Mathematics and Mechanics of Solids最新文献

{"title":"A mechanical model for a system of coupled elastic filaments for terrestrial robot locomotion.","authors":"Bhargav Konidala, Davide Spinello","doi":"10.1177/10812865261421172","DOIUrl":"https://doi.org/10.1177/10812865261421172","url":null,"abstract":"<p><p>Multi-legged robots are a class of devices offering potential solutions in several operational scenarios that involve the deployment in unstructured and uncertain environments, in which trade-offs between specialization and robustness need to be considered. Several aquatic and terrestrial organisms evolutionarily converged to robust locomotion solutions. An important example is the emergence of collective beating dynamics in coupled arrays of flexible protrusions, which is at the core of the locomotion mechanics of small swimmers, and of terrestrial walkers with flexible, elongated bodies. Here, we formulate the dynamics of a system of flexible elastic filaments coupled through a solid medium, intended to be a simplified model for the locomotion mechanism for a legged terrestrial robot. The legs' coupling is modeled via linear elastic lumped elements, and metachronal wave patterns are enforced via ad hoc leg actuation. Simulation results show that this model predicts the persistence of wave patterns that result in locomotion across a flat terrain.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"31 5","pages":"956-974"},"PeriodicalIF":1.7,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13138736/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147845317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 refined analytical model for acoustic waves in elastic fiber composites.","authors":"Amirali Basiri, C Q Ru, Peter Schiavone","doi":"10.1177/10812865251336256","DOIUrl":"https://doi.org/10.1177/10812865251336256","url":null,"abstract":"<p><p>Unidirectional fiber-reinforced composites continue to gain increasing importance in industrial applications particularly in the area of dynamic behavior. Many studies have focused on the determination of wave speed and attenuation of propagating waves in elastic fiber composites. These studies, however, most often use methods which are overly complicated and computationally expensive. Recently, a simple yet effective medium model was developed which provides explicit formulas for the dynamic behavior of P-waves, SV-waves and SH-waves. This model, however, failed to accurately predict the dynamic behavior of fiber-reinforced composites at higher frequencies around and beyond the bandgap region. In the present study, a refined analytical model is presented which supplements the aforementioned model with wave radiation damping. Our results show that the explicit formulas given by the present model are in good agreement with known numerical results in the literature for P-waves, SV-waves, and SH-waves.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"31 5","pages":"975-984"},"PeriodicalIF":1.7,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13138735/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147845292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 compressible liquid inclusion of arbitrary shape in an isotropic elastic matrix.","authors":"Romina Ardeshiri Jouneghani, Xu Wang, Peter Schiavone","doi":"10.1177/10812865251321095","DOIUrl":"10.1177/10812865251321095","url":null,"abstract":"<p><p>We use Muskhelishvili's complex variable formulation to solve the plane-strain problem of a compressible liquid inclusion of arbitrary shape embedded within an infinite isotropic elastic matrix under uniform remote in-plane stresses. First, the exterior of the domain occupied by the liquid inclusion is mapped onto the exterior of a unit circle in the image plane using a mapping function that contains an arbitrary number of terms. With the aid of a modified form of analytic continuation, a set of linear algebraic equations with relatively simple structure is obtained. Once this set of linear algebraic equations is solved, the internal uniform hydrostatic stress field within the liquid inclusion and the elastic field in the matrix (characterized by a pair of analytic functions) are fully determined. We illustrate our theory by deriving a closed-form solution for a hypotrochoidal liquid inclusion and comparing our results with those available in the existing literature. In addition, numerical results for the internal uniform hydrostatic stress within liquid inclusions with an <i>n</i>-fold axis of symmetry are presented graphically to examine the influence of the number of terms used in the mapping function. Finally, we determine the internal hydrostatic stress for the case of a rectangular liquid inclusion with various aspect ratios.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"30 12","pages":"2843-2854"},"PeriodicalIF":1.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12697927/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145757763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Major symmetry of the induced tangent stiffness tensor for the Zaremba-Jaumann rate and Kirchhoff stress in hyperelasticity: Two different approaches.","authors":"Salvatore Federico, Sebastian Holthausen, Nina J Husemann, Patrizio Neff","doi":"10.1177/10812865241306703","DOIUrl":"10.1177/10812865241306703","url":null,"abstract":"<p><p>We recall in this note that the induced tangent stiffness tensor <math> <mrow> <msubsup><mrow><mi>H</mi></mrow> <mrow><mi>τ</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msubsup> <mrow><mo>(</mo> <mi>τ</mi> <mo>)</mo></mrow> </mrow> </math> appearing in a hypoelastic formulation based on the Zaremba-Jaumann corotational derivative and the rate constitutive equation for the Kirchhoff stress tensor <i>τ</i> is minor and major symmetric if the Kirchhoff stress <i>τ</i> is derived from an elastic potential <math><mrow><mi>W</mi> <mrow><mo>(</mo> <mi>F</mi> <mo>)</mo></mrow> </mrow> </math> . This result is vaguely known in the literature. Here, we expose two different notational approaches which highlight the full symmetry of the tangent stiffness tensor <math> <mrow> <msubsup><mrow><mi>H</mi></mrow> <mrow><mi>τ</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msubsup> <mrow><mo>(</mo> <mi>τ</mi> <mo>)</mo></mrow> </mrow> </math> . The first approach is based on the direct use of the definition of each symmetry (minor and major), i.e., via contractions of the tensor with the deformation rate tensor <i>D</i>. The second approach aims at finding an absolute expression of the tensor <math> <mrow> <msubsup><mrow><mi>H</mi></mrow> <mrow><mi>τ</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msubsup> <mrow><mo>(</mo> <mi>τ</mi> <mo>)</mo></mrow> </mrow> </math> , by means of special tensor products and their symmetrisations. In some past works, the major symmetry of <math> <mrow> <msubsup><mrow><mi>H</mi></mrow> <mrow><mi>τ</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msubsup> <mrow><mo>(</mo> <mi>τ</mi> <mo>)</mo></mrow> </mrow> </math> has been missed because not all necessary symmetrisations were applied. The analogous tangent stiffness tensor <math> <mrow> <msup><mrow><mi>H</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msup> <mrow><mo>(</mo> <mi>σ</mi> <mo>)</mo></mrow> </mrow> </math> , relating the Cauchy stress tensor <i>σ</i> to the Zaremba-Jaumann corotational derivative is also obtained, with both methods used for <math> <mrow> <msubsup><mrow><mi>H</mi></mrow> <mrow><mi>τ</mi></mrow> <mrow><mi>ZJ</mi></mrow> </msubsup> <mrow><mo>(</mo> <mi>τ</mi> <mo>)</mo></mrow> </mrow> </math> . The approach is exemplified for the isotropic Hencky energy. Corresponding stability checks of software packages are shortly discussed.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"30 12","pages":"2733-2761"},"PeriodicalIF":1.7,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12697928/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145757733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Interaction between an edge dislocation and a partially debonded circular elastic inhomogeneity with the debonded portion occupied by a liquid slit inclusion.","authors":"Xu Wang, Peter Schiavone","doi":"10.1177/10812865251316568","DOIUrl":"10.1177/10812865251316568","url":null,"abstract":"<p><p>We study the plane strain problem of a circular elastic inhomogeneity partially debonded from an infinite elastic matrix subjected to an edge dislocation at an arbitrary position. The debonded portion of the circular interface is occupied by an incompressible liquid slit inclusion. The original boundary value problem is reduced to a standard Riemann-Hilbert problem with discontinuous coefficients which can be solved analytically. The two unknown constants appearing in the analytical solution are determined by imposing the incompressibility condition of the liquid inclusion. Closed-form expressions for the internal uniform hydrostatic stress field within the liquid slit inclusion, the average mean stress within the circular elastic inhomogeneity, the rigid body rotation at the center of the circular inhomogeneity, and the two complex stress intensity factors at the two tips of the debonded portion induced by the edge dislocation are obtained.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"30 10","pages":"2431-2445"},"PeriodicalIF":1.7,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12674489/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145679213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Finite element analysis of materially uniform dielectric elastomers.","authors":"Mawafag F Alhasadi, Ahmed Bayram, Qiao Sun, Salvatore Federico","doi":"10.1177/10812865241301716","DOIUrl":"10.1177/10812865241301716","url":null,"abstract":"<p><p>In the definition of Noll, a body is uniform if all points are made of the same material. As shown by Noll himself and by Epstein and Maugin, uniformity makes the Helmholtz free energy depend on the material point exclusively through a tensor field, called uniformity tensor or implant tensor or material isomorphism. Uniformity is therefore a particular case of inhomogeneity. In turn, uniformity includes homogeneity as a particular case: indeed, homogeneity is attained when the uniformity tensor happens to be integrable. This work focuses on the non-linear large-deformation behaviour of uniform dielectric elastomers. Building on the foundational works of Toupin, Eringen and others, this work integrates continuum mechanics with electrostatics to develop a finite element framework for analysing uniform dielectric elastomers. This framework allows for considering the inherent inhomogeneity in materials exhibiting non-linear electromechanical coupling such as electro-active polymers. The inhomogeneity is assumed to be self-driven, i.e., not implied by the second law of thermodynamics: rather, it depends on the torsion of the connection (covariant derivative) induced by the uniformity tensor. A MATLAB^®-based finite element solver is developed and applied to the simulation of an electromechanical beam-type actuator. The solver is robust and capable of addressing various simulation scenarios. Numerical simulations demonstrate the significant impact of material uniformity on actuator performance. This research provides a tool for future applications in dielectric elastomers, particularly in sensors, actuators and bio-inspired robotics.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"30 9","pages":"2001-2031"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12626250/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145558181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 coated hypotrochoidal compressible liquid inclusion neutral to a hydrostatic stress field after relaxation by interface slip and diffusion.","authors":"Xu Wang, Peter Schiavone","doi":"10.1177/10812865241284424","DOIUrl":"10.1177/10812865241284424","url":null,"abstract":"<p><p>We study the steady-state response of a three-phase composite composed of an internal hypotrochoidal compressible liquid inclusion, an intermediate isotropic elastic coating and an outer isotropic elastic matrix with simultaneous interface slip and diffusion occurring on the solid-solid interface when the matrix is subjected to a uniform hydrostatic stress field. We design a neutral coated hypotrochoidal liquid inclusion that does not disturb the prescribed uniform hydrostatic stress field in the surrounding matrix. The neutrality is achieved when the plane-strain bulk modulus or the compressibility of the elastic matrix is determined by solving a system of simultaneous linear algebraic equations for given geometric and material parameters of the coated liquid inclusion.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"30 9","pages":"1935-1951"},"PeriodicalIF":1.7,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12626248/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145557522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Plane-stress analysis of a holed membrane at finite equibiaxial stretch","authors":"Idan Z Friedberg, Gal deBotton","doi":"10.1177/10812865241270732","DOIUrl":"https://doi.org/10.1177/10812865241270732","url":null,"abstract":"An equibiaxially stretched thin neo-Hookean circular membrane with a hole at its center under plane-stress condition is analyzed within the framework of finite deformation elasticity. Initially, we introduce a novel form for the differential governing equation to the problem. This enables the introduction of a closed-form solution in the limit of infinite stretch. Comparison of this solution to corresponding finite element simulations reveals a neat agreement for stretch ratios larger than 2.5. In the practically important case of a small hole, at the circumference of the hole, the stress concentration factor is 4 and the tangential stretch ratio is twice the applied far-field stretch ratio. These values are double the corresponding ratios in the well-known limit of infinitesimal deformation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"41 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comment on “Explicit solutions in Cartesian coordinates for an elliptic hole in an infinite elastic plate” by M. Oore and S. Oore","authors":"Milan Batista","doi":"10.1177/10812865241276440","DOIUrl":"https://doi.org/10.1177/10812865241276440","url":null,"abstract":"This comment discusses the derivation procedure of stress distribution formulas for an infinite elastic plate with an elliptic hole under uniform tension, as presented by M. Oore and S. Oore. While the authors use a heuristic three-step procedure, it is shown that these derivations can be simplified using Maple 2023 or manually. This confirms the exactness of the authors’ formulas, asserting their role as definitive closed-form solutions.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"13 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sensitivity analysis of an inflated and extended fiber-reinforced membrane with different natural configurations of its constituents","authors":"Hadi Asghari, Heiko Topol, Jesús Lacalle, José Merodio","doi":"10.1177/10812865241259129","DOIUrl":"https://doi.org/10.1177/10812865241259129","url":null,"abstract":"In this article, we apply sensitivity analysis (SA) to study the pressure–inflation relation and axial force in a pressurized and extended cylindrical tube. The material consists of an isotropic ground substance that is reinforced in the azimuthal direction with one family of fibers which are taken to be dispersed about that (mean) direction. The natural configuration of the fibers may differ from that of the ground substance, either because the fibers are pre-stretched or because the bonding between the fibers and the ground substance is considered to be imperfect. The axial stretch of the cylindrical membrane is given by a constant value. The input parameters data of the mechanical system, namely, the azimuthal stretch of the cylinder, the fiber dispersion, and the fiber natural configurations, are assumed to be distributed according to three probability distribution functions. In the sensitivity analysis, we apply the Sobol method as well as the Fourier amplitude sensitivity test (FAST) method to determine the way in which variations of the input parameters affect the required inflation pressure and corresponding axial force (output variables). The implementation of the Sobol and FAST methods allows us to account for the interplay of different parameters as well as to identify the most influential parameters in both the pressure–inflation relation and the axial force. The analysis singles out all these aspects showing a rich variety of results.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"39 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}