Mathematics and Mechanics of Solids最新文献

{"title":"Finite-strain Poynting–Thomson model: Existence and linearization","authors":"Andrea Chiesa, Martin Kružìk, Ulisse Stefanelli","doi":"10.1177/10812865241263788","DOIUrl":"https://doi.org/10.1177/10812865241263788","url":null,"abstract":"We analyze the finite-strain Poynting–Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin–Voigt viscoelastic element. In the finite-strain case, the total deformation of the body results from the composition of two maps, describing the deformation of the viscoelastic element and the elastic one, respectively. We prove the existence of suitably weak solutions by a time-discretization approach based on incremental minimization. Moreover, we prove a rigorous linx earization result, showing that the corresponding small-strain model is indeed recovered in the small-loading limit.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"14 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201733","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":"Reflection of plane waves from the free surface of a hard sphere-filled elastic metacomposite","authors":"Kosar Samadi-Aghdam, Chongqing Ru, Peter Schiavone","doi":"10.1177/10812865241269732","DOIUrl":"https://doi.org/10.1177/10812865241269732","url":null,"abstract":"We use an effective medium model to study the problem of reflection of plane waves from the free surface of a half-space occupied by an elastic particulate metacomposite. This problem has received little attention in the recent literature despite its significance from both practical and theoretical points of view. Classical formulas for the reflection angles and amplitudes of the reflected waves for a homogeneous elastic half-space with no wave attenuation are extended to a particulate metacomposite half-space with wave attenuation. We also include a detailed discussion concerning the reflected plane shear wave and surface compressional wave in the case of an incident shear wave propagating at an incident angle smaller than the critical angle. The efficiency and accuracy of the model are demonstrated via detailed comparisons between the predicted phase velocity and attenuation coefficient of plane waves in an (infinite) entire space and the corresponding results available in the literature. The implications of our results on the reflection of plane waves from the free surface of a hard sphere-filled elastic metacomposite are discussed. We mention that a quantitative validation of our results cannot be made here as a result of the lack of availability of established data in the existing literature.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201734","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":"Virtual element method for solving a viscoelastic contact problem with long memory","authors":"Wenqiang Xiao, Min Ling","doi":"10.1177/10812865241263039","DOIUrl":"https://doi.org/10.1177/10812865241263039","url":null,"abstract":"In this paper, we use the virtual element method to solve a history-dependent hemivariational inequality arising in contact problems. The contact problem concerns the deformation of a viscoelastic body with long memory, subjected to a contact condition with non-monotone normal compliance and unilateral constraints. A fully discrete scheme based on the trapezoidal rule for the discretization of the time integration and the virtual element method for the spatial discretization are analyzed. We provide a unified priori error analysis for both internal and external approximations. For the linear virtual element method, we obtain the optimal order error estimate. Finally, three numerical examples are reported, providing numerical evidence of the theoretically predicted optimal convergence orders.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"14 4 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201736","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":"On the existence of Rayleigh waves with full impedance boundary condition","authors":"Pham Thi Ha Giang, Pham Chi Vinh","doi":"10.1177/10812865241266809","DOIUrl":"https://doi.org/10.1177/10812865241266809","url":null,"abstract":"The existence of Rayleigh waves (propagating in isotropic elastic half-spaces) with the tangential and normal impedance boundary conditions was investigated. It has been shown that for the tangential impedance boundary condition (TIBC), there always exists a unique Rayleigh wave, while for the normal impedance boundary condition (NIBC), there exists a domain (of impedance and material parameters) in which exactly one Rayleigh wave is possible and outside this domain a Rayleigh wave is impossible. In this paper, we consider the existence of Rayleigh waves with the full impedance boundary condition (FIBC) that contains both TIBC and NIBC. It is shown that the existence picture of Rayleigh waves for this general case is more complicated. It contains domain for which exactly one Rayleigh wave exists, domain where a Rayleigh wave is impossible, and domain for which all three possibilities may occur: two Rayleigh waves exist, one Rayleigh wave exists, and no Rayleigh wave exists at all. The obtained existence results recover the existence results established previously for the cases of TIBC and NIBC. The formulas for the Rayleigh wave velocity are derived. As these formulas are totally explicit, they are very useful in various practical applications, especially in the non-destructive evaluation of the mechanical properties of structures. In order to establish the existence results and derive formulas for the Rayleigh wave velocity, the complex function method, which is based on the Cauchy-type integrals, is employed.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"10 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201735","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":"A Moore-Gibson-Thompson heat conduction problem with second gradient","authors":"Noelia Bazarra, José R Fernández, Ramón Quintanilla","doi":"10.1177/10812865241266992","DOIUrl":"https://doi.org/10.1177/10812865241266992","url":null,"abstract":"In this work, we study, from both analytical and numerical points of view, a heat conduction model which is based on the Moore-Gibson-Thompson equation. The second gradient effects are also included. First, the existence of a unique solution is proved by using the theory of linear semigroups, and the exponential energy decay is also shown when the constitutive tensors are homogeneous. The analyticity of the semigroup is also discussed in the isotropic case, and its spatial behavior is studied. The spatial exponential decay is also proved. Then, we provide the numerical analysis of a fully discrete approximation obtained by using the finite element method and an implicit Euler scheme. A discrete stability property is shown, and some a priori error estimates are derived, from which the linear convergence is concluded under suitable regularity conditions. Finally, some one-dimensional numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the discrete energy.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"41 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201737","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":"Stochastic mesoscale mechanical modeling of metallic foams","authors":"Mujan N Seif, Jake Puppo, Metodi Zlatinov, Denver Schaffarzick, Alexandre Martin, Matthew J Beck","doi":"10.1177/10812865241265049","DOIUrl":"https://doi.org/10.1177/10812865241265049","url":null,"abstract":"Investigating the mechanical properties of complex, porous microstructures by assessing model representative volumes is an established method of determining materials properties across a range of length scales. An understanding of how behavior evolves with length scale is essential for evaluating the material’s suitability for certain applications where the interaction volume is so small that the mechanical response originates from individual features rather than a set of features. Here, we apply the Kentucky Random Structure Toolkit (KRaSTk) to metallic foams, which are crucial to many emerging applications, among them shielding against hypervelocity impacts caused by micrometeoroids and orbital debris (MMOD). The variability of properties at feature-scale and mesoscale lengths originating from the inherently random microstructure makes developing predictive models challenging. It also hinders the optimization of components fabricated with such foams, an especially serious problem for spacecraft design where the benefit–cost–mass optimization is overshadowed by the catastrophic results of component failure. To address this problem, we compute the critical transition between the feature-scale, where mechanical properties are determined by individual features, and the mesoscale, where behavior is determined by ensembles of features. At the mesoscale, we compute distributions of properties—with respect to both expectation value and standard variability—that are consistent and predictable. A universal transition is found to occur when the side length of a cubic sample volume is ~10× greater than the characteristic length. Comparing KRaSTk-computed converged stiffness distributions with experimental measurements of a commercial metallic foam found an excellent agreement for both expectation value and standard variability at all reduced densities. Lastly, we observe that the diameter of a representative MMOD strike is ~30× shorter than the feature-scale to mesoscale transition for the foam at any reduced density, strongly implying that individual features will determine response to hypervelocity impacts, rather than bulk, or even mesoscale, structure.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201756","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":"Analysis of a parabolic bilateral obstacle problem with non-monotone relations in the domain","authors":"Xilu Wang, Xiaoliang Cheng, Hailing Xuan","doi":"10.1177/10812865241261619","DOIUrl":"https://doi.org/10.1177/10812865241261619","url":null,"abstract":"In this paper, we consider a new parabolic bilateral obstacle model. Both upper and lower obstacles are elastic-rigid and assign a non-monotone reactive normal pressure with respect to the interpenetration. The weak form of the model is a parabolic variational–hemivariational inequality with non-monotone multivalued relations in the domain. We show the existence and uniqueness of the solution. Then, a fully discrete numerical method is introduced, with the approximations can be internal or external. We bound the error estimates and obtain the Céa type inequality. Using the linear finite elements, the optimal-order error estimates are derived. Finally, we report the numerical simulation results.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201755","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":"Size-dependent thermoelastic damping analysis of functionally graded polymer micro plate resonators reinforced with graphene nanoplatelets based on three-phase-lag heat conduction model","authors":"Wei Peng, Xu Zhang, Tianhu He, Yaru Gao, Yan Li","doi":"10.1177/10812865241263531","DOIUrl":"https://doi.org/10.1177/10812865241263531","url":null,"abstract":"Nanocomposite materials, such as graphene nanoplatelets (GPLs), have been fabricated into high-efficient resonators due to the excellent thermo-mechanical properties. In addition, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high-performance micro-/nano-resonators. Nevertheless, the classical TED models fail on the micro-/nano-scale due to not considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present work aims to investigate TED analysis of functionally graded (FG) polymer microplate resonators reinforced with GPLs based on the modified couple stress theory (MCST) and the three-phase-lag (TPL) heat conduction model. Four patterns of GPL distribution including the UD, FG-O, FG-X, and FG-A pattern distributions are taken into account, and the effective mechanical properties of the plate-type nanocomposite are evaluated based on the Halpin-Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length-scale parameter, the phase-lag parameters, and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This paper provides a theoretical approach to estimate TED in the design of high-performance micro-resonators.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"94 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945978","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":"Fractionalization of Forchheimer’s correction to Darcy’s law in porous media in large deformations","authors":"Sachin Gunda, Alessandro Giammarini, Ariel Ramírez-Torres, Sundararajan Natarajan, Olga Barrera, Alfio Grillo","doi":"10.1177/10812865241252577","DOIUrl":"https://doi.org/10.1177/10812865241252577","url":null,"abstract":"This work presents a theoretical and numerical study of the flow of the interstitial fluid saturating a porous medium, principally aimed at modeling a bio-mimetic material and assumed to experience a dynamic regime different from the Darcian one, as is typically hypothesized in biomechanical scenarios. The main aspect of our research is the conjecture according to which, for a particular mechanical state of the porous medium, the fluid exhibits two types of deviation from Darcy’s law. One is due to the inertial forces characterizing the pore scale dynamics of the fluid. This aspect can be resolved by turning to the Forchheimer correction to Darcy’s law, which introduces non-linearities in the relationship between the fluid filtration velocity and the dissipative forces describing the interactions between the fluid and the solid matrix. The second source of discrepancies from classical Darcy’s law emerges, for example, when pore scale disturbances to the flow, such as obstructions of the fluid path or clogging of the pores, result in a time delay between drag force and filtration velocity. Recently, models have been proposed in which such delay is described through constitutive laws featuring fractional operators. Whereas, to the best of our knowledge, the aforementioned behaviors have been studied separately or in small deformations, we present a model of fluid flow in a deformable porous medium undergoing large deformations in which the fluid motion obeys a fractionalized Forchheimer’s correction. After reviewing Forchheimer’s formulation, we present a fractionalization of the Darcy–Forchheimer law, and we explain the numerical procedure adopted to solve the highly non-linear boundary value problem resulting from the presence of the two considered deviations from the Darcian regime. We complete our study by highlighting the way in which the fractional order of the model tunes the magnitude of the pore pressure and fluid filtration velocity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"52 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945980","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":"A hidden convexity in continuum mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity","authors":"Amit Acharya","doi":"10.1177/10812865241258154","DOIUrl":"https://doi.org/10.1177/10812865241258154","url":null,"abstract":"A methodology for defining variational principles for a class of PDE (partial differential equations) models from continuum mechanics is demonstrated, and some of its features are explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single-crystal plasticity at finite deformation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"78 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873023","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}