Pub Date : 2018-10-01DOI: 10.2140/MEMOCS.2018.6.267
M. Aleandri, Venanzio Di Giulio
{"title":"A model for interfaces and its mesoscopic limit","authors":"M. Aleandri, Venanzio Di Giulio","doi":"10.2140/MEMOCS.2018.6.267","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.267","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"46 S1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72559432","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.2018.6.321
J. Goddard
The following is an elaboration on the linear non-local model of viscoelastic fluids proposed in a previous work (Goddard, 2010, Int. J. Eng. Sci. 48, 1279). As a recapitulation of that work, the basic theory is presented in terms of the temporal frequency and spatial wave number in the Laplace-Fourier domain. Taylor-series expansions in these variables provides a weakly non-local theory in spatio-temporal gradients that is more comprehensive than the “bi-velocity” model of Brenner. The linearized Chapman-Enskog kinetic theory is shown to provide a confirmation of the more general theory, from which one can reconstruct a fully non-local integral model. Following the work of Davis and Brenner (2012, J. Acoust. Soc. Am. 132, 2963). the general theory is employed to derive dispersion relations for acoustic, thermal and shear-wave propagation in compressible viscoelastic fluids. At Burnett order the Chapman-Enskog theory gives a cubic polynomial in wave number squared which reduces in the dissipative quasi-static limit to a quadratic like that given by the classical Navier-Stokes-Fourier model and the bi-velocity modification of that model. With minor modification, the present analysis applies to viscoelastic shear and dilatational wave propagation in solids with higher-gradient and Cosserat effects, where it may, for example, find application to the field of rotational seismology.
{"title":"On linear non-local thermo-viscoelastic waves in fluids","authors":"J. Goddard","doi":"10.2140/MEMOCS.2018.6.321","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.321","url":null,"abstract":"The following is an elaboration on the linear non-local model of viscoelastic fluids proposed in a previous work (Goddard, 2010, Int. J. Eng. Sci. 48, 1279). As a recapitulation of that work, the basic theory is presented in terms of the temporal frequency and spatial wave number in the Laplace-Fourier domain. Taylor-series expansions in these variables provides a weakly non-local theory in spatio-temporal gradients that is more comprehensive than the “bi-velocity” model of Brenner. The linearized Chapman-Enskog kinetic theory is shown to provide a confirmation of the more general theory, from which one can reconstruct a fully non-local integral model. Following the work of Davis and Brenner (2012, J. Acoust. Soc. Am. 132, 2963). the general theory is employed to derive dispersion relations for acoustic, thermal and shear-wave propagation in compressible viscoelastic fluids. At Burnett order the Chapman-Enskog theory gives a cubic polynomial in wave number squared which reduces in the dissipative quasi-static limit to a quadratic like that given by the classical Navier-Stokes-Fourier model and the bi-velocity modification of that model. With minor modification, the present analysis applies to viscoelastic shear and dilatational wave propagation in solids with higher-gradient and Cosserat effects, where it may, for example, find application to the field of rotational seismology.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"32 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79707500","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.2018.6.353
C. Cluzel, R. Allena
To assess the degree (i.e., isotropy, transverse isotropy, or orthotropy) and the directions of anisotropy of a three-dimensional structure, information about its mesostructure is necessary. Usually, a topological analysis of computed tomography or microcomputed tomography images is performed and requires an interpretation of the constitutive elements of the three-dimensional structure, which may lead to a simplistic description of the geometry. In this paper we propose an alternative technique based on a geometric tensor and we use it to analyze 38 representative elementary volumes extracted from 24 specimens of cortical bone in a human femur whose geometries have been reconstructed via microcomputed tomography images.
{"title":"A general method for the determination of the\u0000local orthotropic directions of heterogeneous materials : application to bone\u0000structures using μCT images","authors":"C. Cluzel, R. Allena","doi":"10.2140/MEMOCS.2018.6.353","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.353","url":null,"abstract":"To assess the degree (i.e., isotropy, transverse isotropy, or orthotropy) and the directions of anisotropy of a three-dimensional structure, information about its mesostructure is necessary. Usually, a topological analysis of computed tomography or microcomputed tomography images is performed and requires an interpretation of the constitutive elements of the three-dimensional structure, which may lead to a simplistic description of the geometry. In this paper we propose an alternative technique based on a geometric tensor and we use it to analyze 38 representative elementary volumes extracted from 24 specimens of cortical bone in a human femur whose geometries have been reconstructed via microcomputed tomography images.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"15 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73988549","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.2018.6.307
D. George, R. Allena, Y. Rémond
Bone remodelling is a complex phenomenon during which old and damage bone is removed and replaced with new one to ensure the physiological functions of the skeletal system. It involves many biological, mechanical, chemical processes at different scales. The objective of the present work is to predict the kinetics of bone density evolution by taking into account both the mechanical and the biological frameworks. In order to do so, we propose a new computational model in which the global stimulus triggering bone remodelling is the result of the contribution of a mechanical (i.e. external loads and consequent strain energy), a cellular (i.e. osteoblasts and osteoclasts activities) and a molecular (i.e. oxygen and glucose supply) stimulus. The evolution of the bone density depends on the overall behaviour of the global stimulus. More specifically, when the global stimulus is positive, bone synthesis occurs, whereas when the global stimulus is negative, resorption takes place. Although the theoretical model has been applied on a very simple two-dimensional geometry, the final results provide new insights on the influence of each stimulus on the bone remodelling process. In particular, we confirm that mechanics plays a critical role and affects the kinetics of bone reconstruction, but it highly depends on the biological events and the distribution of bone density.
{"title":"A multiphysics stimulus for continuum mechanics bone remodeling","authors":"D. George, R. Allena, Y. Rémond","doi":"10.2140/MEMOCS.2018.6.307","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.307","url":null,"abstract":"Bone remodelling is a complex phenomenon during which old and damage bone is removed and replaced with new one to ensure the physiological functions of the skeletal system. It involves many biological, mechanical, chemical processes at different scales. The objective of the present work is to predict the kinetics of bone density evolution by taking into account both the mechanical and the biological frameworks. In order to do so, we propose a new computational model in which the global stimulus triggering bone remodelling is the result of the contribution of a mechanical (i.e. external loads and consequent strain energy), a cellular (i.e. osteoblasts and osteoclasts activities) and a molecular (i.e. oxygen and glucose supply) stimulus. The evolution of the bone density depends on the overall behaviour of the global stimulus. More specifically, when the global \u0000stimulus is positive, bone synthesis occurs, whereas when the global stimulus is negative, resorption takes place. Although the theoretical model has been applied on a very simple two-dimensional geometry, the final results provide new insights on the influence of each stimulus on the bone remodelling process. In particular, we confirm that mechanics plays a critical role and affects the kinetics of bone reconstruction, but it highly depends on the biological events and the distribution of bone density.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77986645","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.2018.6.293
Narindra Ranaivomiarana, F. Irisarri, D. Bettebghor, B. Desmorat
{"title":"Optimal orthotropy and density distribution of two-dimensional structures","authors":"Narindra Ranaivomiarana, F. Irisarri, D. Bettebghor, B. Desmorat","doi":"10.2140/MEMOCS.2018.6.293","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.293","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"6 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91147086","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.251
Elena Lopez Tomas, A. Scheuer, E. Abisset-Chavanne, F. Chinesta
{"title":"On the effect of phase transition on the manifold dimensionality: application to the Ising model","authors":"Elena Lopez Tomas, A. Scheuer, E. Abisset-Chavanne, F. Chinesta","doi":"10.2140/MEMOCS.2018.6.251","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.251","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"56 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89164525","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.213
H. Abdoul-Anziz, P. Seppecher
We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.
{"title":"Strain gradient and generalized continua obtained by homogenizing frame lattices","authors":"H. Abdoul-Anziz, P. Seppecher","doi":"10.2140/MEMOCS.2018.6.213","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.213","url":null,"abstract":"We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"149 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77209870","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 : 2018-07-26DOI: 10.2140/memocs.2018.6.137
Gianpietro Del Piero
{"title":"The variational structure of classical plasticity","authors":"Gianpietro Del Piero","doi":"10.2140/memocs.2018.6.137","DOIUrl":"https://doi.org/10.2140/memocs.2018.6.137","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"2 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82963368","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.201
S. Kumar, D. Mandal
{"title":"Generation of SH-type waves due to shearing stress discontinuity in an anisotropic layer overlying an initially stressed elastic half-space","authors":"S. Kumar, D. Mandal","doi":"10.2140/MEMOCS.2018.6.201","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.201","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"132 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80443388","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.181
L. Russo
The paper summarizes and discusses the main theses exposed in a previous book (L' America dimenticata, Mondadori Universita, 2013 [in Italian]) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy's Geographia and its logical relation with the reduced estimate for the dimension of the Earth there given. The thesis is sustained that, conversely to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of the scale error on the longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according the source of Ptolemy is identified in the Caribbean. The analysis of a passage by Pliny provides an independent and quantitative confirmation of the proposed identification, which sheds new light on possible contact among civilizations.
本文总结并讨论了前一本书(L' America dimenticata, Mondadori Universita, 2013[意大利语])中暴露的主要论文，并结合了最近的研究结果。具体地说，这项工作解决了解释托勒密的《地理学》中经度系统误差的起源问题，以及它与那里给出的地球尺寸缩减估计的逻辑关系。与经常提出的猜想相反，这个论点得到了支持，即地球尺寸的缩小是经度刻度误差的结果，而经度刻度误差又源于对受祝福岛屿的错误识别。根据托勒密的来源，受祝福的岛屿的位置被确定在加勒比海。对普林尼的一篇文章的分析为提出的鉴定提供了独立和定量的证实，这为文明之间可能的接触提供了新的线索。
{"title":"Far-reaching Hellenistic geographical knowledge\u0000hidden in Ptolemy’s data","authors":"L. Russo","doi":"10.2140/MEMOCS.2018.6.181","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.181","url":null,"abstract":"The paper summarizes and discusses the main theses exposed in a previous book (L' America dimenticata, Mondadori Universita, 2013 [in Italian]) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy's Geographia and its logical relation with the reduced estimate for the dimension of the Earth there given. The thesis is sustained that, conversely to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of the scale error on the longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according the source of Ptolemy is identified in the Caribbean. The analysis of a passage by Pliny provides an independent and quantitative confirmation of the proposed identification, which sheds new light on possible contact among civilizations.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"90 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77901468","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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