Philosophical transactions. Series A, Mathematical, physical, and engineering sciences最新文献_第4页

Localized bulging of an inflated rubber tube with fixed ends. 末端固定的充气橡胶管的局部膨出。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0318

Zhiming Guo, Shibin Wang, Yibin Fu

{"title":"Localized bulging of an inflated rubber tube with fixed ends.","authors":"Zhiming Guo, Shibin Wang, Yibin Fu","doi":"10.1098/rsta.2021.0318","DOIUrl":"https://doi.org/10.1098/rsta.2021.0318","url":null,"abstract":"When a rubber tube with free ends is inflated under volume control, the pressure will first reach a maximum and then decrease monotonically to approach a constant asymptote. The pressure maximum corresponds to the initiation of a localized bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a 'two-phase' propagation state. By contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure as a function of the bulge amplitude has both a maximum and a minimum, and the behaviour on the right ascending branch has previously not been fully understood. We show that for all values of the pre-stretch and tube length, the ascending branches all converge to a single curve that is dependent only on the ratio of the tube thickness to the outer radius. This curve represents the Maxwell state to be approached in each case (if Euler buckling or axisymmetric wrinkling does not occur first), but this state is pressure-dependent, in contrast to the free-ends case. We also demonstrate experimentally that localized bulging cannot occur when the pre-stretch is sufficiently large and investigate what strain-energy functions can predict this observed phenomenon. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210318"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441783","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}

引用次数: 6

Exponents of the one-term Ogden model: insights from simple shear. 单项奥格登模型的指数:来自简单剪切的见解。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0328

Cornelius O Horgan, Jeremiah G Murphy

引用次数: 8

An Ogden-like formulation incorporating phase-field fracture in elastomers: from brittle to pseudo-ductile failures. 一个奥格登式公式结合相场断裂弹性体:从脆性到伪延性失效。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0323

Jacopo Ciambella, Giovanni Lancioni, Nico Stortini

{"title":"An Ogden-like formulation incorporating phase-field fracture in elastomers: from brittle to pseudo-ductile failures.","authors":"Jacopo Ciambella, Giovanni Lancioni, Nico Stortini","doi":"10.1098/rsta.2021.0323","DOIUrl":"https://doi.org/10.1098/rsta.2021.0323","url":null,"abstract":"Over the past 50 years the Ogden model has been widely used in material modelling owing to its ability to match accurately the experimental data on elastomers at large strain, as well as its mathematical properties, such as polyconvexity. In this paper, these characteristics are exploited to formulate a finite-strain model that incorporates, through the phase-field approach recently proposed by Wu (Wu 2017 J. Mech. Phys. Solids 103, 72-99) for small strains, a cohesive damage mechanism which leads to the progressive degradation of the material stiffness and to failure under tension. By properly tailoring the constitutive parameters, the model is capable of encompassing a wide range of effects, from brittle to pseudo-ductile failure modes. A plane stress problem is formulated to test the model against experiments on double-network elastomers, which display a pseudo-ductile damage behaviour at large strain, and on conventional rubber compounds with brittle failure. The results show that the proposed model is applicable to fracture coalescence and propagation in a wide range of materials. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210323"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441697","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}

引用次数: 1

Mechanics of pressurized planar hyperelastic membranes. 受压平面超弹性膜力学。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0319

A P S Selvadurai

{"title":"Mechanics of pressurized planar hyperelastic membranes.","authors":"A P S Selvadurai","doi":"10.1098/rsta.2021.0319","DOIUrl":"https://doi.org/10.1098/rsta.2021.0319","url":null,"abstract":"The paper examines the mechanics of inflation of incompressible planar hyperelastic membranes that are rigidly fixed at their boundary and subjected to a uniform pressure. Strain energy functions characterized by the neo-Hookean, Mooney-Rivlin and the Ogden forms are used. Fixity is provided along either circular or elliptical boundaries. The computational results indicate that the strain energy function has a significant influence on the pressure versus inflated volume response of the deformed membrane. When the strain energy function corresponds to a Mooney-Rivlin form, the circular membrane displays no tendency to develop any instability. The equivalent circular membranes composed of both the neo-Hookean and Ogden-type strain energy functions developed an initial 'Wrinkling Instability'. For planar membranes with an elliptical planform, the wrinkling instability is more pronounced; membranes composed of hyperelastic materials with a Mooney-Rivlin form of the strain energy function continue to deform without the development of an initial instability point, whereas membranes composed of both the neo-Hookean and Ogden materials exhibit wrinkling behaviour at critical locations at the interior of the fixed boundary region. The dependency of the strain energy function on the second invariant of the Cauchy-Green strain tensor has an influence in the suppression of hyperelastic effects. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210319"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441784","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}

引用次数: 5

Bifurcation analysis of residually stressed neo-Hookean and Ogden electroelastic tubes. 残余应力新hookean和Ogden电弹性管的分岔分析。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0331

Andrey Melnikov, Jose Merodio, Roger Bustamante, Luis Dorfmann

{"title":"Bifurcation analysis of residually stressed neo-Hookean and Ogden electroelastic tubes.","authors":"Andrey Melnikov, Jose Merodio, Roger Bustamante, Luis Dorfmann","doi":"10.1098/rsta.2021.0331","DOIUrl":"https://doi.org/10.1098/rsta.2021.0331","url":null,"abstract":"The conditions for bifurcation of a circular cylindrical tube of elastic material subjected to combined axial loading and internal pressure are well known and are frequently used as a reference in related works. The present paper takes the theory further by considering a residually stressed circular cylindrical dielectric tube subjected to a combination of internal or external pressure, axial load and radial electric field. We examine axisymmetric incremental deformations and increments in the electric displacement superimposed on a known finitely deformed and residually stressed configuration in the presence of an electric field. The governing equations and boundary conditions are first obtained in general form and then specialized for the neo-Hookean and Ogden electroelastic models. The system of equations is solved numerically for different values of charge density and radial and circumferential residual stresses, and the results are compared with the purely elastic case. The bifurcation curves are presented as the azimuthal stretch on the inner surface versus the axial stretch together with the corresponding zero pressure curves. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210331"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441276","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}

引用次数: 5

A generalized Ogden model for the compressibility of rubber-like solids. 类橡胶固体可压缩性的广义Ogden模型。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0320

Yin Yao, Shaohua Chen, Zhuping Huang

{"title":"A generalized Ogden model for the compressibility of rubber-like solids.","authors":"Yin Yao, Shaohua Chen, Zhuping Huang","doi":"10.1098/rsta.2021.0320","DOIUrl":"https://doi.org/10.1098/rsta.2021.0320","url":null,"abstract":"The aim of this paper is to further demonstrate the advantages and effectiveness of the constitutive formulation proposed by Huang (Huang 2014 J. Appl. Mech. 59, 902-908 (doi:10.1115/1.2894059)). In this formulation, any strain-energy function for an incompressible material can be easily generalized to include the effect of material compressibility, in which only a few material parameters and material functions to be fitted with the experimental data are required. To this end, the Ogden model for incompressible rubber-like solids is chosen as the starting point. By means of this formulation, the generalized Ogden strain-energy function, which takes into account material compressibility, can conveniently be constructed so long as its incompressible counterpart is given. The obvious advantage shown in this paper is that only a few material parameters and material functions are needed, i.e. in addition to the material parameters used in the original Ogden model for incompressible solids, only one material function depending on the volume ratio is involved to characterize the effect of compressibility. Both the material parameters in the original Ogden model and the material function suggested in this paper can be determined by fitting the experimental data for uniaxially tensile test and hydrostatic deformation test of rubbers, respectively. The present model considering compressibility is general since it can be applied to predict the stress-strain responses of rubber-like materials and porous rubbers in various loading conditions. With the present formulation, the applicable range of the celebrated Ogden model can be further broadened, which should be of practical importance for accurately describing the mechanical behaviour of rubber-like solids. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210320"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441277","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}

引用次数: 1

Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification. 奥格登材料校准通过磁共振制图，参数灵敏度和变分系统识别。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0324

Denislav P Nikolov, Siddhartha Srivastava, Bachir A Abeid, Ulrich M Scheven, Ellen M Arruda, Krishna Garikipati, Jonathan B Estrada

{"title":"Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification.","authors":"Denislav P Nikolov, Siddhartha Srivastava, Bachir A Abeid, Ulrich M Scheven, Ellen M Arruda, Krishna Garikipati, Jonathan B Estrada","doi":"10.1098/rsta.2021.0324","DOIUrl":"https://doi.org/10.1098/rsta.2021.0324","url":null,"abstract":"Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210324"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441778","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}

引用次数: 3

Variations on Ogden's model: close and distant relatives. 奥格登模式的变体:近亲和远亲。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0322

A E Ehret, A Stracuzzi

引用次数: 3

The Ogden and the extended tube model as backbone in describing electroactive polymers: advancements in modelling nonlinear behaviour and fracture. 奥格登和扩展管模型作为描述电活性聚合物的主干:非线性行为和断裂建模的进展。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0329

M Kaliske, J Storm, A Kanan, W Klausler

{"title":"The Ogden and the extended tube model as backbone in describing electroactive polymers: advancements in modelling nonlinear behaviour and fracture.","authors":"M Kaliske, J Storm, A Kanan, W Klausler","doi":"10.1098/rsta.2021.0329","DOIUrl":"https://doi.org/10.1098/rsta.2021.0329","url":null,"abstract":"Hyperelastic constitutive relations form the basis of advanced models for novel materials. Such elastic deformation potentials are the backbone for complex material formulations at elastic and inelastic deformations, especially when embedded into powerful frameworks like generalized standard materials, as well as multiphysical and multiscale formulations. With the focus on electroactive polymers, the article at hand demonstrates the derivation of a variational, rate-dependent electromechanical model for quasi-incompressible polymers and the derivation of an electromechanical model for regularized fracture mechanics by means of the phase-field method. Starting at the prominent Ogden and the extended tube model, some developments from the last decades are revisited and presented via the principle of virtual power, for instance, the established mixed element formulation, nonlinear viscoelasticity and electromechanical coupling. An electromechanically fully coupled representative crack element is used to derive a novel phase-field model for fracture. A key property of the proposed model is the ability to describe the electrical free-space behaviour inside the crack gap, which is demonstrated by adopting three common crack-face conditions. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210329"},"PeriodicalIF":5.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33441782","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}

引用次数: 4

Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness? 软组织的线性、弱非线性和全非线性模型:哪一种提供最可靠的刚度估计?

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-10-17 Epub Date: 2022-08-29 DOI: 10.1098/rsta.2021.0321

G Saccomandi, L Vergori, E M Zanetti

引用次数: 2