract":"We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N -phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"263-283"},"PeriodicalIF":0.8,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44451893","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}
In crystal plasticity under prescribed deformation, the incremental material response is potentially non-unique owing to slip system redundancy for most of the crystalline structures. Following Petryk, energy minimizing considerations give the way to select one of these solutions and the set of active systems, which depend on their more or less favorable orientation and their mutual interactions (latent hardening). This variational approach is extended here to confined plasticity in a finite volume, simulating a single crystal embedded in an aggregate. A slip gradient enhanced framework and related micro-hard boundary conditions are considered, using two defect energies introduced by Gurtin and coworkers: the first one takes the slip system polar dislocation densities as internal state variables and the second one is a quadratic potential of the dislocation density tensor. In both cases, micro-hard conditions amount to null flow for the two former quantities. For the classical one dimensional case of a strip in simple shear, the two models yield substantially different solutions, the second one coupling the gradients on the different systems. These results emphasize the necessity for a physically motivated modeling of gradient effects in the vicinity of grain boundary interfaces.
{"title":"Selection of slip systems in confined single crystal gradient plasticity: coupled effects of slip system orientations, latent hardening, and grain boundaries","authors":"J. Dequiedt","doi":"10.24423/AOM.3079","DOIUrl":"https://doi.org/10.24423/AOM.3079","url":null,"abstract":"In crystal plasticity under prescribed deformation, the incremental material response is potentially non-unique owing to slip system redundancy for most of the crystalline structures. Following Petryk, energy minimizing considerations give the way to select one of these solutions and the set of active systems, which depend on their more or less favorable orientation and their mutual interactions (latent hardening). This variational approach is extended here to confined plasticity in a finite volume, simulating a single crystal embedded in an aggregate. A slip gradient enhanced framework and related micro-hard boundary conditions are considered, using two defect energies introduced by Gurtin and coworkers: the first one takes the slip system polar dislocation densities as internal state variables and the second one is a quadratic potential of the dislocation density tensor. In both cases, micro-hard conditions amount to null flow for the two former quantities. For the classical one dimensional case of a strip in simple shear, the two models yield substantially different solutions, the second one coupling the gradients on the different systems. These results emphasize the necessity for a physically motivated modeling of gradient effects in the vicinity of grain boundary interfaces.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"207-238"},"PeriodicalIF":0.8,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42013011","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}
D. Schob, R. Roszak, I. Sagradov, H. Sparr, M. Ziegenhorn, A. Kupsch, Fabien Leonard, B. Müller, G. Bruno
In order to characterise the material and damage behaviour of additively manufactured polyamide 12 (PA12) under quasi-static load and to implement it in a numerical model, experiments under quasi-static load as well as microstructural investigations were carried out. Selective laser sintering (SLS) was used as the manufacturing process. For the classification of the material behaviour, quasi-static cyclic tests with holding times as well as tensile tests were performed. X-ray refraction and computed tomography (CT) were used to investigate the damage behaviour. The Chaboche model, which has already been applied for metallic materials under thermomechanical loading, served as the basis for the selection of the numerical material model. The same procedure was used for the selection of the damage model, where the Gurson–Tvergaard–Needleman (GTN) model was chosen, which was already used for porous metallic materials. The Chaboche model shows very good agreement with experimental results. Furthermore, the coupling with the GTN model allows a very good modelling of the damage behaviour. Finally, it could be shown that the selected models are suitable to simulate the material and damage behaviour of 3D printed PA12.
{"title":"Experimental determination and numerical simulation of material and damage behaviour of 3D printed polyamide 12 under quasi-static loading","authors":"D. Schob, R. Roszak, I. Sagradov, H. Sparr, M. Ziegenhorn, A. Kupsch, Fabien Leonard, B. Müller, G. Bruno","doi":"10.24423/AOM.3162","DOIUrl":"https://doi.org/10.24423/AOM.3162","url":null,"abstract":"In order to characterise the material and damage behaviour of additively manufactured polyamide 12 (PA12) under quasi-static load and to implement it in a numerical model, experiments under quasi-static load as well as microstructural investigations were carried out. Selective laser sintering (SLS) was used as the manufacturing process. For the classification of the material behaviour, quasi-static cyclic tests with holding times as well as tensile tests were performed. X-ray refraction and computed tomography (CT) were used to investigate the damage behaviour. The Chaboche model, which has already been applied for metallic materials under thermomechanical loading, served as the basis for the selection of the numerical material model. The same procedure was used for the selection of the damage model, where the Gurson–Tvergaard–Needleman (GTN) model was chosen, which was already used for porous metallic materials. The Chaboche model shows very good agreement with experimental results. Furthermore, the coupling with the GTN model allows a very good modelling of the damage behaviour. Finally, it could be shown that the selected models are suitable to simulate the material and damage behaviour of 3D printed PA12.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"507-526"},"PeriodicalIF":0.8,"publicationDate":"2019-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68939086","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}
V. Mochalova, A. Utkin, V. Rykova, M. Endres, D. Hoffmann
The experimental study of shock wave compressibility and spall strength of an aramid fiber reinforced epoxy composite (textolite) for two fiber orientations was performed by the VISAR interferometer. The particle velocity profiles were obtained at velocities of the flyer plate from 0.65 to 5.05 km/s. The sound speed of textolite for the longitudinal direction is three times higher than that for transverse one, and as a result, the particle velocity profiles are different for two orientations. For the transverse direction of the fibers, a single shock wave is observed, while for longitudinal one, a two-wave configuration is recorded up to 20 GPa. Hugoniot parameters for both orientations of the fibers were found up to 35 GPa: D = 2.37 + 1.26 ∗ u – for transverse one and D = 1.45 + 2.05 ∗ u – for longitudinal, where D is the shock wave velocity and u is the particle velocity. The spall strength of textolite is equal to 61 MPa for shocks traveling along the fibers, and this is almost twice higher than that for the transverse direction.
{"title":"Shock compressibility and spall strength of textolite depending on fiber orientation","authors":"V. Mochalova, A. Utkin, V. Rykova, M. Endres, D. Hoffmann","doi":"10.24423/AOM.3144","DOIUrl":"https://doi.org/10.24423/AOM.3144","url":null,"abstract":"The experimental study of shock wave compressibility and spall strength of an aramid fiber reinforced epoxy composite (textolite) for two fiber orientations was performed by the VISAR interferometer. The particle velocity profiles were obtained at velocities of the flyer plate from 0.65 to 5.05 km/s. The sound speed of textolite for the longitudinal direction is three times higher than that for transverse one, and as a result, the particle velocity profiles are different for two orientations. For the transverse direction of the fibers, a single shock wave is observed, while for longitudinal one, a two-wave configuration is recorded up to 20 GPa. Hugoniot parameters for both orientations of the fibers were found up to 35 GPa: D = 2.37 + 1.26 ∗ u – for transverse one and D = 1.45 + 2.05 ∗ u – for longitudinal, where D is the shock wave velocity and u is the particle velocity. The spall strength of textolite is equal to 61 MPa for shocks traveling along the fibers, and this is almost twice higher than that for the transverse direction.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"417-431"},"PeriodicalIF":0.8,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45011831","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}
Thermal processes in domain of thin metal film subjected to an ultrashort laser pulse are considered. A mathematical description of the process discussed is based on the system of four equations. Two of them describe the electrons and lattice temperature, while third and fourth equations represent the generalized Fourier law, it means the dependencies between the electrons (lattice) heat flux and the electrons (lattice) temperature gradient. In the generalized Fourier law the heat fluxes are delayed in relation to the temperature gradients which consequently causes the appearance of heat fluxes time derivatives in the appropriate equations. Depending on the order of the generalized Fourier law expansion into the Taylor series, the first- and the second-order model can be obtained. In contrast to the commonly used first-order model, here the second-order two-temperature model is proposed. The problem is solved using the implicit scheme of the finite difference method. The examples of computations are also presented. It turns out that for the low laser intensities the results obtained using the first- and the second-order models are very similar.
{"title":"Second-order two-temperature model of heat transfer processes in a thin metal film subjected to an ultrashort laser pulse","authors":"E. Majchrzak, J. Dziatkiewicz","doi":"10.24423/AOM.3131","DOIUrl":"https://doi.org/10.24423/AOM.3131","url":null,"abstract":"Thermal processes in domain of thin metal film subjected to an ultrashort laser pulse are considered. A mathematical description of the process discussed is based on the system of four equations. Two of them describe the electrons and lattice temperature, while third and fourth equations represent the generalized Fourier law, it means the dependencies between the electrons (lattice) heat flux and the electrons (lattice) temperature gradient. In the generalized Fourier law the heat fluxes are delayed in relation to the temperature gradients which consequently causes the appearance of heat fluxes time derivatives in the appropriate equations. Depending on the order of the generalized Fourier law expansion into the Taylor series, the first- and the second-order model can be obtained. In contrast to the commonly used first-order model, here the second-order two-temperature model is proposed. The problem is solved using the implicit scheme of the finite difference method. The examples of computations are also presented. It turns out that for the low laser intensities the results obtained using the first- and the second-order models are very similar.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"377-391"},"PeriodicalIF":0.8,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44111343","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}
The paper deals with an original methodology for modelling and control system design of the semi-active and active systems. At first a generalised simulation model of the vibration reduction system is formulated in such a way that it represents the dynamics of human body exposed to mechanical vibration. Then a novel control system design is proposed in order to adjust force characteristics of the fundamental elements included in the suspension system and consequently to reduce the harmful effects of vibration. Finally, a computational method is experimentally verified by selecting the vibro-isolation properties of an exemplary horizontal seat suspension for a specific input vibration.
{"title":"Computational method for shaping the vibro-isolation properties of semi-active and active systems","authors":"T. Krzyżyński, I. Maciejewski","doi":"10.24423/AOM.3098","DOIUrl":"https://doi.org/10.24423/AOM.3098","url":null,"abstract":"The paper deals with an original methodology for modelling and control system design of the semi-active and active systems. At first a generalised simulation model of the vibration reduction system is formulated in such a way that it represents the dynamics of human body exposed to mechanical vibration. Then a novel control system design is proposed in order to adjust force characteristics of the fundamental elements included in the suspension system and consequently to reduce the harmful effects of vibration. Finally, a computational method is experimentally verified by selecting the vibro-isolation properties of an exemplary horizontal seat suspension for a specific input vibration.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"291-313"},"PeriodicalIF":0.8,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43952177","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 paper has the goal of defining a class of uncertain structural systems for which it is possible to consider an approach able to give the exact response in terms of the probability density function (PDF). The uncertain structures have been identified in the discretized statically determined ones and the approach has been identified in the coupling of the approximated principal deformation modes method (APDM) and of the probability transformation method (PTM). The first one gives the explicit relationships between the response variables and the uncertainty ones, that are exact when the structures are statically determined. The second method allows to determine the explicit relationship between the PDFs of the response and of the uncertainty variables. The results of some applications have confirmed the goodness of these choices and that the proposed approach gives always exact results for both correlated and uncorrelated uncertainty random variables.
{"title":"Exact response probability density functions of some uncertain structural systems","authors":"Giovanni Falsone, R. Laudani","doi":"10.24423/AOM.3109","DOIUrl":"https://doi.org/10.24423/AOM.3109","url":null,"abstract":"This paper has the goal of defining a class of uncertain structural systems for which it is possible to consider an approach able to give the exact response in terms of the probability density function (PDF). The uncertain structures have been identified in the discretized statically determined ones and the approach has been identified in the coupling of the approximated principal deformation modes method (APDM) and of the probability transformation method (PTM). The first one gives the explicit relationships between the response variables and the uncertainty ones, that are exact when the structures are statically determined. The second method allows to determine the explicit relationship between the PDFs of the response and of the uncertainty variables. The results of some applications have confirmed the goodness of these choices and that the proposed approach gives always exact results for both correlated and uncorrelated uncertainty random variables.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"315-336"},"PeriodicalIF":0.8,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46034777","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}
A singular integral equation (SIE) approach and a finite element method are developed for the solution of the frictional sliding contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-shape considering the plane strain assumption. An exponential shear modulus variation is introduced through the lateral direction. The field variables are obtained applying the Fourier transformation techniques on the governing partial differential equations. A surface displacement gradient is then utilized to derive a SIE of the second kind. A numerical solution of the SIE is performed by using a collation method and the Gauss quadrature integration techniques for the flat, triangular and circular stamp profiles. Finite element analyses (FEA) of the same contact problems are also performed upon selection of the augmented Lagrange contact-solver in ANSYS. For the incomplete (triangular and circular) stamp problems, an iterative algorithm is developed in order to obtain practically computational solutions for any desired contact lengths. Successful convergence of the SIE results and excellent consistency between the SIE and FEA results are attained, that indicate the reliability of both methods. The change in the thickness is shown to alter the contact behavior of the laterally graded solid significantly.
{"title":"Solution of the plane contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-profile","authors":"Onur Arslan","doi":"10.24423/AOM.3207","DOIUrl":"https://doi.org/10.24423/AOM.3207","url":null,"abstract":"A singular integral equation (SIE) approach and a finite element method are developed for the solution of the frictional sliding contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-shape considering the plane strain assumption. An exponential shear modulus variation is introduced through the lateral direction. The field variables are obtained applying the Fourier transformation techniques on the governing partial differential equations. A surface displacement gradient is then utilized to derive a SIE of the second kind. A numerical solution of the SIE is performed by using a collation method and the Gauss quadrature integration techniques for the flat, triangular and circular stamp profiles. Finite element analyses (FEA) of the same contact problems are also performed upon selection of the augmented Lagrange contact-solver in ANSYS. For the incomplete (triangular and circular) stamp problems, an iterative algorithm is developed in order to obtain practically computational solutions for any desired contact lengths. Successful convergence of the SIE results and excellent consistency between the SIE and FEA results are attained, that indicate the reliability of both methods. The change in the thickness is shown to alter the contact behavior of the laterally graded solid significantly.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"531-565"},"PeriodicalIF":0.8,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43054058","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}
We investigate the problem of determining the reach of an inclined cantilever for a given point load suspended from its tip. Two situations are considered. Firstly, we find the maximum reach of the cantilever by varying its angle of inclination. Secondly, we find the reach of the cantilever subject to the condition that its tip is at some specified height, above or below, the level of the clamped end. In the second case, the reach of the cantilever is maximised by shortening its physical length whilst keeping the physical load and physical height of load deployment constant. All of our solutions representing various reaches of an inclined cantilever for a given point load suspended from its tip are shown to be stable to the snap-back instability.
{"title":"Reach of an inclined cantilever with a tip load","authors":"P. Singh, V. Goss","doi":"10.24423/AOM.3254","DOIUrl":"https://doi.org/10.24423/AOM.3254","url":null,"abstract":"We investigate the problem of determining the reach of an inclined cantilever for a given point load suspended from its tip. Two situations are considered. Firstly, we find the maximum reach of the cantilever by varying its angle of inclination. Secondly, we find the reach of the cantilever subject to the condition that its tip is at some specified height, above or below, the level of the clamped end. In the second case, the reach of the cantilever is maximised by shortening its physical length whilst keeping the physical load and physical height of load deployment constant. All of our solutions representing various reaches of an inclined cantilever for a given point load suspended from its tip are shown to be stable to the snap-back instability.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"595-614"},"PeriodicalIF":0.8,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45253602","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 analytic solution to the anti-plane problem of an arbitrary inclusion within an elastic bimaterial under the premise of linear eigenstrains is developed. The bonding along the bimaterial interface is considered to be homogeneously imperfect. The boundary value problem is reduced to a single nonhomogeneous first order differential equation for an analytic function prescribed in the lower half-plane where the inclusion is located. The general solution is given in terms of the imperfect interface parameter and an auxiliary function constructed from the conformal mapping function. In particular, the solution obtained for a circular inclusion demonstrates that the imperfect interface together with the prescribed linear eigenstrains have a pronounced effect on the induced stress field within the inclusion and show a strong non-uniform behaviour especially when the inclusion is near the imperfect interface. Specific solutions are derived in a closed form and verified with existing solutions.
{"title":"Two imperfectly bonded half-planes with an arbitrary inclusion subject to linear eigenstrains in anti-plane shear","authors":"L. Sudak","doi":"10.24423/AOM.3299","DOIUrl":"https://doi.org/10.24423/AOM.3299","url":null,"abstract":"An analytic solution to the anti-plane problem of an arbitrary inclusion within an elastic bimaterial under the premise of linear eigenstrains is developed. The bonding along the bimaterial interface is considered to be homogeneously imperfect. The boundary value problem is reduced to a single nonhomogeneous first order differential equation for an analytic function prescribed in the lower half-plane where the inclusion is located. The general solution is given in terms of the imperfect interface parameter and an auxiliary function constructed from the conformal mapping function. In particular, the solution obtained for a circular inclusion demonstrates that the imperfect interface together with the prescribed linear eigenstrains have a pronounced effect on the induced stress field within the inclusion and show a strong non-uniform behaviour especially when the inclusion is near the imperfect interface. Specific solutions are derived in a closed form and verified with existing solutions.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"71 1","pages":"615-631"},"PeriodicalIF":0.8,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46298839","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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