{"title":"A homogenization method incorporating surface effect for thin metamaterial structure","authors":"Shuo Li, Li Li","doi":"10.1016/j.ijengsci.2024.104093","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104093","url":null,"abstract":"<div><p>Strong surface elasticity has been only found in nanoscale materials due to their large surface-to-volume ratio. In this paper, at the macroscale, the strong surface elasticity is revealed in thin metamaterial structures. Moreover, the metamaterial structures filled with complex microstructures often need computationally prohibitive resources if the fully-resolved microstructures are modeled using high-fidelity approaches. Based on the revealed surface elasticity, a surface-based efficient yet accurate homogenization method is developed for thin metamaterial structures. This study explores the role that microstructure plays in determining the macroscopic properties of a metamaterial continuum and reveals the occurrence of the size-dependent surface effect that is strictly related to the microstructure configuration. The contribution of surface elasticity to the mechanical properties of thin metamaterial structures cannot be neglected, particularly when the size of microstructures is comparable to their thickness. The coupling effect of intrinsic length determined by microstructure and extrinsic length (the thickness) on surface elasticity is investigated using the homogenization method. The intrinsic length can be calibrated by the size-dependent effective elasticity tensor. The strength of surface elasticity is determined by the intrinsic length with a specific thickness. The contribution of surface elasticity to the effective elasticity tensor can be determined by the difference between intrinsic length and extrinsic length. Finally, a simple yet representative metamaterial truss under tension is used to illustrate the application of the homogenization method. Our findings not only provide mechanical insights into metamaterial structures but also offer a surface-based computational method for metamaterial structures filled with complex microstructures.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"201 ","pages":"Article 104093"},"PeriodicalIF":6.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141068773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mahdi Zeidi , Suprabha Islam , Chul B. Park , Chun Il Kim
{"title":"A pseudoelastic response of hyperelastic composites reinforced with nonlinear elastic fibrous materials: Continuum modeling and analysis","authors":"Mahdi Zeidi , Suprabha Islam , Chul B. Park , Chun Il Kim","doi":"10.1016/j.ijengsci.2024.104092","DOIUrl":"10.1016/j.ijengsci.2024.104092","url":null,"abstract":"<div><p>The present study aims to develop a continuum-based model to predict the pseudoelastic behavior of biological composites subjected to finite plane elastostatics. The proposed model incorporates a hyperelastic matrix material reinforced with nonlinear fibers, addressing challenges such as irreversible softening responses, large deformations, and nonlinear stress–strain responses. The kinematics of reinforcing fibers are formulated via the first and second gradient of continuum deformations and, more importantly, damage function and damage variables of Ogden–Roxburgh and Weibull type are integrated into the model to assimilate the various aspects of damage mechanisms present in soft tissues. Adopting the framework of variational principles and a virtual work statement, the Euler equation and admissible boundary conditions are obtained. The proposed model successfully predicts the Mullins effect observed in the human aorta and the Manduca muscle. Experimental validation with elastomeric composites demonstrates its utility to replicate softening and fiber damage phenomena, including deformation profiles. Further, the proposed molecular dynamics scheme offers an enhanced understanding of polymer chain entanglement processes, thereby facilitating the quantification of permanent damage in elastomeric composites. The obtained results may provide valuable insight toward understanding and modeling the mechanical behavior of soft biological tissues with practical implications for the design and analysis of biofabricated composites aimed at mimicking biological tissues.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"201 ","pages":"Article 104092"},"PeriodicalIF":6.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020722524000764/pdfft?md5=1a3531b5f2ac696ea40059889a47c1d0&pid=1-s2.0-S0020722524000764-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141064231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Representing implicit elasticity from a residually stressed reference","authors":"Soumya Mukherjee","doi":"10.1016/j.ijengsci.2024.104079","DOIUrl":"10.1016/j.ijengsci.2024.104079","url":null,"abstract":"<div><p>Implicit elasticity presents the general response of materials without imposing assumptions at the fundamental level. A popular implausible assumption of continuum mechanics is that the reference configuration is stress-free, since residual stress is ubiquitous in Nature. This paper develops large and small deformation implicit elasticity frameworks using residually stressed reference configurations. The general forms of constitutive relations, in finite deformations, are obtained by <em>pull-back</em> or <em>push-forward</em> of all the associated tensors to the same (Eulerian or Lagrangian) configuration. These general forms are used to study the relationship between “residual stress and material symmetry” for implicit elasticity. Further, we use a <em>virtual</em> stress-free body, which is implicit elastic, to exactly determine the response of an initially stressed reference configuration. A number of such exact implicit relations are presented for residually stressed reference configurations, which are further simplified through interesting tensor analysis. The simplified implicit relations directly evaluates strain from a given Cauchy stress and residual stress tensor. One of these constitutive relations are employed for investigating the finite inflation of a residually-stressed, thick sphere. Finally, a small deformation implicit theory is attained by linearizing the developed relations for small strain and small rotation. To represent the small <em>strain</em> from a stressed reference, we need to invert a fourth order tensor. The closed-form inverse is determined in a new approach presented in the paper.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"201 ","pages":"Article 104079"},"PeriodicalIF":6.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141064232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adhesive sliding with a nominal point contact: Postpredictive analysis","authors":"I.I. Argatov , I.A. Lyashenko , V.L. Popov","doi":"10.1016/j.ijengsci.2024.104055","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104055","url":null,"abstract":"<div><p>Quasi-static sliding contact of an axisymmetric convex rigid solid with an adhesive incompressible polymer layer bonded to a rigid base is considered. As generalizations of the state-of-the-art theories of interplay between adhesion and friction, the JKR (Johnson–Kendall–Roberts)-type so-called peeling and sliding models are developed and applied for analyzing a set of experimental data for spherical indenters of various radii, which is available in the literature. A special focus is placed on the acquisition of the model parameters from experimental data in the case of a nominal point contact. The postpredictive analysis of the obtained scaled results indicates the existence of a three-stage adhesive attachment-stick/peeling/sliding periodic instability.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"200 ","pages":"Article 104055"},"PeriodicalIF":6.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020722524000399/pdfft?md5=1dbade3462b5f0ae0f480373f12a710f&pid=1-s2.0-S0020722524000399-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"On a class of implicit constitutive relations for nonlinear elastic bodies","authors":"M.H.B.M. Shariff , R. Bustamante","doi":"10.1016/j.ijengsci.2024.104089","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104089","url":null,"abstract":"<div><p>If an elastic body is defined as one that does not dissipate energy into heat, the classes of elastic bodies not only include the Green elastic solid, but also some types of implicit constitutive relations recently presented in the literature. In this paper one of such new implicit relations is studied in detail, wherein the energy function depend on the second Piola–Kirchhoff stress tensor and the Green Saint-Venant strain tensor. It is assumed that the function is anisotropic having two directions of anisotropy, thus the case of a transversely isotropic body and an isotropic body are special cases of the above function. Spectral invariants are used and explicit expressions for some second derivatives of the energy function are found. Such second derivatives appear in the implicit constitutive relation.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"200 ","pages":"Article 104089"},"PeriodicalIF":6.6,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140914535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Does the conventional reciprocal theorem break down in strain gradient elasticity?","authors":"Xiao-Jian Xu , Zi-Chen Deng","doi":"10.1016/j.ijengsci.2024.104076","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104076","url":null,"abstract":"<div><p>The force method and displacement method on the basis of the reciprocal theorem play an important role in the field of structural mechanics and have been successfully applied in structural mechanics. However, it is interestingly found that the unexpected paradox exists when the authors attempt to apply it to problems of deformations of strain gradient beams. The reciprocal relation between higher order stresses and higher order strains within the framework of linear elastic strain gradient elasticity is proposed with a view toward studying the physical nature of this paradoxical phenomenon, and it is then used to prove the updated reciprocal theorem. At the same time, the reciprocal theorem of any gradients of any second-order symmetric stress tensors and their corresponding gradients of displacements are derived according to the proposed reciprocal relation. The results show that the essential reason for the failure of the conventional reciprocal theorem is that the effect of higher order surface forces and surface stresses that are produced by strain gradients contributes to the reciprocal work. When the strain gradients work-conjugating to stress gradients are considered, they satisfy the local reciprocal relation that cannot be degenerated to the conventional reciprocal theorem in the form of body forces and inertial forces. The theory developed in this paper may have an increasingly profound effect on continuum mechanics and is expected to be a helpful tool for the mechanics of cellular structures homogenized by strain gradient elasticity.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"200 ","pages":"Article 104076"},"PeriodicalIF":6.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Radially transverse isotropic inclusions in isotropic elastic media: Local fields, neutral inclusions, effective elastic properties","authors":"S. Kanaun","doi":"10.1016/j.ijengsci.2024.104078","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104078","url":null,"abstract":"<div><p>Radially transverse isotropic inclusions in homogeneous isotropic elastic host media are considered. Mellin transform method is used for solution of the volume integral equation of the problem for an isolated inclusion subjected to a constant external stress (strain) field. The tensor structure of the solution is revealed with precision to three scalar functions of the radial coordinate, and the system of ordinary differential equations for these functions is derived. For multilayered radially transverse isotropic inclusions with constant elastic coefficients inside layers, explicit solution of these equations is obtained. An efficient numerical algorithm of solution for inclusions with an arbitrary number of the layers is proposed. Neutral inclusions that do not disturb homogeneous external fields applied to the medium are considered. It is shown that an inclusion with an isotropic core and radially transverse isotropic external layer can be weak neutral by appropriate choice of the layer elastic constants. The effective field method is used for determination of the effective elastic stiffness tensor of a homogeneous isotropic medium containing a random set of radially transverse isotropic inclusions.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"200 ","pages":"Article 104078"},"PeriodicalIF":6.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sayed Mohamad Mirfatah , Mohammad Amin Shahmohammadi , Hamzeh Salehipour , Ömer Civalek
{"title":"On nonlinear buckling of microshells","authors":"Sayed Mohamad Mirfatah , Mohammad Amin Shahmohammadi , Hamzeh Salehipour , Ömer Civalek","doi":"10.1016/j.ijengsci.2024.104077","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104077","url":null,"abstract":"<div><p>Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"199 ","pages":"Article 104077"},"PeriodicalIF":6.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140645783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Morphological stability of electrostrictive thin films","authors":"Jin Zhang, Peter W. Voorhees","doi":"10.1016/j.ijengsci.2024.104073","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104073","url":null,"abstract":"<div><p>A large electric field is typically present in anodic or passive oxide films. Stresses induced by such a large electric field are critical in understanding the breakdown mechanism of thin oxide films and improving their corrosion resistance. In this work, we consider electromechanical coupling through the electrostrictive effect. A continuum model incorporating lattice misfit and electric field-induced stresses is developed. We perform a linear stability analysis of the full coupled model and show that, for typical oxides, neglecting electrostriction underestimates the film’s instability, especially in systems with a large electric field. Moreover, a region where electrostriction can potentially provide a stabilizing effect is identified, allowing electrostriction to enhance corrosion resistance. We identified an equilibrium electric field intrinsic to the system and the corresponding equilibrium film thickness. The film’s stability is very sensitive to the electric field: a 40 percent deviation from the equilibrium electric field can change the maximum growth rate by nearly an order of magnitude. Moreover, our model reduces to classical morphological instability models in the limit of misfit-only, electrostatic-only, and no-electrostriction cases. Finally, the effect of various parameters on the film’s stability is studied.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"199 ","pages":"Article 104073"},"PeriodicalIF":6.6,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140639283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Viscoplastic flows in channels with small aspect ratio: Bingham versus regularised models","authors":"A. Farina , L. Fusi , L. Vergori , E.M. Zanetti","doi":"10.1016/j.ijengsci.2024.104074","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2024.104074","url":null,"abstract":"<div><p>We investigate the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. To characterise the mechanical response of the viscoplastic fluid we consider both the celebrated Bingham model and a very general class of its regularisations. In order to make the problem amenable to analysis, we assume that the aspect ratio of the channel is small so that the lubrication approximation can be used. This allows us to obtain analytical solutions, perform an asymptotic analysis of the regularised solutions and compare the results predicted by the Bingham model and its regularisations. We find that in the limit as the regularisation parameter tends to zero, the regularised flow tends to those predicted by the Bingham model only in plane channels. In channels with curved walls, the results are instead markedly different.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"199 ","pages":"Article 104074"},"PeriodicalIF":6.6,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020722524000582/pdfft?md5=c6d662d9fd28923a3fcdd6278f00dca5&pid=1-s2.0-S0020722524000582-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140620903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}