Pub Date : 2023-10-23DOI: 10.2140/memocs.2023.11.19
Riccardo Augello, Erasmo Carrera, Alfonso Pagani, Mário R. T. Arruda, Jiahui Shen
{"title":"Node-dependent kinematic models applied to reinforced concrete structures","authors":"Riccardo Augello, Erasmo Carrera, Alfonso Pagani, Mário R. T. Arruda, Jiahui Shen","doi":"10.2140/memocs.2023.11.19","DOIUrl":"https://doi.org/10.2140/memocs.2023.11.19","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135365549","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 : 2023-10-23DOI: 10.2140/memocs.2023.11.1
Oscar Cosserat, Alexei Kotov, Camille Laurent-Gengoux, Leonid Ryvkin, Vladimir Salnikov
We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formulation of Dirac dynamics.
{"title":"On Dirac structures admitting a variational approach","authors":"Oscar Cosserat, Alexei Kotov, Camille Laurent-Gengoux, Leonid Ryvkin, Vladimir Salnikov","doi":"10.2140/memocs.2023.11.1","DOIUrl":"https://doi.org/10.2140/memocs.2023.11.1","url":null,"abstract":"We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formulation of Dirac dynamics.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322603","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 : 2023-10-23DOI: 10.2140/memocs.2023.11.57
Alfio Grillo, Salvatore Di Stefano
{"title":"An a posteriori approach to the mechanics of volumetric growth","authors":"Alfio Grillo, Salvatore Di Stefano","doi":"10.2140/memocs.2023.11.57","DOIUrl":"https://doi.org/10.2140/memocs.2023.11.57","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135365299","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 : 2023-10-23DOI: 10.2140/memocs.2023.11.45
Oleksiy Kapustyan, Olena Kapustian, Ihor Korol, Bruno Rubino
{"title":"Uniform attractor of impulse-perturbed reaction-diffusion system","authors":"Oleksiy Kapustyan, Olena Kapustian, Ihor Korol, Bruno Rubino","doi":"10.2140/memocs.2023.11.45","DOIUrl":"https://doi.org/10.2140/memocs.2023.11.45","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135365298","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 : 2023-10-23DOI: 10.2140/memocs.2023.11.87
Christian Soize
{"title":"An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials","authors":"Christian Soize","doi":"10.2140/memocs.2023.11.87","DOIUrl":"https://doi.org/10.2140/memocs.2023.11.87","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135366186","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 : 2023-10-12DOI: 10.2140/memocs.2024.12.1
Hussein Nassar
A emph{surface of translation} is a sum $(u,v)mapstogtalpha(u)+gtbeta(v)$ of two space curves: a emph{path} $gtalpha$ and a emph{profile} $gtbeta$. A fundamental problem of differential geometry and shell theory is to determine the ways in which surfaces deform isometrically, i.e., by bending without stretching. Here, we explore how surfaces of translation bend. Existence conditions and closed-form expressions for special bendings of the infinitesimal and finite kinds are provided. In particular, all surfaces of translation admit a purely torsional infinitesimal bending. Surfaces of translation whose path and profile belong to an elliptic cone or to two planes but never to their intersection further admit a torsion-free infinitesimal bending. Should the planes be orthogonal, the infinitesimal bending can be integrated into a torsion-free (finite) bending. Surfaces of translation also admit a torsion-free bending if the path or profile has exactly two tangency directions. Throughout, smooth and piecewise smooth surfaces, i.e., surfaces with straight or curved creases, are invariably dealt with and some extra care is given to situations where the bendings cause new creases to emerge.
{"title":"Isometric deformations of surfaces of translation","authors":"Hussein Nassar","doi":"10.2140/memocs.2024.12.1","DOIUrl":"https://doi.org/10.2140/memocs.2024.12.1","url":null,"abstract":"A emph{surface of translation} is a sum $(u,v)mapstogtalpha(u)+gtbeta(v)$ of two space curves: a emph{path} $gtalpha$ and a emph{profile} $gtbeta$. A fundamental problem of differential geometry and shell theory is to determine the ways in which surfaces deform isometrically, i.e., by bending without stretching. Here, we explore how surfaces of translation bend. Existence conditions and closed-form expressions for special bendings of the infinitesimal and finite kinds are provided. In particular, all surfaces of translation admit a purely torsional infinitesimal bending. Surfaces of translation whose path and profile belong to an elliptic cone or to two planes but never to their intersection further admit a torsion-free infinitesimal bending. Should the planes be orthogonal, the infinitesimal bending can be integrated into a torsion-free (finite) bending. Surfaces of translation also admit a torsion-free bending if the path or profile has exactly two tangency directions. Throughout, smooth and piecewise smooth surfaces, i.e., surfaces with straight or curved creases, are invariably dealt with and some extra care is given to situations where the bendings cause new creases to emerge.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139320177","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 : 2023-07-01DOI: 10.2140/memocs.2024.12.85
D. Benedetto, E. Caglioti, M. Nolasco
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of ensembles does not hold. For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit an arbitrary number of fist-order phase transitions, while the entropy is convex for large energy.
{"title":"Microcanonical phase transitions for the vortex system","authors":"D. Benedetto, E. Caglioti, M. Nolasco","doi":"10.2140/memocs.2024.12.85","DOIUrl":"https://doi.org/10.2140/memocs.2024.12.85","url":null,"abstract":"We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of ensembles does not hold. For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit an arbitrary number of fist-order phase transitions, while the entropy is convex for large energy.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364897","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 : 2022-12-31DOI: 10.2140/memocs.2022.10.389
Aviral Misra, Anil Misra
{"title":"Condorcet’s enlightenment in the age of\u0000alternative facts : A review of Francesco dell’Isola’s book Big-(wo)men, tyrants,chiefs, dictators, emperors and presidents","authors":"Aviral Misra, Anil Misra","doi":"10.2140/memocs.2022.10.389","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.389","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89202227","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 : 2022-12-31DOI: 10.2140/memocs.2022.10.321
N. Auffray, Saad El Ouafa, G. Rosi, B. Desmorat
. In the present contribution the anisotropic structure of the two-dimensional linear Cosserat elasticity is investigated. The symmetry classes of this model are derived and detailed in a synthetic way. Particular attention is paid to specific features of Cosserat Elasticity which are the sensitivity to non-centrosymmetry as well as to chirality. These aspects are important for the application of this continuum theory to the mechanical modelling of lattices and metamaterials. In order to give a parameterisation to the Cosserat constitutive law, an explicit harmonic decomposition of its constitutive tensors is provided. Finally, using an algorithm introduced in a side paper, a minimal integrity basis, which is the minimal set of polynomial invariants generating the algebra of O(2)-invariant polynomials, is finally reported.
{"title":"Anisotropic structure of two-dimensional linear Cosserat elasticity","authors":"N. Auffray, Saad El Ouafa, G. Rosi, B. Desmorat","doi":"10.2140/memocs.2022.10.321","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.321","url":null,"abstract":". In the present contribution the anisotropic structure of the two-dimensional linear Cosserat elasticity is investigated. The symmetry classes of this model are derived and detailed in a synthetic way. Particular attention is paid to specific features of Cosserat Elasticity which are the sensitivity to non-centrosymmetry as well as to chirality. These aspects are important for the application of this continuum theory to the mechanical modelling of lattices and metamaterials. In order to give a parameterisation to the Cosserat constitutive law, an explicit harmonic decomposition of its constitutive tensors is provided. Finally, using an algorithm introduced in a side paper, a minimal integrity basis, which is the minimal set of polynomial invariants generating the algebra of O(2)-invariant polynomials, is finally reported.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74095949","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 : 2022-12-31DOI: 10.2140/memocs.2022.10.357
Filippo Sangiorgio
{"title":"Decomposition method for reliability analysis of structural systems","authors":"Filippo Sangiorgio","doi":"10.2140/memocs.2022.10.357","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.357","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72867153","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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