Journal of Elasticity最新文献

Vertical Dynamic Analysis of Rigid Strip Foundation on Layered Unsaturated Media

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-29 DOI: 10.1007/s10659-024-10099-0

Zhi Yong Ai, Li Wei Shi, Lei Sheng

引用次数: 0

Energy Balance and Damage for Dynamic Fast Crack Growth from a Nonlocal Formulation 从非局部公式看动态快速裂纹生长的能量平衡与损伤

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-27 DOI: 10.1007/s10659-024-10098-1

Robert P. Lipton, Debdeep Bhattacharya

{"title":"Energy Balance and Damage for Dynamic Fast Crack Growth from a Nonlocal Formulation","authors":"Robert P. Lipton, Debdeep Bhattacharya","doi":"10.1007/s10659-024-10098-1","DOIUrl":"10.1007/s10659-024-10098-1","url":null,"abstract":"<div><p>A nonlocal model for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and uniqueness of the displacement-failure set pair follow from an initial value problem describing the evolution. The displacement-failure pair satisfies energy balance. The length of nonlocality <span>(epsilon )</span> is taken to be small relative to the domain in <span>(mathbb{R}^{d})</span>, <span>(d=2,3)</span>. The strain is formulated as a difference quotient of the displacement in the nonlocal model. The two point force is expressed in terms of a weighted difference quotient and delivers an evolution on a subset of <span>(mathbb{R}^{d}times mathbb{R}^{d})</span>. This evolution provides an energy balance between external energy, elastic energy, and damage energy including fracture energy. For any prescribed loading the deformation energy resulting in material failure over a region <span>(R)</span> is uniformly bounded as <span>(epsilon rightarrow 0)</span>. For fixed <span>(epsilon )</span>, the failure energy is discovered to be is nonzero for <span>(d-1)</span> dimensional regions <span>(R)</span> associated with flat crack surfaces. Calculation shows, this failure energy is the Griffith fracture energy given by the energy release rate multiplied by area for <span>(d=3)</span> (or length for <span>(d=2)</span>). The nonlocal field theory is shown to recover a solution of Naiver’s equation outside a propagating flat traction free crack in the limit of vanishing spatial nonlocality. The theory and simulations presented here corroborate the recent experimental findings of (Rozen-Levy et al. in Phys. Rev. Lett. 125(17):175501, 2020) that cracks follow the location of maximum energy dissipation inside the intact material. Simulations show fracture evolution through the generation of a traction free internal boundary seen as a wake left behind a moving strain concentration.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714648","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}

引用次数: 0

Torsion and Extension of Functionally Graded Mooney–Rivlin Cylinders 功能分级穆尼-里夫林圆柱体的扭转和延伸

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-21 DOI: 10.1007/s10659-024-10095-4

Kesna A. Fairclough, Romesh C. Batra

引用次数: 0

An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems 基于非整体系统分析力学的生长力学方法

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-18 DOI: 10.1007/s10659-024-10092-7

Alfio Grillo, Andrea Pastore, Salvatore Di Stefano

{"title":"An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems","authors":"Alfio Grillo, Andrea Pastore, Salvatore Di Stefano","doi":"10.1007/s10659-024-10092-7","DOIUrl":"10.1007/s10659-024-10092-7","url":null,"abstract":"<div><p>Motivated by the convenience, in some biomechanical problems, of interpreting the mass balance law of a growing medium as a nonholonomic constraint on the time rate of a structural descriptor known as growth tensor, we employ some results of analytical mechanics to show that such constraint can be studied variationally. Our purpose is to move a step forward in the formulation of a field theory of the mechanics of volumetric growth by defining a Lagrangian function that incorporates the nonholonomic constraint of the mass balance. The knowledge of such Lagrangian function permits, on the one hand, to deduce the dynamic equations of a growing medium as the result of a variational procedure known as Hamilton–Suslov Principle (clearly, up to non-potential generalized forces that are accounted for by extending this procedure), and, on the other hand, to study the symmetries and conservation laws that pertain to a given growth problem. While this second issue is not investigated in this work, we focus on the first one, and we show that the Euler–Lagrange equations of the considered growing medium, which describe both its motion and the evolution of the growth tensor, can be obtained by reformulating a variational method developed by other authors. We discuss the main features of this method in the context of growth mechanics, and we show how our procedure is able to improve them.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10092-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672724","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}

引用次数: 0

An Analytical Solution for the Periodically Spaced Two Collinear and Symmetric Cracks Under Remote Tension 远距离张力作用下周期性间隔的两平行对称裂缝的解析解

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-06 DOI: 10.1007/s10659-024-10093-6

Jiayao Hu, Fan Jin, Fan Xia, Jicheng Li

{"title":"An Analytical Solution for the Periodically Spaced Two Collinear and Symmetric Cracks Under Remote Tension","authors":"Jiayao Hu, Fan Jin, Fan Xia, Jicheng Li","doi":"10.1007/s10659-024-10093-6","DOIUrl":"10.1007/s10659-024-10093-6","url":null,"abstract":"<div><p>The present paper provides an analytical solution for a periodic array of two collinear and symmetric cracks (P-TCSC) under remote tension. This is achieved by representing the multiple collinear cracks problem as the contact problem with discrete ligament regions, and the governing equations are obtained as integral equations with Cauchy-type kernel. Closed-form expressions are derived for the crack opening profile, normal stress distribution and mode I stress intensity factors (SIFs), which can reduce to the classical solutions of two collinear and symmetric cracks (TCSC) or a periodic row of collinear cracks with equal length and equal spacing (PCEE) under special conditions. Finite element analysis is also performed to validate the analytical solutions obtained. Different from the TCSC case, results show that crack initiation for P-TCSC seems more complicated depending on a combination of two nondimensional parameters, and a SIFs map for P-TCSC is further constructed to give a more precise evaluation. The proposed method relies solely on solving the integral equations with Cauchy-type kernel combined with the corresponding boundary conditions without a prior knowledge of the complex potential function in traditional complex variable method of plane elasticity, and it may find application in plastic zone evaluation and fracture criteria of collinear cracks.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595324","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}

引用次数: 0

Universal Displacements in Anisotropic Linear Cauchy Elasticity 各向异性线性考氏弹性中的普遍位移

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-11-06 DOI: 10.1007/s10659-024-10094-5

Arash Yavari, Dimitris Sfyris

引用次数: 0

Axisymmetric Indentation of Circular Rigid Plate on Layered Elastic Halfspace with Transverse Isotropy 具有横向各向同性的层状弹性半空间上的圆形刚性板轴对称压痕

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-10-09 DOI: 10.1007/s10659-024-10090-9

Sha Xiao, Zhongqi Quentin Yue

{"title":"Axisymmetric Indentation of Circular Rigid Plate on Layered Elastic Halfspace with Transverse Isotropy","authors":"Sha Xiao, Zhongqi Quentin Yue","doi":"10.1007/s10659-024-10090-9","DOIUrl":"10.1007/s10659-024-10090-9","url":null,"abstract":"<div><p>This paper investigates the contact problem of a layered elastic halfspace with transverse isotropy under the axisymmetric indentation of a circular rigid plate. Fourier integral transforms and a backward transfer matrix method are used to obtain the analytical solution of the contact problem. The interaction between the rigid plate and the layered halfspace can be expressed with the standard Fredholm integral equations of the second kind. The induced elastic field in the layered halfspace can be expressed as the semi-infinite integrals of four known kernel functions. The convergence and singularity of the semi-infinite integrals near or at the surface of the layered halfspace are resolved using an isolating technique. The efficient numerical algorithms are used and developed for accurately calculating the Fredholm integral equations and the semi-infinite integrals. Numerical results show the correctness of the proposed method and the effect of layering non-homogeneity on the elastic fields in layered transversely isotropic halfspace induced by the axisymmetric indentation of a circular rigid plate.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 4-5","pages":"1145 - 1169"},"PeriodicalIF":1.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10090-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447410","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}

引用次数: 0

Self-Oscillations of Submerged Liquid Crystal Elastomer Beams Driven by Light and Self-Shadowing 由光和自阴影驱动的浸没液晶弹性体光束的自振荡

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-10-09 DOI: 10.1007/s10659-024-10091-8

Reza Norouzikudiani, Luciano Teresi, Antonio DeSimone

{"title":"Self-Oscillations of Submerged Liquid Crystal Elastomer Beams Driven by Light and Self-Shadowing","authors":"Reza Norouzikudiani, Luciano Teresi, Antonio DeSimone","doi":"10.1007/s10659-024-10091-8","DOIUrl":"10.1007/s10659-024-10091-8","url":null,"abstract":"<div><p>Liquid Crystal Elastomers (LCEs) are responsive materials that undergo significant, reversible deformations when exposed to external stimuli such as light, heat, and humidity. Light actuation, in particular, offers versatile control over LCE properties, enabling complex deformations. A notable phenomenon in LCEs is self-oscillation under constant illumination. Understanding the physics underlying this dynamic response, and especially the role of interactions with a surrounding fluid medium, is still crucial for optimizing the performance of LCEs. In this study, we have developed a multi-physics fluid-structure interaction model to explore the self-oscillation phenomenon of immersed LCE beams exposed to light. We consider a beam clamped at one end, originally vertical, and exposed to horizontal light rays of constant intensity focused near the fixed edge. Illumination causes the beam to bend towards the light due to a temperature gradient. As the free end of the beam surpasses the horizontal line through the clamp, self-shadowing induces cooling, initiating the self-oscillation phenomenon. The negative feedback resulting from self-shadowing injects energy into the system, with sustained self-oscillations in spite of the energy dissipation in the surrounding fluid. Our investigation involves parametric studies exploring the impact of beam length and light intensity on the amplitude, frequency, and mode of oscillation. Our findings indicate that the self-oscillation initiates above a certain critical light intensity, which is length-dependent. Also, shorter lengths induce oscillations in the beam with the first mode of vibration, while increasing the length changes the elasticity property of the beam and triggers the second mode. Additionally, applying higher light intensity may trigger composite complex modes, while the frequency of oscillation increases with the intensity of the light if the mode of oscillation remains constant.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 4-5","pages":"1243 - 1260"},"PeriodicalIF":1.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10091-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447409","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}

引用次数: 0

Residual Stress Concentration Due to Nano-Scaled Particulate Contamination at Direct Bonding Interface with Localized Material Inhomogeneity 局部材料不均匀性直接粘合界面上的纳米级微粒污染导致的残余应力集中

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-09-30 DOI: 10.1007/s10659-024-10089-2

X. W. Chen, Wendal Victor Yue

{"title":"Residual Stress Concentration Due to Nano-Scaled Particulate Contamination at Direct Bonding Interface with Localized Material Inhomogeneity","authors":"X. W. Chen, Wendal Victor Yue","doi":"10.1007/s10659-024-10089-2","DOIUrl":"10.1007/s10659-024-10089-2","url":null,"abstract":"<div><p>Direct bonding is an attractive technique to join material components without the use of intermediate adhesive medium. Usually, the bonding interface can experience high level of residual stress concentration due to entrapped nano-scale particulate contamination. Existing theoretical models are not capable of analyzing such residual stress concentration, since they fail to consider the localized material inhomogeneity formed between the bonding pairs as result of thermal and diffusion processes. This paper proposes a new theoretical model to analyze the residual stress concentration in the bonding interface with the consideration of localized material inhomogeneity. Following the idea of Selvadurai and Singh (Int. J. Fract. 25:69–77, 1984), the nano-scaled particulate contamination induced interfacial defect is simulated as a penny-shaped crack indented by a smooth rigid disc inclusion. This mode I crack-inclusion model is interpreted as a three-part mixed boundary value problem in the theory of elasticity, which is solved by a series expansion technique. Mathematical difficulties associated with modelling arbitrary localized material inhomogeneity are overcome by the use of the General Kelvin Solution (GKS) based method. Exact analytical solutions for the stress intensity factors (SIFs) and resultant force on the inclusion are obtained. Our results show that the inclusion-crack radius ratio and the localized material inhomogeneity can have significance effect on the residual stress concentration at the bonding interface.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 4-5","pages":"1121 - 1144"},"PeriodicalIF":1.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447334","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}

引用次数: 0

De-Hydration and Remodeling of Biological Materials: Swelling Theory for Multi-Domain Bodies 生物材料的脱水和重塑：多域体的膨胀理论

IF 1.8 3区工程技术

Journal of Elasticity Pub Date : 2024-09-25 DOI: 10.1007/s10659-024-10088-3

Michele Curatolo, R. G. M. van der Sman, Luciano Teresi

{"title":"De-Hydration and Remodeling of Biological Materials: Swelling Theory for Multi-Domain Bodies","authors":"Michele Curatolo, R. G. M. van der Sman, Luciano Teresi","doi":"10.1007/s10659-024-10088-3","DOIUrl":"10.1007/s10659-024-10088-3","url":null,"abstract":"<div><p>Biological materials always exhibit heterogeneous physical properties, both mechanical and chemical, which give them a rich phenomenology that poses significant challenges in the developing of effective models. The Flory–Rehner theory revolutionized our understanding of the dynamics of the liquid-polymers coupling in soft swollen gels, recognizing polymers as elastic networks stretched by the presence of liquid. Despite its foundational role, applying this theory to bodies with non uniform physical properties requires further improvements. This article proposes a unified approach to address mechano-diffusion challenges in multi-domain bodies, that is in material bodies made of regions having different chemo-mechanical properties, and focuses on the dehydration and remodeling of biological-like materials. Drawing inspiration from natural systems, we integrate principles from nonlinear mechanics and swelling theories; in particular, what is specifically new is the idea of applying the notion of the multiplicative decomposition of the strain–developed for plasticity–to model the swelling properties of a body made of two or more materials. The article gives a systematic presentation of the subject, and guides readers through key concepts and practical insights, aiming to provide a robust framework for modeling chemo-mechanical interactions. Moreover, it paves the way for the modeling of heterogenous bodies having spatially-varying properties.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 4-5","pages":"1195 - 1241"},"PeriodicalIF":1.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10088-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447405","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}

引用次数: 0