Journal of Elasticity最新文献

{"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}

{"title":"The Euler–Bernoulli Limit of Thin Brittle Linearized Elastic Beams","authors":"Janusz Ginster,&nbsp;Peter Gladbach","doi":"10.1007/s10659-023-10040-x","DOIUrl":"10.1007/s10659-023-10040-x","url":null,"abstract":"<div><p>We show that the linear brittle Griffith energy on a thin rectangle <span>(varGamma )</span>-converges after rescaling to the linear one-dimensional brittle Euler–Bernoulli beam energy.</p><p>In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"125 - 155"},"PeriodicalIF":1.8,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10040-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513226","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":"Complete General Solutions for Equilibrium Equations of Isotropic Strain Gradient Elasticity","authors":"Yury Solyaev","doi":"10.1007/s10659-023-10039-4","DOIUrl":"10.1007/s10659-023-10039-4","url":null,"abstract":"<div><p>In this paper, we consider isotropic Mindlin–Toupin strain gradient elasticity theory, in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory, we developed an extended form of Boussinesq–Galerkin (BG) and Papkovich–Neuber (PN) general solutions. The obtained form of BG solution allows to define the displacement field through a single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and the completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"107 - 124"},"PeriodicalIF":1.8,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513217","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":"Controllable Deformations of Unconstrained Ideal Nematic Elastomers","authors":"L. Angela Mihai,&nbsp;Alain Goriely","doi":"10.1007/s10659-023-10038-5","DOIUrl":"10.1007/s10659-023-10038-5","url":null,"abstract":"<div><p>We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen’s theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"95 - 106"},"PeriodicalIF":1.8,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10038-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888226","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":"On the Question of the Sign of Size Effects in the Elastic Behavior of Foams","authors":"Stephan Kirchhof,&nbsp;Alfons Ams,&nbsp;Geralf Hütter","doi":"10.1007/s10659-023-10037-6","DOIUrl":"10.1007/s10659-023-10037-6","url":null,"abstract":"<div><p>Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam’s mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.</p><p>In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is “cut” from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are “measured” directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"79 - 93"},"PeriodicalIF":1.8,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10037-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346592","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}