Pub Date : 2024-08-08DOI: 10.1177/10812865241263531
Wei Peng, Xu Zhang, Tianhu He, Yaru Gao, Yan Li
Nanocomposite materials, such as graphene nanoplatelets (GPLs), have been fabricated into high-efficient resonators due to the excellent thermo-mechanical properties. In addition, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high-performance micro-/nano-resonators. Nevertheless, the classical TED models fail on the micro-/nano-scale due to not considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present work aims to investigate TED analysis of functionally graded (FG) polymer microplate resonators reinforced with GPLs based on the modified couple stress theory (MCST) and the three-phase-lag (TPL) heat conduction model. Four patterns of GPL distribution including the UD, FG-O, FG-X, and FG-A pattern distributions are taken into account, and the effective mechanical properties of the plate-type nanocomposite are evaluated based on the Halpin-Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length-scale parameter, the phase-lag parameters, and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This paper provides a theoretical approach to estimate TED in the design of high-performance micro-resonators.
{"title":"Size-dependent thermoelastic damping analysis of functionally graded polymer micro plate resonators reinforced with graphene nanoplatelets based on three-phase-lag heat conduction model","authors":"Wei Peng, Xu Zhang, Tianhu He, Yaru Gao, Yan Li","doi":"10.1177/10812865241263531","DOIUrl":"https://doi.org/10.1177/10812865241263531","url":null,"abstract":"Nanocomposite materials, such as graphene nanoplatelets (GPLs), have been fabricated into high-efficient resonators due to the excellent thermo-mechanical properties. In addition, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high-performance micro-/nano-resonators. Nevertheless, the classical TED models fail on the micro-/nano-scale due to not considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present work aims to investigate TED analysis of functionally graded (FG) polymer microplate resonators reinforced with GPLs based on the modified couple stress theory (MCST) and the three-phase-lag (TPL) heat conduction model. Four patterns of GPL distribution including the UD, FG-O, FG-X, and FG-A pattern distributions are taken into account, and the effective mechanical properties of the plate-type nanocomposite are evaluated based on the Halpin-Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length-scale parameter, the phase-lag parameters, and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This paper provides a theoretical approach to estimate TED in the design of high-performance micro-resonators.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"94 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945978","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}
This work presents a theoretical and numerical study of the flow of the interstitial fluid saturating a porous medium, principally aimed at modeling a bio-mimetic material and assumed to experience a dynamic regime different from the Darcian one, as is typically hypothesized in biomechanical scenarios. The main aspect of our research is the conjecture according to which, for a particular mechanical state of the porous medium, the fluid exhibits two types of deviation from Darcy’s law. One is due to the inertial forces characterizing the pore scale dynamics of the fluid. This aspect can be resolved by turning to the Forchheimer correction to Darcy’s law, which introduces non-linearities in the relationship between the fluid filtration velocity and the dissipative forces describing the interactions between the fluid and the solid matrix. The second source of discrepancies from classical Darcy’s law emerges, for example, when pore scale disturbances to the flow, such as obstructions of the fluid path or clogging of the pores, result in a time delay between drag force and filtration velocity. Recently, models have been proposed in which such delay is described through constitutive laws featuring fractional operators. Whereas, to the best of our knowledge, the aforementioned behaviors have been studied separately or in small deformations, we present a model of fluid flow in a deformable porous medium undergoing large deformations in which the fluid motion obeys a fractionalized Forchheimer’s correction. After reviewing Forchheimer’s formulation, we present a fractionalization of the Darcy–Forchheimer law, and we explain the numerical procedure adopted to solve the highly non-linear boundary value problem resulting from the presence of the two considered deviations from the Darcian regime. We complete our study by highlighting the way in which the fractional order of the model tunes the magnitude of the pore pressure and fluid filtration velocity.
{"title":"Fractionalization of Forchheimer’s correction to Darcy’s law in porous media in large deformations","authors":"Sachin Gunda, Alessandro Giammarini, Ariel Ramírez-Torres, Sundararajan Natarajan, Olga Barrera, Alfio Grillo","doi":"10.1177/10812865241252577","DOIUrl":"https://doi.org/10.1177/10812865241252577","url":null,"abstract":"This work presents a theoretical and numerical study of the flow of the interstitial fluid saturating a porous medium, principally aimed at modeling a bio-mimetic material and assumed to experience a dynamic regime different from the Darcian one, as is typically hypothesized in biomechanical scenarios. The main aspect of our research is the conjecture according to which, for a particular mechanical state of the porous medium, the fluid exhibits two types of deviation from Darcy’s law. One is due to the inertial forces characterizing the pore scale dynamics of the fluid. This aspect can be resolved by turning to the Forchheimer correction to Darcy’s law, which introduces non-linearities in the relationship between the fluid filtration velocity and the dissipative forces describing the interactions between the fluid and the solid matrix. The second source of discrepancies from classical Darcy’s law emerges, for example, when pore scale disturbances to the flow, such as obstructions of the fluid path or clogging of the pores, result in a time delay between drag force and filtration velocity. Recently, models have been proposed in which such delay is described through constitutive laws featuring fractional operators. Whereas, to the best of our knowledge, the aforementioned behaviors have been studied separately or in small deformations, we present a model of fluid flow in a deformable porous medium undergoing large deformations in which the fluid motion obeys a fractionalized Forchheimer’s correction. After reviewing Forchheimer’s formulation, we present a fractionalization of the Darcy–Forchheimer law, and we explain the numerical procedure adopted to solve the highly non-linear boundary value problem resulting from the presence of the two considered deviations from the Darcian regime. We complete our study by highlighting the way in which the fractional order of the model tunes the magnitude of the pore pressure and fluid filtration velocity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"52 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945980","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}
Pub Date : 2024-07-31DOI: 10.1177/10812865241258154
Amit Acharya
A methodology for defining variational principles for a class of PDE (partial differential equations) models from continuum mechanics is demonstrated, and some of its features are explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single-crystal plasticity at finite deformation.
{"title":"A hidden convexity in continuum mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity","authors":"Amit Acharya","doi":"10.1177/10812865241258154","DOIUrl":"https://doi.org/10.1177/10812865241258154","url":null,"abstract":"A methodology for defining variational principles for a class of PDE (partial differential equations) models from continuum mechanics is demonstrated, and some of its features are explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single-crystal plasticity at finite deformation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"78 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873023","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}
Pub Date : 2024-07-31DOI: 10.1177/10812865241255048
Valeriy A Buryachenko
We consider static problems for composite materials (CMs) with either locally elastic or peridynamic constitutive properties. The general integral equation (GIE) is the exact integral equationWe consider static problems for composite materials connecting the random fields at the point being considered and the surrounding points. There is a very long and colored history of the development of GIE which goes back to Lord Rayleigh. Owing to the new GIE (forming the second background of micromechanics also called the computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of random structures. By now, the GIEs are generalized to CMs (of statistically homogeneous and inhomogeneous structures) with the phases described by local models, strongly nonlocal models (strain type and displacement type, peridynamics), and weakly nonlocal models (strain-gradient theories, stress-gradient theories, and higher-order models). However, a fundamental restriction of all mentioned GIEs is their linearity with respect to a primary unknown variable. The goal of this study is obtaining nonlinear GIEs for PM, and, in a particular case, for LM. For the presentation of PM as a unified theory, we describe PM as the formalized schemes of blocked (or modular) structures so that the experts developing one block need not be experts in the underlying another block (this is a good background for effective collaborations of different teams in so many multidisciplinary areas as PM). The opportunity for the creation of this blocked structure of the PM is supported by a critical generalization of CAM which is extremely flexible, robust, and general.
{"title":"Nonlinear elastic general integral equations in micromechanics of random structure composites","authors":"Valeriy A Buryachenko","doi":"10.1177/10812865241255048","DOIUrl":"https://doi.org/10.1177/10812865241255048","url":null,"abstract":"We consider static problems for composite materials (CMs) with either locally elastic or peridynamic constitutive properties. The general integral equation (GIE) is the exact integral equationWe consider static problems for composite materials connecting the random fields at the point being considered and the surrounding points. There is a very long and colored history of the development of GIE which goes back to Lord Rayleigh. Owing to the new GIE (forming the second background of micromechanics also called the computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of random structures. By now, the GIEs are generalized to CMs (of statistically homogeneous and inhomogeneous structures) with the phases described by local models, strongly nonlocal models (strain type and displacement type, peridynamics), and weakly nonlocal models (strain-gradient theories, stress-gradient theories, and higher-order models). However, a fundamental restriction of all mentioned GIEs is their linearity with respect to a primary unknown variable. The goal of this study is obtaining nonlinear GIEs for PM, and, in a particular case, for LM. For the presentation of PM as a unified theory, we describe PM as the formalized schemes of blocked (or modular) structures so that the experts developing one block need not be experts in the underlying another block (this is a good background for effective collaborations of different teams in so many multidisciplinary areas as PM). The opportunity for the creation of this blocked structure of the PM is supported by a critical generalization of CAM which is extremely flexible, robust, and general.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"4 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873024","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}
Pub Date : 2024-07-26DOI: 10.1177/10812865241262491
YS Wang, BL Wang, KF Wang
The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials.
{"title":"Transient mode-III problem of the elastic matrix with a line inclusion","authors":"YS Wang, BL Wang, KF Wang","doi":"10.1177/10812865241262491","DOIUrl":"https://doi.org/10.1177/10812865241262491","url":null,"abstract":"The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"245 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776123","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}
Pub Date : 2024-07-26DOI: 10.1177/10812865241252368
Lennart Behlen, Daniel Wallenta, Andreas Ricoeur
The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.
以无限介质板中椭圆介质腔的解析解为基础，研究了通过让半小轴趋向于零而得到的格里菲斯裂缝问题。在此过程中，纠正了文献中常用的错误保角映射，这种映射只在物理空间的一部分正确再现电场。将椭圆形界面解释为暴露在斜向远程电场中的机械开裂面，计算出表面电荷和静电牵引力。与已建立的电容器类比模型（根据未变形裂缝配置中的位移和电动势近似得出电荷密度和库仑牵引力）相比，目前的研究提供了精确的解决方案，考虑到了裂缝曲率和电场倾斜度的不同影响。裂纹权重函数最终用于计算应力和电位移强度因子。结果表明，在相关参数范围内，电容器类比的表面电荷可以很好地替代精确的电边界条件，而裂纹尖端附近不准确的库仑牵引力可能会导致模式 I 应力强度因子被大大高估。
{"title":"Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?","authors":"Lennart Behlen, Daniel Wallenta, Andreas Ricoeur","doi":"10.1177/10812865241252368","DOIUrl":"https://doi.org/10.1177/10812865241252368","url":null,"abstract":"The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776122","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}
Pub Date : 2024-07-26DOI: 10.1177/10812865231219163
JD Humphrey
Rupture of intracranial aneurysms, either fusiform or saccular in shape, associates with significant morbidity and mortality. The progressive enlargement and eventual rupture of these lesions depends strongly on the associated mechanics and mechanobiology. In this paper, we review results from past biomechanical analyses of intracranial aneurysms and highlight lessons learned in the general area of vascular mechanobiology with the goal of guiding future research.
{"title":"Mechanics and mechanobiology of intracranial aneurysms","authors":"JD Humphrey","doi":"10.1177/10812865231219163","DOIUrl":"https://doi.org/10.1177/10812865231219163","url":null,"abstract":"Rupture of intracranial aneurysms, either fusiform or saccular in shape, associates with significant morbidity and mortality. The progressive enlargement and eventual rupture of these lesions depends strongly on the associated mechanics and mechanobiology. In this paper, we review results from past biomechanical analyses of intracranial aneurysms and highlight lessons learned in the general area of vascular mechanobiology with the goal of guiding future research.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"160 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776126","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}
Pub Date : 2024-07-26DOI: 10.1177/10812865241249751
Mordecai Oore, Sageev Oore
An explicit analytical solution for an elliptical hole in an infinite elastic plate is derived for uniaxial load from the earliest work on this configuration. This is used along with the biaxial loading case and more recent solutions, available in curvilinear coordinates, to transform the stress fields into Cartesian coordinates along the x and y axes, reducing the curvilinear solutions to simplified short-form expressions of x and y. The present closed-form results are the functions of polynomials of the second and third order of x or y along the x or y axes, respectively, and have the most concise form to the best of the authors’ knowledge. The displacements for plain stress condition are calculated directly from the present stress field expressions, as functions of second-order polynomials of x or y and demonstrate overall consistency. Application of the present stress field and displacements results to special cases, such as a circular hole, a crack, and an elliptical hole in a pressurized cylindrical shell, are shown to agree with published solutions where available.
根据有关该构造的最早研究成果，得出了无限弹性板中椭圆孔的单轴载荷显式解析解。本封闭式结果分别是 x 或 y 的二阶和三阶多项式沿 x 或 y 轴的函数，是作者所知的最简洁的形式。平应力条件下的位移是直接从本应力场表达式中计算出来的，是 x 或 y 的二阶多项式的函数，并显示出整体一致性。将本应力场和位移结果应用于特殊情况，如受压圆柱形壳体中的圆孔、裂缝和椭圆孔，结果表明与已公布的解法一致。
{"title":"Explicit solutions in Cartesian coordinates for an elliptic hole in an infinite elastic plate","authors":"Mordecai Oore, Sageev Oore","doi":"10.1177/10812865241249751","DOIUrl":"https://doi.org/10.1177/10812865241249751","url":null,"abstract":"An explicit analytical solution for an elliptical hole in an infinite elastic plate is derived for uniaxial load from the earliest work on this configuration. This is used along with the biaxial loading case and more recent solutions, available in curvilinear coordinates, to transform the stress fields into Cartesian coordinates along the x and y axes, reducing the curvilinear solutions to simplified short-form expressions of x and y. The present closed-form results are the functions of polynomials of the second and third order of x or y along the x or y axes, respectively, and have the most concise form to the best of the authors’ knowledge. The displacements for plain stress condition are calculated directly from the present stress field expressions, as functions of second-order polynomials of x or y and demonstrate overall consistency. Application of the present stress field and displacements results to special cases, such as a circular hole, a crack, and an elliptical hole in a pressurized cylindrical shell, are shown to agree with published solutions where available.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"63 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785488","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}
Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.
{"title":"Transient heat transfer analysis of a sandwich panel with a cracked honeycomb core","authors":"Wenzhi Yang, Ruchao Gao, Jinxing Liu, Zengtao Chen","doi":"10.1177/10812865241261638","DOIUrl":"https://doi.org/10.1177/10812865241261638","url":null,"abstract":"Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"86 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785487","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}
Pub Date : 2024-07-26DOI: 10.1177/10812865241241002
Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke
We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.
{"title":"Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach","authors":"Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke","doi":"10.1177/10812865241241002","DOIUrl":"https://doi.org/10.1177/10812865241241002","url":null,"abstract":"We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"61 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776121","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：