Mathematics and Mechanics of Solids最新文献_第5页

Flexural–torsional buckling with enforced axis of twist and related problems 具有强制扭转轴的挠曲扭转屈曲及相关问题

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-10 DOI: 10.1177/10812865241239647

Ciprian D Coman, Andrew P Bassom

{"title":"Flexural–torsional buckling with enforced axis of twist and related problems","authors":"Ciprian D Coman, Andrew P Bassom","doi":"10.1177/10812865241239647","DOIUrl":"https://doi.org/10.1177/10812865241239647","url":null,"abstract":"The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, [Formula: see text] (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as [Formula: see text], the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940555","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}

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Initiation of decohesion between a flat punch and a thin bonded incompressible layer 平冲头与不可压缩的薄粘合层之间的解粘性启动

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-07 DOI: 10.1177/10812865241240484

Ivan I Argatov, Gennady S Mishuris, Valentin L Popov

引用次数: 0

Stability of arches with internal hinge 带内铰链拱门的稳定性

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-06 DOI: 10.1177/10812865241245338

László Péter Kiss

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A note on the Hill–Ogden generalised strains 关于希尔-奥格登广义应变的说明

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-04 DOI: 10.1177/10812865241233675

Salvatore Federico

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A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations 受力构型中圆柱变形的混合触发体积增长定律

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-02 DOI: 10.1177/10812865241242998

Xin Zhuan, Debao Guan, Hao Gao, Peter Theobald, Xiaoyu Luo

{"title":"A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations","authors":"Xin Zhuan, Debao Guan, Hao Gao, Peter Theobald, Xiaoyu Luo","doi":"10.1177/10812865241242998","DOIUrl":"https://doi.org/10.1177/10812865241242998","url":null,"abstract":"Soft tissue growth is crucial across various physiological applications, with mathematical modelling playing a pivotal role in understanding the underlying processes. The volumetric growth theory serves as a commonly used mathematical framework in this context. Our previous research on volumetric growth theory primarily concentrated on defining the incremental growth tensor in loaded and stressed configurations, revealing that this approach closely aligns with experimental observations of residual hoop stress distribution. However, given the assumptions employed, the approach has limitations in accurately predicting the growth timeline. In this work, we address these issues by incorporating the effect of initial residual strain and introducing a new mixed trigger growth evolution law. In this growth law, we do not use growth saturation as an upper limit, as this assumption cannot represent many physiological conditions. Instead, we propose that growth in soft tissues leads to a new equilibrium state. To illustrate this idea, we introduce a growth incompatibility function, denoted as [Formula: see text]. We establish the analytical relationship between [Formula: see text] and the opening angle in a simplified cylindrical geometry resembling the structure of the heart or arteries. We put forth a revised growth law that is both stress and incompatibility driven/Our results show that by using this mixed trigger growth law, tissues will not grow indefinitely. Instead, a stress-driven homeostasis incompatibility state will be reached. In addition, by accounting for the initial opening angle in the model, we can accurately trace the growth history of the heart, aligning with experimental data obtained from measuring the opening angle in young pigs from birth to maturity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"64 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838531","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

Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials 连接各向同性超弹性材料的弱非线性弹性理论

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-04-27 DOI: 10.1177/10812865241238985

Yangkun Du, Nicholas A Hill, Xiaoyu Luo

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Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch 轴向拉伸下残余应力圆柱体局部不稳定性的简化模型和非线性分析

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-04-26 DOI: 10.1177/10812865241242432

Yang Liu, Xiang Yu, Luis Dorfmann

{"title":"Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch","authors":"Yang Liu, Xiang Yu, Luis Dorfmann","doi":"10.1177/10812865241242432","DOIUrl":"https://doi.org/10.1177/10812865241242432","url":null,"abstract":"In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801136","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

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

引用次数: 0