Journal of Elasticity最新文献

{"title":"On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains","authors":"Constantin Krauß,&nbsp;Julian Karl Bauer,&nbsp;Johannes Mitsch,&nbsp;Thomas Böhlke,&nbsp;Luise Kärger","doi":"10.1007/s10659-024-10050-3","DOIUrl":"10.1007/s10659-024-10050-3","url":null,"abstract":"<div><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></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"279 - 306"},"PeriodicalIF":1.8,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10050-3.pdf","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":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Internally Balanced Elasticity Tensor in Terms of Principal Stretches","authors":"Ashraf Hadoush","doi":"10.1007/s10659-024-10049-w","DOIUrl":"10.1007/s10659-024-10049-w","url":null,"abstract":"<div><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></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"255 - 278"},"PeriodicalIF":1.8,"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}

{"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":"132 1","pages":""},"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}

{"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":"10.1007/s10659-024-10048-x","url":null,"abstract":"<div><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></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"237 - 254"},"PeriodicalIF":1.8,"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}

{"title":"Potential Functions for Functionally Graded Transversely Isotropic Media Subjected to Thermal Source in Thermoelastodynamics Problems","authors":"Siavash Panahi,&nbsp;Bahram Navayi Neya","doi":"10.1007/s10659-023-10024-x","DOIUrl":"10.1007/s10659-023-10024-x","url":null,"abstract":"<div><p>This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study, a systematic method is used to decouple the elasticity and heat equations. Hence one sixth-order differential equation and two second-order differential equations are obtained. Completeness of the solution is proved using a retarded logarithmic Newtonian potential function for functionally graded transversely isotropic domain. To verify the obtained solution, in a simpler case, potential functions are generated for homogeneous transversely isotropic media that coincide with respective equations. Presented potential functions can be used to solve the problems in various media like infinite and semi-infinite space, beams and columns, plates, shells, etc., with arbitrary boundary conditions and subjected to arbitrary mechanical and thermal loads.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"215 - 236"},"PeriodicalIF":1.8,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560840","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}

{"title":"Revisiting Stress Propagation in a Two-Dimensional Elastic Circular Disk Under Diametric Loading","authors":"Yosuke Sato,&nbsp;Haruto Ishikawa,&nbsp;Satoshi Takada","doi":"10.1007/s10659-023-10047-4","DOIUrl":"10.1007/s10659-023-10047-4","url":null,"abstract":"<div><p>In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"193 - 213"},"PeriodicalIF":1.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423611","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}

{"title":"A Novel Approach to Setting the Problem of Lagrange for Dynamical Systems and Nonlinear Elastodynamics","authors":"","doi":"10.1007/s10659-023-10045-6","DOIUrl":"https://doi.org/10.1007/s10659-023-10045-6","url":null,"abstract":"&lt;h3&gt;Abstract&lt;/h3&gt; &lt;p&gt;The classical Lagrange problem for dynamical systems introduces a &lt;em&gt;Lagrangian action functional&lt;/em&gt; defined for any dynamical process that is envisioned to take place over a fixed interval of time with its state at each time lying on an unknown, but prescribed, configuration between two given end points in an &lt;span&gt; &lt;span&gt;(n)&lt;/span&gt; &lt;/span&gt;-dimensional state space &lt;span&gt; &lt;span&gt;(mathbb{R}^{n})&lt;/span&gt; &lt;/span&gt;. It is proposed that the fundamental dynamical field equation that characterizes the dynamical process and determines the precise motion between the two given end points is the Euler–Lagrange equation related to the stationarity of the Lagrangian action functional, expressed as the integral of a particularly formulated &lt;em&gt;action density&lt;/em&gt; over the fixed time interval, among all admissible configurations that span the two given end points. Thus stated, this variational calculus problem introduces &lt;em&gt;variations of a configuration&lt;/em&gt; that carries a dynamical process, and emphasizes the novelty and need to express explicitly how the configuration influences the state of that process. At each time during a dynamical process the state is subjected to an extrinsic force (classically taken to be conservative) which must be transmitted to the configuration that carries the process and, by action-reaction the configuration responds with a configuration contact force on the state of equal magnitude but opposite direction. This allows the Lagrangian action functional for a dynamical process to be interpreted as the &lt;em&gt;difference&lt;/em&gt; between the &lt;em&gt;average kinetic energy of the dynamical process that is carried by that configuration&lt;/em&gt; and the &lt;em&gt;average configurational work done by the configuration contact force on the moving state&lt;/em&gt; as the state traverses that configuration during the fixed time interval. The aim in the Problem of Lagrange is to extremize this difference over all admissible configurations. The implication is that given a time interval and initial and final end points in the space of all states, the dynamical process of physical interest must follow a configuration that optimizes the gap between the average expended kinetic energy and the average expended configurational work. When the optimal condition is met and the dynamical process is so restricted, the difference between these average expenditures of energy and work will be at a local maximum, a local minimum, or a saddle point known as a condition of “least action”.&lt;/p&gt; &lt;p&gt;Herein, we investigate the optimization implications of this novel interpretation of the action functional for the Problem of Lagrange for dynamical systems for a general, possibly non-conservative, state-dependent extrinsic force field. We show that only a conservative state-dependent extrinsic force field is allowable within the statement of the problem and, thus, reaffirm the predominant classical hypothesis of restricting attention to conservative extrinsic force field","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"23 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139412375","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}

{"title":"Scholarly Works, Academic Lineage, and Doctoral Advisees of Jerald L. Ericksen","authors":"Roger Fosdick, Eliot Fried, Chi-Sing Man","doi":"10.1007/s10659-023-10044-7","DOIUrl":"https://doi.org/10.1007/s10659-023-10044-7","url":null,"abstract":"<p>In this tribute to Jerald L. Ericksen, we present a multifaceted contribution that honors his exceptional legacy as a scientist, educator, and mentor. The contribution is divided into three sections, each providing a unique perspective on his life and work. Through these sections, we aim to preserve and celebrate Jerry’s legacy, a legacy that extends far beyond his scholarly contributions and reverberates through the lives and careers of those he inspired and guided.</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"50 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093655","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}

{"title":"Translation of Jerald L. Ericksen’s Introduction to the Collection “Studies on Mechanics of Continua”","authors":"Alexander B. Freidin","doi":"10.1007/s10659-023-10043-8","DOIUrl":"https://doi.org/10.1007/s10659-023-10043-8","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"133 37","pages":"1-4"},"PeriodicalIF":2.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139387684","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}

{"title":"The Distance to Cubic Symmetry Class as a Polynomial Optimization Problem","authors":"P. Azzi,&nbsp;R. Desmorat,&nbsp;B. Kolev,&nbsp;F. Priziac","doi":"10.1007/s10659-023-10041-w","DOIUrl":"10.1007/s10659-023-10041-w","url":null,"abstract":"<div><p>Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickel-based CMSX-4, cubic symmetry is nevertheless expected. It is in practice necessary to compute the nearest cubic elasticity tensor to a given raw one. Mathematically formulated, the problem consists in finding the distance between a given tensor and the cubic symmetry stratum.</p><p>It has recently been proved that closed symmetry strata are affine algebraic sets (for any tensorial representation of the rotation group): they are defined by polynomial equations without requirement to polynomial inequalities. Such equations have furthermore been derived explicitly for the closed cubic elasticity stratum. We propose to make use of this mathematical property to formulate the distance to cubic symmetry problem as a polynomial (in fact quadratic) optimization problem, and to derive its quasi-analytical solution using the technique of Gröbner bases. The proposed methodology also applies to cubic Hill elasto-plasticity (where two fourth-order constitutive tensors are involved).</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"157 - 191"},"PeriodicalIF":1.8,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981791","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}