Xibin Li, Yanghai Shen, Xianlin Jia, Zhiqing Zhang, Ernian Pan
{"title":"Transient Response of an Ice-Water-Covered Transversely Isotropic Poroelastic and Multilayered Medium Under Vertical P-Wave Incidence","authors":"Xibin Li, Yanghai Shen, Xianlin Jia, Zhiqing Zhang, Ernian Pan","doi":"10.1007/s10659-025-10145-5","DOIUrl":"10.1007/s10659-025-10145-5","url":null,"abstract":"<div><p>Formation of ice layers during winter is a common natural phenomenon in high-latitude regions. To evaluate the impact of the ice layer on the seismic response of a poroelastic medium, we develop a novel model to describe the dynamic interaction among the ice layer, water layer, and transversely isotropic poroelastic rock under vertical P-wave excitation. First, the general solutions for the poroelastic rock and overlying water and ice layers are derived by applying the Laplace transform. Then the dual-variable and position (DVP) method is employed to obtain a semi-analytical solution of the layered media in the transform domain. By applying a numerical inverse Laplace transform scheme, the time response of free-field motion in the layered rock under P-wave excitation is obtained. Numerical results show that the ice layer causes more complex waveforms and amplifies the vertical displacement in deeper locations in the poroelastic medium with low permeability. A higher anisotropic modulus ratio leads to an earlier arrival of displacement peaks and troughs, with this effect strengthening over time. Stiff interlayers amplify the displacement and advance the waveform, while soft interlayers have the opposite effect.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10145-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169580","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":"Axisymmetric Elastic Fields in Transversely Isotropic Layered Half-Space with Cavity Subjected to Internal Pressure","authors":"Sha Xiao, Zhongqi Quentin Yue","doi":"10.1007/s10659-025-10148-2","DOIUrl":"10.1007/s10659-025-10148-2","url":null,"abstract":"<div><p>This paper develops an axisymmetric boundary element method (BEM) for analyzing a transversely isotropic (TI) layered half-space with an internal cavity subjected to pressure. The BEM formulation utilizes the fundamental solution of a TI layered solid of infinite extent under body forces uniformly concentrated along a circular ring. Three types of isoparametric elements are used to discretize the core region surrounding the cavity and an infinite element is utilized to discretize the external boundary away from the cavity. A novel numerical quadrature scheme is introduced to calculate the regular and singular integrals in the BEM formulation. Numerical verifications are carried out to confirm the accuracy and computational efficiency of the proposed BEM. The numerical results demonstrate the influence of the heterogeneity and anisotropy of the TI layered solid on the elastic fields in the surrounding rocks around the cavity of either sphere or ellipsoid.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10148-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169579","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":"The Explicit Determination of the (p)-th Root of an Arbitrary Second-Order Tensor and Its Derivative","authors":"C. S. Jog","doi":"10.1007/s10659-025-10149-1","DOIUrl":"10.1007/s10659-025-10149-1","url":null,"abstract":"<div><p>In nonlinear elasticity, the square root of a tensor arises in the polar decomposition of the deformation gradient, and in many other applications in other areas as well. In this work, given a positive integer <span>(p)</span>, we derive an explicit expression for the principal <span>(p)</span>-th root of a real-valued second-order tensor, which is not necessarily diagonalizable, whose eigenvalues do not lie on the closed negative real axis, but which is otherwise arbitrary, for any underlying space dimension <span>(n)</span>. We also present a method for the explicit evaluation of the derivative of the <span>(p)</span>-th root of a tensor.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169110","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":"Elastic Displacements and Viscous Flows in Wedge-Shaped Geometries with a Straight Edge: Green’s Functions for Perpendicular Forces","authors":"Abdallah Daddi-Moussa-Ider, Andreas M. Menzel","doi":"10.1007/s10659-025-10146-4","DOIUrl":"10.1007/s10659-025-10146-4","url":null,"abstract":"<div><p>Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this purpose, we solve the governing elasticity equations for linearly elastic, potentially compressible solids, as well as the low-Reynolds-number flow equations for incompressible fluids. Technically speaking, we derive the associated Green’s functions under confinement by two planar boundaries that meet at a straight edge. The two boundaries both feature no-slip or free-slip conditions, or one of these two conditions per boundary. Previously, we solved the simpler case of the force being oriented parallel to the straight edge. Here, we complement this solution by the more challenging case of the force pointing into a direction perpendicular to the edge. Together, these two cases provide the general solution. Specific situations in which our analysis may find application in terms of quantitative theoretical descriptions are particle motion in confined colloidal suspensions, dynamics of active microswimmers near edges, or actuated distortions of elastic materials due to activated contained functionalized particles.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10146-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166751","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":"Mindlin’s Problem for a Surface-Stiffened Exponentially-Graded Transversely Isotropic Half-Space","authors":"Parham Samea, S. Farzad Ahmadi","doi":"10.1007/s10659-025-10147-3","DOIUrl":"10.1007/s10659-025-10147-3","url":null,"abstract":"<div><p>This study presents an analytical solution for an exponentially-graded transversely isotropic half-space reinforced by a thin plate, subjected to frictionless contact conditions and buried static point loads. The adopted material model captures the behavior of anisotropic and functionally graded media with improved accuracy compared to the assumption of transverse isotropy. Expressions for displacement field are derived, integrating material anisotropy, functional gradation, and interface conditions. The results show that increasing the thin plate stiffness significantly reduces the normal displacement of the half-space, with displacement nearly vanishing under extreme conditions. Additionally, variations in material gradation initially lead to a substantial reduction in displacement, while specific reinforcement conditions may result in localized increases. These findings provide insights into the mechanical behavior of surface-reinforced anisotropic media and multi-layered structures in applications such as protective coatings, pavements, and ground reinforcements.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166752","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":"Rayleigh Wave Propagation in Micropolar Layered Media with Perfect and Slip Interfaces","authors":"Santanu Manna, Deepak, Manasa Bhat","doi":"10.1007/s10659-025-10143-7","DOIUrl":"10.1007/s10659-025-10143-7","url":null,"abstract":"<div><p>This study investigates the dispersion of Rayleigh waves propagating in fiber-reinforced medium over a compressible porous semi-infinite medium under the influence of micropolar elasticity. Perfect and slip boundary conditions are applied on the interface of stratum and substrate to yield the dispersion relation. The model incorporates one of the most effective scheme, the Finite Difference Scheme (FDS) to compute the phase velocities and group velocities of Rayleigh waves. Stability condition of FDS has been derived for the phase velocity and group velocity. The effects of porosity, reinforcement, and micropolarity on Rayleigh waves propagation are studied graphically. A higher mode of the dispersion curve is also analyzed with respect to welded (perfect) and slip boundary conditions.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167051","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}
K. Yoonirundorn, T. Senjuntichai, S. Keawsawasvong, R. K. N. D. Rajapakse
{"title":"Elastodynamic Fundamental Solutions of a Transversely Isotropic Unsaturated Half-Space Subjected to Axisymmetric Buried Vertical and Fluid Loading","authors":"K. Yoonirundorn, T. Senjuntichai, S. Keawsawasvong, R. K. N. D. Rajapakse","doi":"10.1007/s10659-025-10144-6","DOIUrl":"10.1007/s10659-025-10144-6","url":null,"abstract":"<div><p>This paper presents solutions for a transversely isotropic unsaturated half-space subjected to axisymmetric time-harmonic vertical and fluid pressure loading. The Biot’s coupled poroelastodynamic equations are modified to include the unsaturated case by adding the air phase into the balance equations. The resulting fully coupled field equations of the three-phase medium are analytically solved to obtain the frequency-domain general solutions by using Hankel integral transforms in the radial direction. A boundary value problem is then formulated to obtain explicit expressions for the solutions of a half-space subjected to internally applied time-harmonic vertical loading and applied fluid pressure. To validate the accuracy of the proposed formulation, a comparison is made with existing solutions for surface loading on an unsaturated half-space. Numerical results are presented to illustrate the influence of the degree of saturation and the frequency of excitation on the dynamic response of the unsaturated half-space under internal excitations. The analysis reveals significant differences in profiles of displacement, stress, and pore pressure for the unsaturated soils compared to fully saturated cases, highlighting the importance of incorporating partial saturation in dynamic poroelastic modelling for geotechnical and earthquake engineering applications.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166683","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":"Some Remarks on the Principal Stretch Versus Invariant Formulation for Constitutive Modeling of Incompressible Isotropic Hyperelastic Materials","authors":"C. O. Horgan, J. G. Murphy","doi":"10.1007/s10659-025-10142-8","DOIUrl":"10.1007/s10659-025-10142-8","url":null,"abstract":"<div><p>It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10142-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161635","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":"A Note on the Universal Deformations of Incompressible Isotropic Bodies","authors":"Seyedemad Motaghian","doi":"10.1007/s10659-025-10141-9","DOIUrl":"10.1007/s10659-025-10141-9","url":null,"abstract":"<div><p>This study provides an example demonstrating that a universal deformation does not constrain the shape of a body. We show that bending, inflation, azimuthal shearing, and expansion or contraction of the major radius of a toroidal sector belong to the class of Family 5 deformations. Therefore, this family of universal deformations for incompressible isotropic solids is not restricted to an annular wedge. The proposed example is shown to be a family of inhomogeneous deformations in which the Cauchy deformation tensor has constant principal invariants — a property which is found only in the Family 5 class of deformations.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161634","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":"In-Plane Static Behavior of Nonlocal Curved Nanobeams Resting on an Elastic Foundation Determined Using the Initial Value Method","authors":"Reha Artan, Ayşegül Tepe","doi":"10.1007/s10659-025-10140-w","DOIUrl":"10.1007/s10659-025-10140-w","url":null,"abstract":"<div><p>Curved nanobeams are fundamental components of nanoscale systems, such as nano and microelectromechanical systems, where accurate modeling of small-scale effects is essential for achieving high precision. This study introduces a novel framework for analyzing the in-plane static behavior of curved nanobeams resting on an elastic foundation, particularly for small displacements. Nonlocal constitutive equations are derived based on nonlocal elasticity theory and solved using the initial value method and the approximate transfer matrix approach to address the challenges arising from the high degree of statical indeterminacy. A convergence analysis is conducted, showing that the proposed method provides a systematic and computationally efficient solution. A parametric analysis reveals that the nonlocal parameter, elastic foundation, and opening angle significantly influence the displacements in the tangential and normal directions, the rotation and bending moment in the binormal direction, the shear force in the normal direction, and the axial force in the tangential direction. These findings further elucidate the mechanics of curved nanostructures, contributing to the design and optimization of nanoscale devices.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10140-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170791","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}