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Some decay properties in extensible thermoelastic beam with Gurtin–Pipkin’s law 具有古尔廷-皮普金定律的可伸展热弹性梁的一些衰变特性
Mathematics and Mechanics of Solids Pub Date : 2024-02-07 DOI: 10.1177/10812865231226112
M. Aouadi
{"title":"Some decay properties in extensible thermoelastic beam with Gurtin–Pipkin’s law","authors":"M. Aouadi","doi":"10.1177/10812865231226112","DOIUrl":"https://doi.org/10.1177/10812865231226112","url":null,"abstract":"In this article, we derive the equations that constitute the mathematical model of extensible thermoelastic beam in the context of second sound model which turns to the Gurtin–Pipkin’s one. These nonlinear governing equations are derived according to the von Kármán theory and simplified by the Euler–Bernoulli approximation in the context of Gurtin–Pipkin’s law. Even more so, the case of Fourier’s law can be recovered from the derived system one through a proper singular limit procedure, where the memory kernel collapses into the Dirac mass at zero. Then, we show that the Gurtin–Pipkin’s derived model is globally well-posed using the semigroup theory and the corresponding solutions decay exponentially under a condition on physical coefficients of the model. Finally, by an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we prove that the linear (without extensibility) associated semigroup is not analytic. Finally, we show that Cattaneo’s law is a particular example of Gurtin–Pipkin’s law for suitable choice of the memory kernel.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139856062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moving from theory to application: Evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals 从理论到应用：评估多孔塑性金属韧性断裂建模中空隙形状效应和损伤局部化的数值实施情况
Mathematics and Mechanics of Solids Pub Date : 2024-02-07 DOI: 10.1177/10812865231226384
K. Enakoutsa, Yanni Bills
{"title":"Moving from theory to application: Evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals","authors":"K. Enakoutsa, Yanni Bills","doi":"10.1177/10812865231226384","DOIUrl":"https://doi.org/10.1177/10812865231226384","url":null,"abstract":"In this paper, we present a robust exploration of the Gologanu–Leblond–Devaux (GLD) model, an advanced iteration of the Gurson model, designed to predict ductile fractures in porous metals. Going beyond the limits of the original Gurson model, the GLD model accounts for cavity shape effects and non-local strain localization, marking a significant leap in fracture mechanics. We also present a comprehensive exposition of the GLD model and its non-local extension, establishing their compatibility with the concept of GSMs. Notably, we emphasize the uniqueness of solutions in the numerical implementation, underlining the imperative need for a meticulously devised mixed implicit/explicit algorithm. Furthermore, we set out to validate the GLD model through rigorous comparisons of our numerical simulations with experimental data. Employing a damage delocalization approach rooted in the natural logarithm of porosity, our study provides compelling evidence of the model’s performance. This approach mitigates issues observed with the original porosity rate, preventing excessive smoothing of porosity and maintaining the fidelity of stress–strain curves. In addition, we gave a profound theoretical elucidation of this phenomenon via Fourier’s analysis of porosity rate. Through this work, we not only enhance our understanding of ductile fracture behavior but also establish a robust numerical framework for its predictive modeling. The GLD model emerges as a powerful tool for the accurate analysis and prediction of fracture phenomena in porous materials, further advancing the field of materials science and engineering.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"27 44","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139795823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Refined linearly anisotropic couple-stress elasticity 完善的线性各向异性耦合应力弹性体
Mathematics and Mechanics of Solids Pub Date : 2024-02-07 DOI: 10.1177/10812865231222898
K. Soldatos
{"title":"Refined linearly anisotropic couple-stress elasticity","authors":"K. Soldatos","doi":"10.1177/10812865231222898","DOIUrl":"https://doi.org/10.1177/10812865231222898","url":null,"abstract":"A recently developed, refined version of the conventional linear couple-stress theory of isotropic elasticity is extended to include the influence of anisotropic material effects. With this development, the implied refined theory (1) retains ability to determine the spherical part of the couple-stress and (2) is further furnished with constitutive ability to embrace modelling of linearly elastic solids that exhibit inherent polar material anisotropy of advanced levels that reach the class of locally monoclinic materials. This type of anisotropy embraces most of the structural material subclasses met in practice, such as those of general and special orthotropy, as well as the subclass of transverse isotropy. The thus obtained, enhanced version of the refined theory is furnished with ability to also handle structural analysis problems of polar fibrous composites reinforced by families of perfectly flexible fibres or, more generally, polar anisotropic solids possessing one or more material preference directions that do not possess bending resistance. A relevant example application considers and studies in detail the subclass of polar transverse isotropy caused by the presence of a single family of perfectly flexible fibres. By developing the relevant constitutive equation, and explicitly presenting it in a suitable matrix rather than indicial notation form, that application also exemplifies the way that the spherical part of the couple-stress is determined when the fibres are straight. It further enables this communication to initiate a discussion of further important issues stemming from (1) the positive definiteness of the full, polar form of the relevant strain energy function and (2) the lack of ellipticity of the final form attained by the governing differential equations.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"39 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139797287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Moving from theory to application: Evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals 从理论到应用：评估多孔塑性金属韧性断裂建模中空隙形状效应和损伤局部化的数值实施情况
Mathematics and Mechanics of Solids Pub Date : 2024-02-07 DOI: 10.1177/10812865231226384
K. Enakoutsa, Yanni Bills
{"title":"Moving from theory to application: Evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals","authors":"K. Enakoutsa, Yanni Bills","doi":"10.1177/10812865231226384","DOIUrl":"https://doi.org/10.1177/10812865231226384","url":null,"abstract":"In this paper, we present a robust exploration of the Gologanu–Leblond–Devaux (GLD) model, an advanced iteration of the Gurson model, designed to predict ductile fractures in porous metals. Going beyond the limits of the original Gurson model, the GLD model accounts for cavity shape effects and non-local strain localization, marking a significant leap in fracture mechanics. We also present a comprehensive exposition of the GLD model and its non-local extension, establishing their compatibility with the concept of GSMs. Notably, we emphasize the uniqueness of solutions in the numerical implementation, underlining the imperative need for a meticulously devised mixed implicit/explicit algorithm. Furthermore, we set out to validate the GLD model through rigorous comparisons of our numerical simulations with experimental data. Employing a damage delocalization approach rooted in the natural logarithm of porosity, our study provides compelling evidence of the model’s performance. This approach mitigates issues observed with the original porosity rate, preventing excessive smoothing of porosity and maintaining the fidelity of stress–strain curves. In addition, we gave a profound theoretical elucidation of this phenomenon via Fourier’s analysis of porosity rate. Through this work, we not only enhance our understanding of ductile fracture behavior but also establish a robust numerical framework for its predictive modeling. The GLD model emerges as a powerful tool for the accurate analysis and prediction of fracture phenomena in porous materials, further advancing the field of materials science and engineering.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"107 3-4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139855414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some decay properties in extensible thermoelastic beam with Gurtin–Pipkin’s law 具有古尔廷-皮普金定律的可伸展热弹性梁的一些衰变特性
Mathematics and Mechanics of Solids Pub Date : 2024-02-07 DOI: 10.1177/10812865231226112
M. Aouadi
{"title":"Some decay properties in extensible thermoelastic beam with Gurtin–Pipkin’s law","authors":"M. Aouadi","doi":"10.1177/10812865231226112","DOIUrl":"https://doi.org/10.1177/10812865231226112","url":null,"abstract":"In this article, we derive the equations that constitute the mathematical model of extensible thermoelastic beam in the context of second sound model which turns to the Gurtin–Pipkin’s one. These nonlinear governing equations are derived according to the von Kármán theory and simplified by the Euler–Bernoulli approximation in the context of Gurtin–Pipkin’s law. Even more so, the case of Fourier’s law can be recovered from the derived system one through a proper singular limit procedure, where the memory kernel collapses into the Dirac mass at zero. Then, we show that the Gurtin–Pipkin’s derived model is globally well-posed using the semigroup theory and the corresponding solutions decay exponentially under a condition on physical coefficients of the model. Finally, by an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we prove that the linear (without extensibility) associated semigroup is not analytic. Finally, we show that Cattaneo’s law is a particular example of Gurtin–Pipkin’s law for suitable choice of the memory kernel.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"3 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139796356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole 带任意形状孔的正交半无限平面的解析解
Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231225131
Yulin Zhou, A. Lu, Ning Zhang
{"title":"An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole","authors":"Yulin Zhou, A. Lu, Ning Zhang","doi":"10.1177/10812865231225131","DOIUrl":"https://doi.org/10.1177/10812865231225131","url":null,"abstract":"The application of analytical methods to solve the problem of an anisotropic semi-infinite plane with a hole has not been observed thus far. This paper presents an analytical solution for an orthotropic semi-infinite plane with an arbitrary-shaped hole, considering the condition of a uniform stress applied at the hole boundary. First, the shapes of holes on the [Formula: see text]- and [Formula: see text]-planes are determined based on the shape of the hole on the z-plane. Next, the regions outside the holes on these physical planes are mapped to the rings on the [Formula: see text]- and [Formula: see text]-planes, respectively. Therefore, the boundary conditions with [Formula: see text] and [Formula: see text] as independent variables are established. Then, the boundary collocation method is used to solve the stress boundary conditions along the upper boundary and the hole boundary, thereby obtaining two analytical functions for calculating the stress and displacement of the structure. Finally, the correctness of the proposed method is verified by conducting boundary condition checks and comparing the stress and displacement results obtained by the proposed method with those obtained from ANSYS, and further investigates the influence of anisotropic parameters on normal stress and displacement.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"1 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139858232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linear elastic diatomic multilattices: Three-dimensional constitutive modeling and solutions of the shift vector equation 线性弹性二原子多晶格：三维构成模型和位移矢量方程的求解
Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231217464
Dimitrios Sfyris, G. I. Sfyris
{"title":"Linear elastic diatomic multilattices: Three-dimensional constitutive modeling and solutions of the shift vector equation","authors":"Dimitrios Sfyris, G. I. Sfyris","doi":"10.1177/10812865231217464","DOIUrl":"https://doi.org/10.1177/10812865231217464","url":null,"abstract":"Diatomic multilattices are congruences of simple lattices each made out of atoms of two possible chemical species. We here constitutively characterize, in three dimensions, diatomic multilattices for the geometrically and materially linear elastic regime. We give the most generic expression for the energy for [Formula: see text] diatomic multilattices and characterize explicitly the tensors present in such an expression for all 122 two-color point groups. For the specific case of diatomic 2- and 3-lattices, we delineate how one can solve the shift vector equation in the static case. For cases where the unique solution of the shift vector in terms of the strain tensor is not possible, we give conditions for the existence of solutions based on the standard Fredholm alternative theorem.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"191 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139861316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A study on the effect of defects on the buckling of double-walled carbon nanotubes under compression based on a new atomic-continuum coupling method 基于原子-真空耦合新方法的缺陷对双壁碳纳米管压缩屈曲影响的研究
Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231217705
Xiangyang Wang, H. Qi, Jiqiang Li, Junying Bi, Renpeng Qiao, Jingrui Zhang
{"title":"A study on the effect of defects on the buckling of double-walled carbon nanotubes under compression based on a new atomic-continuum coupling method","authors":"Xiangyang Wang, H. Qi, Jiqiang Li, Junying Bi, Renpeng Qiao, Jingrui Zhang","doi":"10.1177/10812865231217705","DOIUrl":"https://doi.org/10.1177/10812865231217705","url":null,"abstract":"An atomic-continuum coupling (ACC) method is developed for the nonlinear mechanical analysis of defective double-walled carbon nanotubes (DWCNTs). The moving least squares (MLS) approximation is resorted to bridge the fully atomic discrete structures of defective DWCNTs and the corresponding virtual continuum solids. The intrinsic mechanic laws implied in nanostructures can be accurately mapped into the mechanical governing equations of the continuum models. Based on ACC method, a numerical computational scheme is developed for predicting the buckling and contact behaviors of defective DWCNTs, which do not need any numerical integration method to calculate potential functional and its derivatives. The numerical tests show that this method can furnish good predictions even with a small number of nodes. It is found that Stone–Wales (SW) defects can lead to greatly decrease in the buckling properties of DWCNTs. In contrary, the complex interlayer van der Waals (vdW) interactions can enhance the buckling resistance of DWCNTs.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"60 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139860670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring 用于形状传感和结构健康监测的二维四节点四边形反演元件
Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231224384
Mingyang Li, Erkan Oterkus, S. Oterkus
{"title":"A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring","authors":"Mingyang Li, Erkan Oterkus, S. Oterkus","doi":"10.1177/10812865231224384","DOIUrl":"https://doi.org/10.1177/10812865231224384","url":null,"abstract":"The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional four-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution, and very good agreement is observed between the two solutions demonstrating the capability of iFEM approach.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"43 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139798465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linear elastic diatomic multilattices: Three-dimensional constitutive modeling and solutions of the shift vector equation 线性弹性二原子多晶格：三维构成模型和位移矢量方程的求解
Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231217464
Dimitrios Sfyris, G. I. Sfyris
{"title":"Linear elastic diatomic multilattices: Three-dimensional constitutive modeling and solutions of the shift vector equation","authors":"Dimitrios Sfyris, G. I. Sfyris","doi":"10.1177/10812865231217464","DOIUrl":"https://doi.org/10.1177/10812865231217464","url":null,"abstract":"Diatomic multilattices are congruences of simple lattices each made out of atoms of two possible chemical species. We here constitutively characterize, in three dimensions, diatomic multilattices for the geometrically and materially linear elastic regime. We give the most generic expression for the energy for [Formula: see text] diatomic multilattices and characterize explicitly the tensors present in such an expression for all 122 two-color point groups. For the specific case of diatomic 2- and 3-lattices, we delineate how one can solve the shift vector equation in the static case. For cases where the unique solution of the shift vector in terms of the strain tensor is not possible, we give conditions for the existence of solutions based on the standard Fredholm alternative theorem.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"39 156","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139801501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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