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Fast Fourier transform method in peridynamic micromechanics of composites 复合材料周动态微观力学中的快速傅立叶变换方法
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-04-17 DOI: 10.1177/10812865241236878
Valeriy A Buryachenko
{"title":"Fast Fourier transform method in peridynamic micromechanics of composites","authors":"Valeriy A Buryachenko","doi":"10.1177/10812865241236878","DOIUrl":"https://doi.org/10.1177/10812865241236878","url":null,"abstract":"We consider a static linear bond–based peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175–209) composite materials (CMs) of a periodic structure. In the framework of the second background of micromechanics (also called computational analytical micromechanics), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally analogous to each other for CM of both random and periodic structures. It allows a straightforward generalization of LM methods (including fast Fourier transform, FFT) to their PM counterparts. So, in the PM counterpart of the implicit periodic Lippmann–Schwinger (L-S) equation in LM, we have three convolution kernels corresponding to the properties of the matrix, inclusions, and interactive interface. Eshelby tensor in LM, depending on the inclusion shape, is replaced by PM counterparts depending on the shapes of inclusions, and the interaction interface (although the Eshelby concept of homogeneous eigenfields does not work in PM). The mentioned tensors are estimated once (as in LM) in a frequency domain (also by the FFT method). The possible incorrectness of FFT applications to PM is analyzed and corrected. The polarization schemes of the solution of the L-S equation in the Fourier space have one primary unknown variable (polarization), whereas the PM counterpart contains three primary ones estimated at each step, which are formally similar to the LM case. A description of the generalized basic scheme and the Krylov approach is presented. Computational complexities O(N log2 N) of the FFT methods are the same in both LM and PM.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"29 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614024","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}
引用次数: 0
Anti-plane waves in a liquid-loaded piezo-flexo-electric layered model with interface energy 具有界面能量的液体负载压电柔电层状模型中的反面波
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-04-15 DOI: 10.1177/10812865241239600
Sonam Singh, Abhishek K Singh
{"title":"Anti-plane waves in a liquid-loaded piezo-flexo-electric layered model with interface energy","authors":"Sonam Singh, Abhishek K Singh","doi":"10.1177/10812865241239600","DOIUrl":"https://doi.org/10.1177/10812865241239600","url":null,"abstract":"The basic design of a Love wave (LW) bio-sensor contains the loading of a viscoelastic liquid on top of a layered structure with distinct viscoelastic properties. Changes in the characteristics of the propagating acoustic wave caused by biochemical interactions at the sensing area can be detected at the output Inter digital transducer (IDT). The propagation of the anti-plane (AP) wave is discussed in this work in a layered structure of piezo-flexo-electric (PFE) layer bonded with a PFE half-space having a soft reinforced layer at the interface. The free surface of the PFE layer is loaded with viscous liquid. The viscosity of the loaded liquid introduces losses and results in the damping of the wave. For the formulation of the problem with interface energy, the Gurtin–Murdoch approach is used. Using suitable conditions, a dispersion relation for propagating waves is derived in complex form. On separating the dispersion relation in real and non-real parts, the expressions relating the phase and damp velocities with wave number are derived. The obtained theoretical results are portrayed for the numerical data of PFE materials and distinct data of the interface layer. The obtained results are validated with pre-existing literature.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"144 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574054","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}
引用次数: 0
A hemivariational damageable elastoplastic vertex-spring model for masonry analysis 用于砌体分析的半变量可破坏弹塑性顶点弹簧模型
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-16 DOI: 10.1177/10812865241233008
Chuong Anthony Tran, Francisco James Leòn Trujillo, Antonello Salvatori, Margherita Solci, Andrea Causin, Luca Placidi, Emilio Barchiesi
{"title":"A hemivariational damageable elastoplastic vertex-spring model for masonry analysis","authors":"Chuong Anthony Tran, Francisco James Leòn Trujillo, Antonello Salvatori, Margherita Solci, Andrea Causin, Luca Placidi, Emilio Barchiesi","doi":"10.1177/10812865241233008","DOIUrl":"https://doi.org/10.1177/10812865241233008","url":null,"abstract":"This work is an intermediate step towards the extension of a recently proposed block-based model for masonry structures, which was based on a hemivariational approach and inspired from granular micromechanics. Here, contrarily to the previous model, plastic effects will also be taken into account along with damage and elastic behaviours, and the full hemivariational derivation of the strong-form (in)equations will be detailed for the case of a lone vertex spring. The resulting model and methods shall then be used in future works to enrich the behaviours modelled by the previously mentioned masonry model.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150428","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}
引用次数: 0
An energy-balanced method for determining the optimized parameter of the incompatible generalized mixed element 确定不相容广义混合元素优化参数的能量平衡法
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-14 DOI: 10.1177/10812865241233997
Yonggang Wang, Guanghui Qing
{"title":"An energy-balanced method for determining the optimized parameter of the incompatible generalized mixed element","authors":"Yonggang Wang, Guanghui Qing","doi":"10.1177/10812865241233997","DOIUrl":"https://doi.org/10.1177/10812865241233997","url":null,"abstract":"A novel method for determining the optimized parameter of the four-node incompatible generalized mixed element is presented based on the equilibrium between strain energy and complementary energy. The presented energy formulations are derived from the generalized mixed variational principle, which contains an arbitrary additional parameter. The initial solutions expressed by the displacement field are firstly assumed for the description of the energy of each generalized mixed element. Then, the identical relationship between strain energy and complementary energy is subsequently expressed at element level, which includes the arbitrary parameter. At the same time, a formulation for determining the optimized parameter at element level is proposed. Several representative examples with varying geometrical parameters, boundary and loading conditions are used to validate this method. By contrasting with the results of generalized mixed elements with different parameter values and other traditional finite elements. The effectiveness of the presented method has been demonstrated. On one hand, by ensuring the strain energy and complementary energy remain consistent under both coarse and fine meshes, the optimized parameter can adjust the stiffness of the generalized mixed element, thereby enhancing its resemblance to the real elastic body. On the other hand, the generalized mixed element has the additional advantage of conveniently introducing stress boundary conditions, thereby satisfying the requirement for zero-conditions of shear stresses on the exterior surfaces of beams. The numerical results obtained by the proposed method are accurate and stable.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150432","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}
引用次数: 0
Models of fractional viscous stresses for incompressible materials 不可压缩材料的分数粘性应力模型
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-13 DOI: 10.1177/10812865241233973
Harold Berjamin, Michel Destrade
{"title":"Models of fractional viscous stresses for incompressible materials","authors":"Harold Berjamin, Michel Destrade","doi":"10.1177/10812865241233973","DOIUrl":"https://doi.org/10.1177/10812865241233973","url":null,"abstract":"We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We also briefly introduce Prony-type approximations of these theories. Here, we investigate the issues of material frame-indifference and thermodynamic consistency for these models and find that on these bases, some are physically unacceptable. Next, we study elementary shearing and tensile motions, observing that some models are more convenient to use than others for the analysis of creep and relaxation. Finally, we compute the incremental stresses due to small-amplitude wave propagation in a deformed material, with a view to establish acoustoelastic formulas for prospective experimental calibrations.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"10 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125452","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}
引用次数: 0
Analysis of planar arbitrarily curved microbeams with simplified strain gradient theory and Timoshenko–Ehrenfest beam model 用简化应变梯度理论和 Timoshenko-Ehrenfest 梁模型分析平面任意弯曲微梁
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-13 DOI: 10.1177/10812865241232463
Duy Vo, Zwe Yan Aung, Toan Minh Le, Pana Suttakul, Elena Atroshchenko, Jaroon Rungamornrat
{"title":"Analysis of planar arbitrarily curved microbeams with simplified strain gradient theory and Timoshenko–Ehrenfest beam model","authors":"Duy Vo, Zwe Yan Aung, Toan Minh Le, Pana Suttakul, Elena Atroshchenko, Jaroon Rungamornrat","doi":"10.1177/10812865241232463","DOIUrl":"https://doi.org/10.1177/10812865241232463","url":null,"abstract":"As the first endeavor in the context of Mindlin’s strain gradient theory, this study contributes a systematic and rigorous derivation for governing equations and boundary conditions of planar arbitrarily curved microbeams. The Timoshenko–Ehrenfest beam model is incorporated into a simplified version of Mindlin’s strain gradient theory. Kinematic unknowns include displacement components of the beam axis in the local coordinate system and the rotation of cross-section. Since the derived governing equations and boundary conditions are extremely complex, analytical solutions are not achievable for microbeams having non-uniform curvature. To facilitate the numerical analysis, two isogeometric collocation formulations are proposed, that is, displacement-based and mixed formulations. Several tests are designed to evaluate the accuracy and reliability of the proposed isogeometric collocation formulations, especially with respect to the well-known locking pathology. It is found that the mixed formulation is more accurate and robust than the displacement-based one. Therefore, the mixed formulation is then used to numerically investigate the size-dependent behavior and stiffening effect. Furthermore, some informative tests are performed to delineate the significance of the curviness in the prediction of structural responses of planar arbitrarily curved microbeams, which appears to be still an unanswered issue.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"15 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125540","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}
引用次数: 0
Newtonian laws of motion and conservation principles 牛顿运动定律和守恒原理
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-12 DOI: 10.1177/10812865241227972
James M Hill
{"title":"Newtonian laws of motion and conservation principles","authors":"James M Hill","doi":"10.1177/10812865241227972","DOIUrl":"https://doi.org/10.1177/10812865241227972","url":null,"abstract":"Newton’s laws of motion and Newtonian conservation principles such as those for energy and momentum involve the assumption that the vanishing of a certain total time derivative, on integration, yields a fixed constant value as an immediate consequence. While this may ultimately be the case for additional reasons, it is possible to have a properly vanishing total time derivative and yet the individual partial derivates are non-zero. Here, for a particular problem and based only on the requirement that the total time derivative of the quantity vanishes, we investigate the particular mechanism leading to a conventional conservation principle. For the energy and angular momentum totals for planar steady orbiting motion, the partial differential conditions may be formally solved to obtain the general solutions. We determine the general structure for variable energy and angular momentum for which the total time derivatives vanish, and from which it is apparent that the standard expression for constant energy and angular momentum is recovered.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125510","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}
引用次数: 0
Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material 热弹性材料中下环状裂纹的应力强度因子和全场应力
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-12 DOI: 10.1177/10812865241230274
Yi-Lun Liao, Chien-Ching Ma, Ching-Kong Chao
{"title":"Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material","authors":"Yi-Lun Liao, Chien-Ching Ma, Ching-Kong Chao","doi":"10.1177/10812865241230274","DOIUrl":"https://doi.org/10.1177/10812865241230274","url":null,"abstract":"This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"83 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125547","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}
引用次数: 0
A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell 重访弹性圆柱壳低频声散射的平面问题
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-11 DOI: 10.1177/10812865241233737
Hazel Yücel, Nihal Ege, Barış Erbaş, Julius Kaplunov
{"title":"A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell","authors":"Hazel Yücel, Nihal Ege, Barış Erbaş, Julius Kaplunov","doi":"10.1177/10812865241233737","DOIUrl":"https://doi.org/10.1177/10812865241233737","url":null,"abstract":"The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this case, numerical implementations would greatly benefit from preliminary asymptotic predictions. The normal incidence of an acoustic wave is studied for a circular cylindrical shell governed by plane strain equations in elasticity. A novel high-order asymptotic procedure is established considering for the first time all the peculiarities of the low-frequency behavior of a thin fluid-loaded cylinder. The obtained results are exposed in the form suggested by the Resonance Scattering Theory. It is shown that the pressure scattered by rigid cylinder is the best choice for a background component. Simple explicit formulae for resonant frequencies, amplitudes, and widths are presented. They support various important observations, including comparison between widths and the error of the asymptotic expansion for frequencies.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"73 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106286","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}
引用次数: 0
In-plane surface waves propagating in a coated half-space based on the strain-gradient elasticity theory 基于应变梯度弹性理论的平面内表面波在涂层半空间中传播
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2024-03-11 DOI: 10.1177/10812865241235117
Bowen Zhao, Jianmin Long
{"title":"In-plane surface waves propagating in a coated half-space based on the strain-gradient elasticity theory","authors":"Bowen Zhao, Jianmin Long","doi":"10.1177/10812865241235117","DOIUrl":"https://doi.org/10.1177/10812865241235117","url":null,"abstract":"By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"31 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106139","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}
引用次数: 0
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