Journal of Elasticity最新文献

{"title":"Microstructural Basis of Complex Mechanical Programming in Liquid Crystal Elastomers","authors":"Morgan Barnes,&nbsp;John S. Biggins","doi":"10.1007/s10659-025-10138-4","DOIUrl":"10.1007/s10659-025-10138-4","url":null,"abstract":"<div><p>Liquid crystal elastomers (LCEs) are actuating soft solids that exhibit large and reversible contractions along the liquid crystal director on heating through the nematic-isotropic transition. Recently, mechanical programming was used to fabricate LCEs that can actuate into arbitrarily complex shapes such as a face. Here, we combine theoretical and experimental observations to explain how such complex mechanical programming works. Crucially, we identify the intermediate pre-programmed state as an isotropic genesis polydomain, which, during programming, can accommodate the imposed strains via a pure soft-mode response enabled by director rotation and laminar microstructures. Second cross-linking fixes these microstructures as preferred but, since they were achieved softly, they do not involve any reconfiguration of the isotropic state, allowing it to be restored on heating. Experimental observations of programmed LCEs reveal both single and double laminate structures, as anticipated by the theory, and also a quantitative match between the 3D deformations that can and cannot be programmed. The set of programmable deformations includes all modest isochoric deformations, explaining why arbitrary shape programming works. Finally, we demonstrate theoretically and experimentally that programming also allows one to engineer samples with desired extents of softness in different directions.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12122613/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144197980","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 Mappings and Deformation Processes","authors":"M. B. Rubin,&nbsp;Lorenzo Bardella","doi":"10.1007/s10659-025-10139-3","DOIUrl":"10.1007/s10659-025-10139-3","url":null,"abstract":"<div><p>This Note focuses on kinematics in continuum mechanics and suggests the need for distinguishing between a <i>mapping</i> and a <i>deformation process</i>. As an example, it is shown that the standard discussion of isochoric bending of a cube into sectors of circular tubes is actually an isochoric <i>deformation process</i> that continuously deforms <i>only</i> members of the set of sectors of circular tubes. Specifically, this mapping cannot continuously deform a cube into sectors of circular tubes.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171404","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":"On the Constitutive Behavior of Linear Viscoelastic Solids Under the Plane Stress Condition","authors":"Bojan B. Guzina,&nbsp;Marc Bonnet","doi":"10.1007/s10659-025-10136-6","DOIUrl":"10.1007/s10659-025-10136-6","url":null,"abstract":"<div><p>Motivated by the recent experimental and analytical developments enabling high-fidelity material characterization of (heterogeneous) sheet-like solid specimens, we seek to elucidate the constitutive behavior of linear viscoelastic solids under the plane stress condition. More specifically, our goal is to expose the relationship between the plane-stress viscoelastic constitutive parameters and their (native) “bulk” counterparts. To facilitate the sought reduction of the three-dimensional (3D) constitutive behavior, we deploy the concept of projection operators and focus on the frequency-domain behavior by resorting to the Fourier transform and the mathematical framework of tempered distributions, which extends the Fourier analysis to functions (common in linear viscoelasticity) for which Fourier integrals are not convergent. In the analysis, our primary focus is the on class of linear viscoelastic solids whose 3D rheological behavior is described by a set of constant-coefficient ordinary differential equations, each corresponding to a generic arrangement of “springs” and “dashpots”. On reducing the general formulation to the isotropic case, we proceed with an in-depth investigation of viscoelastic solids whose bulk and shear modulus each derive from a suite of classical “spring and dashpot” configurations. To enable faithful reconstruction of the 3D constitutive parameters of natural and engineered solids via (i) thin-sheet testing and (ii) applications of the error-in-constitutive-relation approach to the inversion of (kinematic) sensory data, we also examine the reduction of thermodynamic potentials describing linear viscoelasticity under the plane stress condition. The analysis is complemented by a set of analytical and numerical examples, illustrating the effect on the plane stress condition on the behavior of isotropic and anisotropic viscoelastic solids.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10136-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140277","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":"Work and Activation in a Nematic Polymer Network Ribbon","authors":"Harmeet Singh,&nbsp;Krishnan Suryanarayanan,&nbsp;Epifanio G. Virga","doi":"10.1007/s10659-025-10137-5","DOIUrl":"10.1007/s10659-025-10137-5","url":null,"abstract":"<div><p>We study spontaneous deformations of a ribbon made of nematic polymer networks and activated under the action of a mechanical load. We show that when such ribbons are activated appropriately, the deformations produced can pull back and perform work against the externally applied load. We perform two numerical experiments to demonstrate this effect: (1) the <i>pulling</i> experiment, where the ribbon is pulled longitudinally by a point force, and (2) the <i>bending</i> experiment, where the ribbon is bent out of plane by a terminally applied point force. We quantify the capacity of the ribbon to work against external loads, and compute its dependence on both the ribbon thickness and the imprinted nematic texture (that is, the distribution of the nematic directors across the ribbon’s length). Finally, we compute the efficiency of the activation process. Building on the outcomes of our numerical explorations, we formulate two educated conjectures on how the activation efficiency can in general be improved by acting on both the applied load and the imprinted nematic texture.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170707","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":"On the Influence of a Dilatant Asperity Patch on the Seismic Moment","authors":"P. A. Selvadurai,&nbsp;A. P. S. Selvadurai","doi":"10.1007/s10659-025-10135-7","DOIUrl":"10.1007/s10659-025-10135-7","url":null,"abstract":"<div><p>This paper proposes a novel procedure to examine the influences of friction, dilatancy, and normal stresses at fault zones on the estimation of seismic moment. For illustrative purposes, the study focuses on a circular frictional dilatant patch located within a frictionless pre-compressed fault zone undergoing relative shear. When dilatancy occurs, the interface beyond the dilatant region may experience separation due to the normal stresses acting on the fault plane, affecting the deformational response of the pre-stressed asperity. This approach allows for an evaluation of the normal stress on the dilatant region, leading to a re-interpretation of the conventional definition of seismic moment. We compare our model against a comprehensive catalog of earthquakes spanning 16 orders of magnitude, utilizing seismologically inferred source properties as well as data from two separate experimental studies that directly measure the shear-dilatant response of shear fractures in both laboratory and field settings. Our findings indicate that friction-induced dilatancy exerts minimal influence on the estimation of seismic moment. However, we emphasize that the discrepancies between our direct measurements and inferred estimates of seismic moment highlight the need for focused campaigns and in situ and on-fault assessments of earthquake mechanics. <b>Plain Language summary</b>. The conventional definition of the <i>Seismic Moment</i> has been central to unifying information from plate tectonics, geology, geodesy, and seismology. It looks at how the ground moves along a fault plane and the strength of the surrounding rocks. However, it often overlooks other factors that might affect this movement, such as the stress on the fault and the local topography that can induce additional physical responses. This study explores how these additional factors, particularly a process called dilatancy, can change our understanding of the seismic moment. The authors found that while these factors do play a role, they have a minimal impact on the traditional definition of seismic moment initially proposed by Aki in 1966.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10135-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108511","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":"Analytical Structural Constitutive Models for Collagenous Soft Tissue: Treatment of Waviness Integrals","authors":"Jia Lu","doi":"10.1007/s10659-025-10134-8","DOIUrl":"10.1007/s10659-025-10134-8","url":null,"abstract":"<div><p>This article presents two structural constitutive models for collagenous tissues. A salient feature of these models is that they are represented analytically by probability distribution functions that are directly available in standard scientific computing packages. No numerical integration is needed at the user’s end. The models are apt for describing the realistic behavior of collagenous tissues. Most notably, they are able to generate response curves whose slopes are sigmoid. The models can delineate, analytically, the transition from the initial quasi-exponential response to the subsequent non-exponential phase characterized by a sigmoid slope. The constitutive equations have an additive structure, and this structure is leveraged to develop response functions relative to a pre-deformed configuration. The models are evaluated against experimental and simulated response data. Spot-on fits are achieved in all cases. The predictive capability is assessed in the context of biaxial response by fitting a subset of loading paths and predicting the responses of unfitted paths. The models provide indicators of waviness exposure, and these indicators can be used to estimate the trustworthiness of the parameters obtained from regression.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944380","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":"Influence of Thickness Variation on Elastic Critical Buckling of Compressed Thin Plate","authors":"Ming Ji","doi":"10.1007/s10659-025-10133-9","DOIUrl":"10.1007/s10659-025-10133-9","url":null,"abstract":"<div><p>In the plane-stress problem of the classical plate theory, the constant thickness assumption is conventionally used as one of the assumptions in the Kirchhoff-Love hypothesis, which almost becomes a fixed concept for such thin-plate models. However, for some situations of uniformly stretched mid-surface (variable plate thickness), such as the elastic buckling of an in-plane uniformly compressed thin plate, this assumption is a deformation constraint on the plate free surface, thereby increasing the unnecessary anti-deformation stiffness. Herein, by introducing the mean stress and strain into Hooke’s law of a three-dimensional infinitesimal element, transforming the corresponding stress–strain relations, shrinking (dimension-reducing) them, and copying them onto the mid-surface of the plane-stress plate, the corresponding two-dimensional stress–strain relations can be obtained, which include a variable thickness strain. Furthermore, by combining with the corresponding stretching-type geometric relations at the mid-surface, the resultant stretching force on the transverse cross-section can be determined. Simultaneously, the Kirchhoff-Love hypothesis (bending geometric relations) can still be considered applicable to such an already uniformly stretched mid-surface, thereby the cross-section resultant moment relations throughout the thickness can also be determined. Finally, a modified approach is proposed to evaluate the influence of thickness variation on the elastic critical buckling of uniformly compressed thin plates by replacing the flexural stiffness value, which is believed to have a better prediction accuracy.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908813","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":"Analysis of One-Dimensional Hexagonal Piezoelectric Quasicrystal with a Periodic Distribution of Slant Mode-III Cracks","authors":"Xue Rang,&nbsp;Yan-Bin Zhou","doi":"10.1007/s10659-025-10132-w","DOIUrl":"10.1007/s10659-025-10132-w","url":null,"abstract":"<div><p>The electroelastic problems of one-dimensional hexagonal piezoelectric quasicrystal materials with a periodic distribution of slant mode-III cracks under anti-plane shear and electromechanical loading are analyzed in this paper. Based on the three electrical boundary conditions at the crack surfaces, electrically permeable, electrically semi-permeable and electrically impermeable condition, the problems are classified as solving singular integral equations by using screw dislocation solutions. For two special cases of coplanar and parallel periodic crack arrays, the closed form solutions for the electroelastic fields, including stress fields, electric fields and tearing displacements, have been determined. The solutions of the singular integral equations for slant cracks can be transformed into the solutions of algebraic equations, the field intensity factors and mechanical strain energy release rates have been determined. The numerical solutions show that the normalized mechanical strain energy release rates increase under the influence of phonon field stress, phason field stress as well as electric fields, indicating that cracks are more likely to propagate in piezoelectric quasicrystal materials. In addition, it is found that the stress fields at the crack tips exhibited singularity, and the variation law of the total energy release rates with the applied electrical loading are also obtained.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908814","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":"Wrinkling of Hyperelastic Thin Film on Hyperelastic Semibounded Substrate in Cases of Rigid Connection and Frictionless Sliding of Components","authors":"A. L. Kipnis","doi":"10.1007/s10659-025-10130-y","DOIUrl":"10.1007/s10659-025-10130-y","url":null,"abstract":"<div><p>Using general solutions of the equilibrium equations of linearized stability theory, transcendental equations for determining the critical strains corresponding to the onset of wrinkling of a thin coating film located on a semibounded substrate are obtained. The substrate/film (bilayer) system is assumed to be under plane strain conditions, and the body materials are nonlinearly elastic with arbitrary structures of elastic potentials. Two variants of the boundary conditions at the interface are considered: perfectly bonded layers and perfectly lubricated layers, corresponding to the “strongest” and “weakest” types of bonding between the bilayer components. Numerical results for determining the critical values of the wrinkling strain are presented for the harmonic potential (compressible bodies, large strains), the quadratic potential (compressible bodies, small strains), the Treloar potential, and the Bartenev–Khazanovich potential (incompressible bodies, large strains). The nature of the dependence of the critical strain and critical wavelength on the elastic constants of the substrate and film materials and on the type of elastic potential was studied. A comparison of the obtained results with known theoretical and experimental results was carried out.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861316","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":"Collection of the Journal of Elasticity: Mechanics of Growth and Remodeling in Biology","authors":"Paola Nardinocchi,&nbsp;Eric Puntel,&nbsp;Giuseppe Zurlo","doi":"10.1007/s10659-025-10131-x","DOIUrl":"10.1007/s10659-025-10131-x","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861329","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}