Pub Date : 2019-08-10DOI: 10.2140/MEMOCS.2019.7.175
Ksenia Frolova, P. Grigoreva, Konstantin Lezhnev, G. Paderin
{"title":"A model of the proppant flowback: setup of the theoretical framework","authors":"Ksenia Frolova, P. Grigoreva, Konstantin Lezhnev, G. Paderin","doi":"10.2140/MEMOCS.2019.7.175","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.175","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84285311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-27DOI: 10.2140/MEMOCS.2019.7.159
I. Giorgio, D. Vescovo
{"title":"Energy-based trajectory tracking and vibration control for multilink highly flexible manipulators","authors":"I. Giorgio, D. Vescovo","doi":"10.2140/MEMOCS.2019.7.159","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.159","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"46 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80370163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-27DOI: 10.2140/MEMOCS.2019.7.99
Eduard Penner, I. Caylak, A. Dridger, R. Mahnken
{"title":"A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics","authors":"Eduard Penner, I. Caylak, A. Dridger, R. Mahnken","doi":"10.2140/MEMOCS.2019.7.99","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.99","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"56 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89853058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-22DOI: 10.2140/MEMOCS.2019.7.75
S. Eugster, F. dell’Isola, D. Steigmann
A three-dimensional continuum theory for fibrous mechanical metamaterials is proposed, in which the fibers are assumed to be spatial Kirchhoff rods whose mechanical response is controlled by a deformation field and a rotation field, the former accounting for strain of the rod and the latter for flexure and twist of the rod as it deforms. This leads naturally to a model based on Cosserat elasticity. Rigidity constraints are introduced that effectively reduce the model to a variant of second-gradient elasticity theory.
{"title":"Continuum theory for mechanical metamaterials with a cubic lattice substructure","authors":"S. Eugster, F. dell’Isola, D. Steigmann","doi":"10.2140/MEMOCS.2019.7.75","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.75","url":null,"abstract":"A three-dimensional continuum theory for fibrous mechanical metamaterials is proposed, in which the fibers are assumed to be spatial Kirchhoff rods whose mechanical response is controlled by a deformation field and a rotation field, the former accounting for strain of the rod and the latter for flexure and twist of the rod as it deforms. This leads naturally to a model based on Cosserat elasticity. Rigidity constraints are introduced that effectively reduce the model to a variant of second-gradient elasticity theory.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"39 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78078006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-22DOI: 10.2140/MEMOCS.2019.7.63
F. Messelmi
{"title":"On the blocking limit of steady-state flow of\u0000Herschel–Bulkley fluid","authors":"F. Messelmi","doi":"10.2140/MEMOCS.2019.7.63","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.63","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"10 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86620059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Homogenization of nonlinear inextensible\u0000pantographic structures by Γ-convergence","authors":"J. Alibert, A. D. Corte","doi":"10.2140/MEMOCS.2019.7.1","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.1","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"613 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76801846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-22DOI: 10.2140/MEMOCS.2019.7.51
F. Browning, H. Askes
Analytical solutions, based on the Ritz method, are derived for the lowest natural frequency of rectangular symmetric angle-ply laminated plates. Since symmetric angle-ply plates have nonzero cross-elasticity constants, the solutions are approximate. The accuracy of these solutions is tested with a convergence study using the Rayleigh quotient iteration method. With the solutions available in symbolic form, parameter studies are presented that establish the effect of plate aspect ratio and ply orientation angle for a number of stacking geometries. The results are also verified through a comparison with numerical Ritz solutions, showing a maximum error of 5% in our approximate solution.
{"title":"Analytical solutions for the natural frequencies of rectangular symmetric angle-ply laminated plates","authors":"F. Browning, H. Askes","doi":"10.2140/MEMOCS.2019.7.51","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.51","url":null,"abstract":"Analytical solutions, based on the Ritz method, are derived for the lowest natural frequency of rectangular symmetric angle-ply laminated plates. Since symmetric angle-ply plates have nonzero cross-elasticity constants, the solutions are approximate. The accuracy of these solutions is tested with a convergence study using the Rayleigh quotient iteration method. With the solutions available in symbolic form, parameter studies are presented that establish the effect of plate aspect ratio and ply orientation angle for a number of stacking geometries. The results are also verified through a comparison with numerical Ritz solutions, showing a maximum error of 5% in our approximate solution.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"369 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76275104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-22DOI: 10.2140/MEMOCS.2019.7.25
Wilhelm Rickert, E. Vilchevskaya, W. Müller
{"title":"A note on Couette flow of micropolar fluids\u0000according to Eringen’s theory","authors":"Wilhelm Rickert, E. Vilchevskaya, W. Müller","doi":"10.2140/MEMOCS.2019.7.25","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.25","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"14 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85576769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-17DOI: 10.2140/memocs.2019.7.131
S. Gavrilyuk, H. Gouin
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature consider the dependence of surface energy only on mean curvature with an added linear term for Gauss curvature. Therefore, for closed surfaces the Gauss curvature term can be eliminated because of the Gauss-Bonnet theorem. In [18], the dependence on the mean and Gaussian curvatures was considered in statics. The authors derived the shape equation as well as two scalar boundary conditions on the contact line. In this paper-thanks to the principle of virtual working-the equations of motion and boundary conditions governing the fluid membranes subject to general dynamical bending are derived. We obtain the dynamic 'shape equa-tion' (equation for the membrane surface) and the dynamic conditions on the contact line generalizing the classical Young-Dupr{'e} condition.
{"title":"Dynamic boundary conditions for membranes whose surface energy depends on the mean and Gaussian curvatures","authors":"S. Gavrilyuk, H. Gouin","doi":"10.2140/memocs.2019.7.131","DOIUrl":"https://doi.org/10.2140/memocs.2019.7.131","url":null,"abstract":"Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature consider the dependence of surface energy only on mean curvature with an added linear term for Gauss curvature. Therefore, for closed surfaces the Gauss curvature term can be eliminated because of the Gauss-Bonnet theorem. In [18], the dependence on the mean and Gaussian curvatures was considered in statics. The authors derived the shape equation as well as two scalar boundary conditions on the contact line. In this paper-thanks to the principle of virtual working-the equations of motion and boundary conditions governing the fluid membranes subject to general dynamical bending are derived. We obtain the dynamic 'shape equa-tion' (equation for the membrane surface) and the dynamic conditions on the contact line generalizing the classical Young-Dupr{'e} condition.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"221 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88670972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-10-01DOI: 10.2140/MEMOCS.2018.6.339
R. Allena, C. Cluzel
Heterogeneous materials such as bone or woven composites show mesostruc-tures whose constitutive elements are all oriented locally in the same direction and channel the stress flow throughout the mechanical structure. The interfaces between such constitutive elements and the matrix are regions of potential degra-dations. Then, when building a numerical model, one has to take into account the local systems of orthotropic coordinates in order to properly describe the damage behavior of such materials. This can be a difficult task if the orthotropic directions constantly change across the complex three-dimensional geometry as is the case for bone structures or woven composites. In the present paper, we propose a finite element technique to estimate the continuum field of orthotropic directions based on the main hypothesis that they are mainly triggered by the external surface of the structure itself and the boundary conditions. We employ two diffusion equations, with specific boundary conditions, to build the radial and the initial longitudinal unit vectors. Then, to ensure the orthonormality of the basis, we compute the longitudinal, the circumferential, and the radial vectors via a series of vector products. To validate the numerical results, a comparison with the average directions of the experimentally observed Haversian canals is used. Our method is applied here to a human femur.
{"title":"Heterogeneous directions of orthotropy in three-dimensional structures: finite element description based on diffusion equations","authors":"R. Allena, C. Cluzel","doi":"10.2140/MEMOCS.2018.6.339","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.339","url":null,"abstract":"Heterogeneous materials such as bone or woven composites show mesostruc-tures whose constitutive elements are all oriented locally in the same direction and channel the stress flow throughout the mechanical structure. The interfaces between such constitutive elements and the matrix are regions of potential degra-dations. Then, when building a numerical model, one has to take into account the local systems of orthotropic coordinates in order to properly describe the damage behavior of such materials. This can be a difficult task if the orthotropic directions constantly change across the complex three-dimensional geometry as is the case for bone structures or woven composites. In the present paper, we propose a finite element technique to estimate the continuum field of orthotropic directions based on the main hypothesis that they are mainly triggered by the external surface of the structure itself and the boundary conditions. We employ two diffusion equations, with specific boundary conditions, to build the radial and the initial longitudinal unit vectors. Then, to ensure the orthonormality of the basis, we compute the longitudinal, the circumferential, and the radial vectors via a series of vector products. To validate the numerical results, a comparison with the average directions of the experimentally observed Haversian canals is used. Our method is applied here to a human femur.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"29 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89070087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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