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A Reformulation of the Browaeys and Chevrot Decomposition of Elastic Maps 弹性图的布劳瓦伊斯和切弗罗特分解重述
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-03-08 DOI: 10.1007/s10659-024-10056-x
Walter Tape, Carl Tape
{"title":"A Reformulation of the Browaeys and Chevrot Decomposition of Elastic Maps","authors":"Walter Tape, Carl Tape","doi":"10.1007/s10659-024-10056-x","DOIUrl":"https://doi.org/10.1007/s10659-024-10056-x","url":null,"abstract":"<p>An elastic map <span>(mathbf{T})</span> associates stress with strain in some material. A symmetry of <span>(mathbf{T})</span> is a rotation of the material that leaves <span>(mathbf{T})</span> unchanged, and the symmetry group of <span>(mathbf{T})</span> consists of all such rotations. The symmetry class of <span>(mathbf{T})</span> describes the symmetry group but without the orientation information. With an eye toward geophysical applications, Browaeys &amp; Chevrot developed a theory which, for any elastic map <span>(mathbf{T})</span> and for each of six symmetry classes <span>(Sigma )</span>, computes the “<span>(Sigma )</span>-percentage” of <span>(mathbf{T})</span>. The theory also finds a “hexagonal approximation”—an approximation to <span>(mathbf{T})</span> whose symmetry class is at least transverse isotropic. We reexamine their theory and recommend that the <span>(Sigma )</span>-percentages be abandoned. We also recommend that the hexagonal approximations to <span>(mathbf{T})</span> be replaced with the closest transverse isotropic maps to <span>(mathbf{T})</span>.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140074457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Modelling the Deformation of Polydomain Liquid Crystal Elastomers as a State of Hyperelasticity 将多域液晶弹性体的变形模拟为超弹性状态
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-26 DOI: 10.1007/s10659-024-10055-y
Afshin Anssari-Benam, Zhengxuan Wei, Ruobing Bai
{"title":"Modelling the Deformation of Polydomain Liquid Crystal Elastomers as a State of Hyperelasticity","authors":"Afshin Anssari-Benam, Zhengxuan Wei, Ruobing Bai","doi":"10.1007/s10659-024-10055-y","DOIUrl":"https://doi.org/10.1007/s10659-024-10055-y","url":null,"abstract":"<p>A hyperelasticity modelling approach is employed for capturing various and complex mechanical behaviours exhibited by macroscopically isotropic polydomain liquid crystal elastomers (LCEs). These include the highly non-linear behaviour of nematic-genesis polydomain LCEs, and the soft elasticity plateau in isotropic-genesis polydomain LCEs, under finite multimodal deformations (uniaxial and pure shear) using in-house synthesised acrylate-based LCE samples. Examples of application to capturing continuous softening (i.e., in the primary loading path), discontinuous softening (i.e., in the unloading path) and auxetic behaviours are also demonstrated on using extant datasets. It is shown that our comparatively simple model, which breaks away from the neo-classical theory of liquid crystal elastomers, captures the foregoing behaviours favourably, simply as states of hyperelasticity. Improved modelling results obtained by our approach compared with the existing models are also discussed. Given the success of the considered model in application to these datasets and deformations, the simplicity of its functional form (and thereby its implementation), and comparatively low(er) number of parameters, the presented isotropic hyperelastic strain energy function here is suggested for: (i) modelling the general mechanical behaviour of LCEs, (ii) the backbone in the neo-classical theory, and/or (iii) the basic hyperelastic model in other frameworks where the incorporation of the director, anisotropy, viscoelasticity, temperature, softening etc parameters may be required.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Strain Energy Function for Planar Response of a Constrained Cosserat Extensible Elastica with a General Reference Planar Shape 具有一般参考平面形状的受约束 Cosserat 可伸缩弹性体平面响应的应变能函数
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-21 DOI: 10.1007/s10659-024-10053-0
{"title":"A Strain Energy Function for Planar Response of a Constrained Cosserat Extensible Elastica with a General Reference Planar Shape","authors":"","doi":"10.1007/s10659-024-10053-0","DOIUrl":"https://doi.org/10.1007/s10659-024-10053-0","url":null,"abstract":"<h3>Abstract</h3> <p>An analytical expression for the strain energy of a constrained extensible Cosserat elastica is developed for general planar shapes and deformations of the rod. This strain energy function naturally couples tangential stretch and reference and current curvatures of the centroidal curve. The model considers a rigid rectangular cross-section of the rod which remains normal to the centroidal curve. The constitutive equations for the tangential force, shear force and bending moment are consistent with a restriction based on the balance of angular momentum that requires a stress-like tensor to be symmetric in a similar manner to the symmetry of the Cauchy stress in a three-dimensional continuum. Examples show that coupling of tangential stretch and reference and current curvatures of the centroidal curve in the new strain energy function can significantly influence predictions of tangential force, shear force and bending moments.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An Approximate Stress Distribution in a Conical Heap of Jammed Dry Granular Material 干颗粒物料锥形堆中的近似应力分布
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-20 DOI: 10.1007/s10659-024-10054-z
M. B. Rubin
{"title":"An Approximate Stress Distribution in a Conical Heap of Jammed Dry Granular Material","authors":"M. B. Rubin","doi":"10.1007/s10659-024-10054-z","DOIUrl":"https://doi.org/10.1007/s10659-024-10054-z","url":null,"abstract":"<p>This paper develops an approximate stress distribution in a conical heap of jammed dry granular material loaded by gravity. An Eulerian formulation of elastic-inelastic response is used to explain why the residual stresses in the heap can be approximated by the current state of stress in the material. The proposed normalized stress components are functions of the normalized radial and vertical coordinates and are parameterized by only the angle of repose. It is shown that the vertical stress distribution applied to the base of the heap compares well with experiments using a rain procedure for sand deposition.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139911268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fiber-Reinforced Elastic Shells: A Direct Cosserat Approach 纤维增强弹性壳：直接 Cosserat 方法
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-19 DOI: 10.1007/s10659-024-10052-1
Ryan C. McAvoy
{"title":"Fiber-Reinforced Elastic Shells: A Direct Cosserat Approach","authors":"Ryan C. McAvoy","doi":"10.1007/s10659-024-10052-1","DOIUrl":"https://doi.org/10.1007/s10659-024-10052-1","url":null,"abstract":"<p>We formulate a direct theory for fiber-reinforced elastic shells. Our framework utilizes the Cosserat theory of elasticity to model both the shell-like nature of the structure and the embedded fiber response. To this end, we merge the multiple-director theory of Cosserat continua with the additional constraint that the fibers convect as material curves on the surface. The virtual power statement furnishes the equilibrium equations. We also present a coordinate-free formulation and close with a discussion of material symmetry.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139902970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity 具有表面弹性的薄微极板弯曲理论中的边界值问题
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-13 DOI: 10.1007/s10659-024-10051-2
Alireza Gharahi
{"title":"Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity","authors":"Alireza Gharahi","doi":"10.1007/s10659-024-10051-2","DOIUrl":"https://doi.org/10.1007/s10659-024-10051-2","url":null,"abstract":"<p>We generalize a recent theory of bending of thin micropolar plates by incorporating surface effects through the modeling of plate surfaces as adjacent two-dimensional micropolar elastic bodies. By incorporating both elastic surface effects and the micropolar elastic behavior of the plate, the proposed model is capable of taking into account the contribution of high surface-to-volume ratios as well as the influence of microstructural mechanics at micro/nano scales. We determine the fundamental solution of the resulting system of equations and establish uniqueness results for the corresponding Dirichlet and Neumann boundary value problems. Moreover, we provide a numerical example to demonstrate the efficiency of the model in representing the size-dependence arising from various factors that incorporate characteristic lengths. Furthermore, we showcase the sensitivity of the results to different types of characteristic lengths present in the model.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains 论虚拟过程链中纤维方向张量的平均与闭合
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-05 DOI: 10.1007/s10659-024-10050-3
{"title":"On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains","authors":"","doi":"10.1007/s10659-024-10050-3","DOIUrl":"https://doi.org/10.1007/s10659-024-10050-3","url":null,"abstract":"<h3>Abstract</h3> <p>Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Internally Balanced Elasticity Tensor in Terms of Principal Stretches 以主伸展为单位的内部平衡弹性张量
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-02-05 DOI: 10.1007/s10659-024-10049-w
Ashraf Hadoush
{"title":"Internally Balanced Elasticity Tensor in Terms of Principal Stretches","authors":"Ashraf Hadoush","doi":"10.1007/s10659-024-10049-w","DOIUrl":"https://doi.org/10.1007/s10659-024-10049-w","url":null,"abstract":"<p>A new scheme for hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. Then, Piola–Kirchhoff stress is coupled with internal balance equation. Strain energy function is expressed in terms of principal invariants of the deformation gradient decomposed counterparts. Recent work introduces a strain energy function in terms of principal stretches of the deformation gradient multiplicatively decomposed counterparts directly. Hence, a new reformulation of Piola–Kirchhoff stress and internal balance equation are provided. This work focuses on developing the mathematical framework to calculate the elasticity tensor for material model formulated in terms of decomposed principal stretches. This paves the way for future implementation of these classes of material model in FE formulation.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Mechanical Theory of Growth 增长的机械理论
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-01-29 DOI: 10.1007/s10659-023-10042-9
Yi-chao Chen
{"title":"A Mechanical Theory of Growth","authors":"Yi-chao Chen","doi":"10.1007/s10659-023-10042-9","DOIUrl":"https://doi.org/10.1007/s10659-023-10042-9","url":null,"abstract":"<p>A theory of growth is developed, utilizing the notion of a directional density function that captures the number and distribution of the material particles and their changes in time. A spatial (or Eulerian) description of kinematics is adopted, and the constitutive theory for a growing body is developed that relates the stress to the directional density function. The equation that governs the evolution of the directional density function is derived. An example of internal surface growth is presented.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139580455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Pure Torsion for Stretch-Based Constitutive Models for Incompressible Isotropic Hyperelastic Soft Materials 基于拉伸的不可压缩各向同性超弹性软材料构造模型的纯扭转
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2024-01-25 DOI: 10.1007/s10659-024-10048-x
Cornelius O. Horgan
{"title":"Pure Torsion for Stretch-Based Constitutive Models for Incompressible Isotropic Hyperelastic Soft Materials","authors":"Cornelius O. Horgan","doi":"10.1007/s10659-024-10048-x","DOIUrl":"https://doi.org/10.1007/s10659-024-10048-x","url":null,"abstract":"<p>Stretch-based constitutive models for isotropic hyperelastic materials as alternatives to the classical strain invariant models have been the subject of considerable recent attention largely motivated by application to modelling the mechanical response of soft tissues. One such four-parameter constitutive model was proposed recently by Anssari-Benam (J. Elast. 153:219–244, 2023) for incompressible isotropic hyperelastic soft materials. The model was deemed to be <i>comprehensive</i> in that several well-known strain-energies may be recovered for some particular and limiting values of some of the parameters. The model is a generalization of several related simpler models based on microstructural considerations that have been shown to match well with experimental data for a wide variety of soft materials. In particular, the celebrated one-term Ogden model is obtained as a special case. Here we examine the response of the new model for the problem of pure torsion for a solid circular cylinder with particular emphasis on the Poynting effects governing the lengthening or shortening of the cylinder.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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