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":"17 1","pages":""},"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":"9 1","pages":""},"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":"3 1","pages":""},"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":"43 1","pages":""},"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":"244 1","pages":""},"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}
Pub Date : 2022-12-31DOI: 10.2140/memocs.2022.10.395
R. Burson, K. Enakoutsa
Gologanu, Leblond, Perrin, and Devaux (GLPD) developed a constitutive model for ductile fracture for porous metals based on generalized continuum mechanics assump-tions. The model predicted with high accuracy ductile fracture process in porous metals subjected to several complex loads. The GLDP model performances over its competitors has attracted the attention of several authors who explored additional capabilities of the model. This paper provides analytical solutions for the problem of a porous hollow sphere subjected to hydrostatic loadings, the matrix of the hollow sphere obeying the GLPD model. The exact solution for the expressions of the stress and the generalized stress the GLPD model involved are illustrated for the case where the matrix material does not contain any voids. The results show that the singularities obtained in the stress distribution with the local Gurson model are smoothed out, as expected with any generalized continuum model. The paper also presents some elements of the analytical solution for the case where the matrix is porous and obeys the full GLPD model at the initial time when the porosity is fixed. The later analytical solution can serve to predict the mechanisms of ductile fracture in porous ductile solids with two populations of cavities with different sizes.
Gologanu, Leblond, Perrin, and Devaux (GLPD)基于广义连续介质力学假设，开发了多孔金属韧性断裂的本构模型。该模型对多孔金属在多种复杂载荷作用下的韧性断裂过程进行了高精度预测。GLDP模型优于其竞争对手的表现吸引了一些作者的注意，他们探索了该模型的其他功能。本文给出了受静水作用的多孔空心球问题的解析解，空心球的矩阵服从GLPD模型。给出了在基体材料不含空洞的情况下，GLPD模型的应力和广义应力表达式的精确解。结果表明，与广义连续体模型一样，局部Gurson模型得到的应力分布奇异点被平滑了。本文还给出了初始孔隙率固定时基质为多孔且服从全GLPD模型的解析解的若干要素。后一解析解可用于预测具有两种不同大小孔洞的多孔塑性固体的韧性断裂机制。
{"title":"Ductile void growing in micromorphic GLPD porous plastic solids containing two populations of cavities with different sizes","authors":"R. Burson, K. Enakoutsa","doi":"10.2140/memocs.2022.10.395","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.395","url":null,"abstract":"Gologanu, Leblond, Perrin, and Devaux (GLPD) developed a constitutive model for ductile fracture for porous metals based on generalized continuum mechanics assump-tions. The model predicted with high accuracy ductile fracture process in porous metals subjected to several complex loads. The GLDP model performances over its competitors has attracted the attention of several authors who explored additional capabilities of the model. This paper provides analytical solutions for the problem of a porous hollow sphere subjected to hydrostatic loadings, the matrix of the hollow sphere obeying the GLPD model. The exact solution for the expressions of the stress and the generalized stress the GLPD model involved are illustrated for the case where the matrix material does not contain any voids. The results show that the singularities obtained in the stress distribution with the local Gurson model are smoothed out, as expected with any generalized continuum model. The paper also presents some elements of the analytical solution for the case where the matrix is porous and obeys the full GLPD model at the initial time when the porosity is fixed. The later analytical solution can serve to predict the mechanisms of ductile fracture in porous ductile solids with two populations of cavities with different sizes.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"34 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79977120","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.2022.10.413
Reema H Alasfar, S. Ahzi, N. Barth, V. Kochkodan, M. Koç
{"title":"Modeling and experimental validation of the elastic modulus of polysulfone membranes reinforced with cellulose nanofibers","authors":"Reema H Alasfar, S. Ahzi, N. Barth, V. Kochkodan, M. Koç","doi":"10.2140/memocs.2022.10.413","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.413","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"2 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75469321","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 : 2022-12-04DOI: 10.2140/memocs.2022.10.265
A. M. Bersani, Paolo Caressa, A. Ciallella
{"title":"Numerical evidence for the approximation of dissipative systems by gyroscopically coupled oscillator chains","authors":"A. M. Bersani, Paolo Caressa, A. Ciallella","doi":"10.2140/memocs.2022.10.265","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.265","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"79 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82466754","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 : 2022-12-04DOI: 10.2140/memocs.2022.10.245
Pikaso Pal, Vivek Mukherjee, Gang-Gyoo Jin
{"title":"Adaptive chaos synchronization of a mechanical system with disturbances and uncertainties","authors":"Pikaso Pal, Vivek Mukherjee, Gang-Gyoo Jin","doi":"10.2140/memocs.2022.10.245","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.245","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"88 12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84062074","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 : 2022-12-04DOI: 10.2140/memocs.2022.10.205
C. Polizzotto, P. Fuschi, A. Pisano
{"title":"Nonlocal strain gradient elastic beam models with two-step differential approach and decoupling of standard and extra boundary conditions, I","authors":"C. Polizzotto, P. Fuschi, A. Pisano","doi":"10.2140/memocs.2022.10.205","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.205","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88033403","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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