Mathematics and Mechanics of Solids最新文献_第7页

An experimentally informed continuum grain boundary model 基于实验的连续晶界模型

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865231223921

S Syed Ansari, Amit Acharya, Alankar Alankar

{"title":"An experimentally informed continuum grain boundary model","authors":"S Syed Ansari, Amit Acharya, Alankar Alankar","doi":"10.1177/10812865231223921","DOIUrl":"https://doi.org/10.1177/10812865231223921","url":null,"abstract":"A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"195 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948522","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}

引用次数: 0

Numerical methods in Poisson geometry and their application to mechanics 泊松几何中的数值方法及其在力学中的应用

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-25 DOI: 10.1177/10812865231217096

Oscar Cosserat, Camille Laurent-Gengoux, Vladimir Salnikov

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Growth-induced delamination of an elastic film adhered to a cylinder 粘附在圆柱体上的弹性薄膜的生长诱导分层

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-08 DOI: 10.1177/10812865231209412

Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi

{"title":"Growth-induced delamination of an elastic film adhered to a cylinder","authors":"Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi","doi":"10.1177/10812865231209412","DOIUrl":"https://doi.org/10.1177/10812865231209412","url":null,"abstract":"We study the delamination induced by the growth of a thin adhesive sheet from a cylindrical, rigid substrate. Neglecting the deformations along the axis of the cylinder, we treat the sheet as a one-dimensional flexible and compressible ring, which adheres to the substrate by capillary adhesion. Using the calculus of variations, we obtain the equilibrium equations and in particular arrive at a transversality condition involving in a non-trivial way the curvature of the substrate, the extensibility of the ring and capillary adhesion. By numerically solving the equilibrium equations, we show that delamination by growth occurs through a discontinuous transition from the fully adherent solution to the partially delaminated one. The shape of the delaminated part can take the form either of a ruck, with a small slope, or a fold, with a large slope. Furthermore, in the weak adhesion regime, complete delamination may occur. We construct the phase diagram between the different solutions in the parameter space. In the quasi-incompressible limit, numerical results are also supported by asymptotic calculations both in the strong and weak adhesion regimes.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"34 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139446521","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}

引用次数: 0

The mathematics and mechanics of tug of war 拔河的数学和力学

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-06 DOI: 10.1177/10812865231203154

Derek E Moulton, H. Oliveri

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Identifying composition-mechanics relations in human brain tissue based on neural-network-enhanced inverse parameter identification 基于神经网络增强的逆参数识别，确定人脑组织的成分与力学关系

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-06 DOI: 10.1177/10812865231206544

Jan Hinrichsen, Lea Feiler, Nina Reiter, Lars Bräuer, M. Schicht, Friedrich Paulsen, S. Budday

{"title":"Identifying composition-mechanics relations in human brain tissue based on neural-network-enhanced inverse parameter identification","authors":"Jan Hinrichsen, Lea Feiler, Nina Reiter, Lars Bräuer, M. Schicht, Friedrich Paulsen, S. Budday","doi":"10.1177/10812865231206544","DOIUrl":"https://doi.org/10.1177/10812865231206544","url":null,"abstract":"The mechanical properties of human brain tissue remain far from being fully understood. One aspect that has gained more attention recently is their regional dependency, as the brain’s microstructure varies significantly from one region to another. Understanding the correlation between tissue components and the mechanical behavior is an important step toward better understanding how human brain tissue properties change in space and time and to develop highly spatially resolved constitutive models for large-scale brain simulations. Here, we analyze the correlation between human brain tissue components quantified through enzyme-linked immunosorbent assays (ELISA) and material parameters obtained through an inverse parameter identification scheme based on a hyperelastic Ogden model and multimodal mechanical testing data for eight regions of the brain. We use neural networks as a metamodel to save computational costs. The networks are trained on finite element simulation outputs and are able to replace the simulations in the initial optimization step. We identified strong dependencies between mechanical properties and Iba1 associated with microglia cells, collagen VI, GFAP associated with astrocytes, and collagen IV. These results advance our understanding of microstructure-mechanics relations in human brain tissue and will contribute to the development of highly spatially resolved microstructure-informed constitutive models.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"11 24","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139380181","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}

引用次数: 0

Author’s response to Shariff et al. [1]: Basic errors in couple-stress hyperelasticity articles 作者对 Shariff 等人[1]的回应：耦合应力超弹性文章中的基本错误

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-04 DOI: 10.1177/10812865231213321

KP Soldatos

引用次数: 0

Basic errors in couple-stress hyperelasticity articles 耦合应力超弹性文章中的基本错误

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-04 DOI: 10.1177/10812865231213311

M. Shariff, R. Bustamante, J. Merodio

引用次数: 0

On the inflation, bulging/necking bifurcation and post-bifurcation of a cylindrical membrane under limited extensibility of its constituents 论圆柱形膜在其成分的有限延伸性条件下的膨胀、隆起/颈部分叉和后分叉

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-03 DOI: 10.1177/10812865231214262

Heiko Topol, Alejandro Font, Andrey Melnikov, Jesús Lacalle, M. Stoffel, J. Merodio

{"title":"On the inflation, bulging/necking bifurcation and post-bifurcation of a cylindrical membrane under limited extensibility of its constituents","authors":"Heiko Topol, Alejandro Font, Andrey Melnikov, Jesús Lacalle, M. Stoffel, J. Merodio","doi":"10.1177/10812865231214262","DOIUrl":"https://doi.org/10.1177/10812865231214262","url":null,"abstract":"We consider the bifurcation and post-bifurcation of an extended and inflated circular cylindrical membrane under limited extensibility of its constituents. First, for illustration of the limited extensibility effect, a membrane made of the (isotropic) Gent model is briefly analyzed. Second, the membrane is considered to be made of an isotropic ground substance reinforced with fibers symmetrically arranged in two helically distributed families which are mechanically equivalent. The mechanical behavior of the fibers in a similar way to the (isotropic) Gent model is taken to reflect fiber limited extensibility. In particular, the materials under consideration are NH models augmented with two functions called reinforcing models, each one accounting for unidirectional reinforcement. For a specific material, since both families are mechanically equivalent, the reinforcing models are equal. The nature of the anisotropy considered, i.e., the reinforcing model, can depend only on the stretch in the fiber direction or can depend on the fiber stretch and also can have an influence on the shear response of the material (i.e., it also captures shearing in the fiber direction). The limitation associated with the material anisotropic deformability as well as the arrangement of the material constituents is discussed with respect to the initiation of bulging and necking for the membrane. The subsequent consequences for configurations in equilibrium during post-bifurcation are also studied in detail and a variety of results are given in terms of the limited extensibility (deformability) of the fibers as well as their mechanical response and arrangement (fiber winding angle).","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"142 18","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139387469","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}

引用次数: 0

Quasiconvexity in a model of fiber-reinforced solids based on Cosserat elasticity theory 基于 Cosserat 弹性理论的纤维增强固体模型中的准凸性

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-02 DOI: 10.1177/10812865231217640

M. Shirani, Mircea Bîrsan, D. Steigmann

引用次数: 0

The shape of the mitral annulus: A hypothesis of mechanical morphogenesis 二尖瓣环的形状：机械形态发生假说

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-18 DOI: 10.1177/10812865231208016

Davide Ambrosi, L. Deorsola, Stefano Turzi, Marta Zoppello

{"title":"The shape of the mitral annulus: A hypothesis of mechanical morphogenesis","authors":"Davide Ambrosi, L. Deorsola, Stefano Turzi, Marta Zoppello","doi":"10.1177/10812865231208016","DOIUrl":"https://doi.org/10.1177/10812865231208016","url":null,"abstract":"This paper investigates the role of mechanics in the morphogenesis of the annulus of the mitral valve. We represent the annulus in its embryonic stage as an elastic ring and we perform a mechanical simulation of the development process applying a distributed torque on the rod: because of the mechanical action of the other growing cardiac chambers on the atrio-ventricular region, it departs from a planar circular shape. The numerical integration of the mathematical rod model subject to a bending load yields a shape very near to the one reported in the medical literature as anatomical reference for healthy patients. To make the comparison quantitative, we illustrate a numerical approach to match two curves in 3D defining their distance in a proper mathematical way. Such a methodology is first applied to compare the annular shape resulting from the mechanical model with an anatomical reference “master” shape and it is then applied to set to clinical data extracted from MRI for a cohort of healthy patients. The good agreement among anatomical master description, numerical mechanical model, and clinical data supports our speculation about a possible role of mechanics in determining the shape of the mitral valve.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":" 17","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138994827","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}

引用次数: 0