Pub Date : 2025-02-17DOI: 10.1007/s00161-025-01364-1
Reuven Segev
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell’s equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a p-form in an n-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an ((n-p-1))-form, a generalization of the Maxwell 2-form.
{"title":"Electrodynamics and geometric continuum mechanics","authors":"Reuven Segev","doi":"10.1007/s00161-025-01364-1","DOIUrl":"10.1007/s00161-025-01364-1","url":null,"abstract":"<div><p>This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell’s equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a <i>p</i>-form in an <i>n</i>-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an <span>((n-p-1))</span>-form, a generalization of the Maxwell 2-form.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01364-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1007/s00161-025-01361-4
Randy Llerena, Paolo Piovano
A novel variational model is proposed to address design control for composite multilayered metamaterials self-assembled via vapor deposition. The model is formulated within the framework of continuum mechanics, with the reference configuration corresponding to the equilibrium lattice of the substrate material. To account for the potential mismatch with the free-standing equilibrium lattices of each layer’s material, following the literature on Stress-Driven Rearrangement Instabilities, a nonzero mismatch strain varying across layers is considered. Moreover, building on the results of [47], the model allows for the treatment of the interplay between coherent and incoherent regions, which can coexist at each interlayer interface, as both elastic and surface effects—and their competition—are taken into account. The surface of each film layer is assumed to satisfy the“exterior graph condition” introduced in [47], which allows bulk cracks to be of non-graph type. By applying the direct method of calculus of variations under a constraint on the number of connected components of the cracks that are not connected to the surface of the film layers, the existence of energy minimizers is established in two dimensions. As a byproduct of the analysis, advancements are also made in the state of the art in the variational modeling of single-layered films by allowing the substrate surface to be free and including the possibility of delamination from the substrate.
{"title":"Variational modeling of multilayer films with coherent and incoherent interlayer interfaces","authors":"Randy Llerena, Paolo Piovano","doi":"10.1007/s00161-025-01361-4","DOIUrl":"10.1007/s00161-025-01361-4","url":null,"abstract":"<div><p>A novel variational model is proposed to address design control for composite multilayered metamaterials self-assembled via vapor deposition. The model is formulated within the framework of continuum mechanics, with the reference configuration corresponding to the equilibrium lattice of the substrate material. To account for the potential mismatch with the free-standing equilibrium lattices of each layer’s material, following the literature on Stress-Driven Rearrangement Instabilities, a nonzero mismatch strain varying across layers is considered. Moreover, building on the results of [47], the model allows for the treatment of the interplay between coherent and incoherent regions, which can coexist at each interlayer interface, as both elastic and surface effects—and their competition—are taken into account. The surface of each film layer is assumed to satisfy the“exterior graph condition” introduced in [47], which allows bulk cracks to be of non-graph type. By applying the direct method of calculus of variations under a constraint on the number of connected components of the cracks that are not connected to the surface of the film layers, the existence of energy minimizers is established in two dimensions. As a byproduct of the analysis, advancements are also made in the state of the art in the variational modeling of single-layered films by allowing the substrate surface to be free and including the possibility of delamination from the substrate.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01361-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-10DOI: 10.1007/s00161-025-01360-5
Ahmed E. Abouelregal, Mohamed E. Elzayady, M. Marin, Abdelaziz Foul, Sameh S. Askar
This article examined the thermoelastic behavior of functionally graded (FG) materials using a partially modified thermoelastic heat transfer model. The model utilized the three-phase lag thermoelasticity theory and incorporated higher-order fractional derivatives of Caputo and Fabrizio to address advanced thermodynamic and mechanical properties. These improvements showed great potential for applications in engineering fields such as aerospace, pressure vessel design, and structural engineering. The study applied the proposed model to analyze a thermoelastic problem involving an infinite FG medium with a cylindrical cavity subjected to thermal shock. The medium’s radially varying thermal and mechanical properties, characteristic of FG materials, played a central role in the analysis. The results revealed that the gradient coefficient and fractional derivative coefficient significantly affected the distribution of physical fields within the medium. Adjusting these parameters optimized the thermoelastic response, enabling tailored performance to meet specific engineering requirements.
{"title":"Thermoelastic modeling of functionally graded materials with cylindrical cavities utilizing higher-order fractional heat transfer models incorporating time delays","authors":"Ahmed E. Abouelregal, Mohamed E. Elzayady, M. Marin, Abdelaziz Foul, Sameh S. Askar","doi":"10.1007/s00161-025-01360-5","DOIUrl":"10.1007/s00161-025-01360-5","url":null,"abstract":"<div><p>This article examined the thermoelastic behavior of functionally graded (FG) materials using a partially modified thermoelastic heat transfer model. The model utilized the three-phase lag thermoelasticity theory and incorporated higher-order fractional derivatives of Caputo and Fabrizio to address advanced thermodynamic and mechanical properties. These improvements showed great potential for applications in engineering fields such as aerospace, pressure vessel design, and structural engineering. The study applied the proposed model to analyze a thermoelastic problem involving an infinite FG medium with a cylindrical cavity subjected to thermal shock. The medium’s radially varying thermal and mechanical properties, characteristic of FG materials, played a central role in the analysis. The results revealed that the gradient coefficient and fractional derivative coefficient significantly affected the distribution of physical fields within the medium. Adjusting these parameters optimized the thermoelastic response, enabling tailored performance to meet specific engineering requirements.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379846","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 : 2025-02-05DOI: 10.1007/s00161-025-01363-2
Rafał Wyczółkowski, Mariusz Salwin, Marek Gała, Dominika Strycharska, Tomasz Chmielewski
The article analyzes the impact of contact conduction on the intensity of heat flow in a bundle of steel round bars. This issue is related to the optimization of the heat treatment of the bars, as contact conduction is a key mechanism in the heating process of the considered charge. A proprietary computational model, based on the analysis of thermal resistances, was used for the analysis. To quantify heat flow intensity in the bar bundle, the concept of effective thermal conductivity was utilized. The impact of contact conduction on the phenomenon under consideration was expressed using a parameter called the multiplication of effective thermal conductivity (({M}_{ ETC})), defined by Eq. (36). Calculations were conducted across a temperature range of 25–800 °C, considering variables such as bar diameters (10, 20, and 30 mm), bundle porosity, and type of gas (air and hydrogen). Results indicate that temperature has the greatest influence on the course of the analyzed phenomenon, as this parameter increases, the influence of contact conduction decreases rapidly. Across the entire temperature range, contact conduction increases heat transfer intensity by approximately: four times (for air) and twice (for hydrogen).
{"title":"Analysis of the influence of thermal contact conduction on the intensity of heat flow in a bundle of round steel bars","authors":"Rafał Wyczółkowski, Mariusz Salwin, Marek Gała, Dominika Strycharska, Tomasz Chmielewski","doi":"10.1007/s00161-025-01363-2","DOIUrl":"10.1007/s00161-025-01363-2","url":null,"abstract":"<div><p>The article analyzes the impact of contact conduction on the intensity of heat flow in a bundle of steel round bars. This issue is related to the optimization of the heat treatment of the bars, as contact conduction is a key mechanism in the heating process of the considered charge. A proprietary computational model, based on the analysis of thermal resistances, was used for the analysis. To quantify heat flow intensity in the bar bundle, the concept of effective thermal conductivity was utilized. The impact of contact conduction on the phenomenon under consideration was expressed using a parameter called the multiplication of effective thermal conductivity (<span>({M}_{ ETC}))</span>, defined by Eq. (36). Calculations were conducted across a temperature range of 25–800 °C, considering variables such as bar diameters (10, 20, and 30 mm), bundle porosity, and type of gas (air and hydrogen). Results indicate that temperature has the greatest influence on the course of the analyzed phenomenon, as this parameter increases, the influence of contact conduction decreases rapidly. Across the entire temperature range, contact conduction increases heat transfer intensity by approximately: four times (for air) and twice (for hydrogen).</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184813","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}
Viscous fingering instability has been analyzed through empirical studies using miscible flow displacement in fractured porous media. While significant research has been conducted on viscous fingering, limited information is available regarding its behavior in fractured porous structures. The experiments were conducted in rectangular porous models with fractures oriented at ({0}^circ ), ({45}^circ ), and ({90}^circ ), to investigate how fracture orientation influences fluid displacement, where both channeling and fingering mechanisms play significant roles. This paper, which is the second part of a previous study, places particular emphasis on the impact of the viscosity ratio, a crucial parameter in determining the complexity of the fingering patterns. Quantitative parameters such as sweep efficiency, tip location, and breakthrough time were evaluated and analyzed using image processing techniques. The results indicate that increasing the viscosity ratio leads to more complex finger formations. Additionally, as the injection rate increases, the size of the finger patterns slightly increases, while the channeling effect becomes less pronounced. Notably, fractures aligned at ({0}^circ ) had the most significant impact on the rate of sweep efficiency and tip location, increasing the tip velocity of the fingers by up to 90%.
{"title":"Experimental study of fluid displacement and viscous fingering in fractured porous media: effect of viscosity ratio","authors":"Amirhosein Zadehkabir, Pouria Mazinani, Behrouz Zare Vamerzani, Christian Cardillo, Hamid Saffari, Seyed Mostafa Hosseinalipour","doi":"10.1007/s00161-025-01362-3","DOIUrl":"10.1007/s00161-025-01362-3","url":null,"abstract":"<div><p>Viscous fingering instability has been analyzed through empirical studies using miscible flow displacement in fractured porous media. While significant research has been conducted on viscous fingering, limited information is available regarding its behavior in fractured porous structures. The experiments were conducted in rectangular porous models with fractures oriented at <span>({0}^circ )</span>, <span>({45}^circ )</span>, and <span>({90}^circ )</span>, to investigate how fracture orientation influences fluid displacement, where both channeling and fingering mechanisms play significant roles. This paper, which is the second part of a previous study, places particular emphasis on the impact of the viscosity ratio, a crucial parameter in determining the complexity of the fingering patterns. Quantitative parameters such as sweep efficiency, tip location, and breakthrough time were evaluated and analyzed using image processing techniques. The results indicate that increasing the viscosity ratio leads to more complex finger formations. Additionally, as the injection rate increases, the size of the finger patterns slightly increases, while the channeling effect becomes less pronounced. Notably, fractures aligned at <span>({0}^circ )</span> had the most significant impact on the rate of sweep efficiency and tip location, increasing the tip velocity of the fingers by up to 90%.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01362-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143083897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-31DOI: 10.1007/s00161-024-01356-7
N. Challamel, C. Combescure, V. Picandet, M. Ferretti, A. Luongo
This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with (p = 2) nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this n-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in (n−1) unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case (p= 1) interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems.
{"title":"Exact bifurcation analysis of the static response of a Fermi–Pasta–Ulam softening chain with short and long-range interactions","authors":"N. Challamel, C. Combescure, V. Picandet, M. Ferretti, A. Luongo","doi":"10.1007/s00161-024-01356-7","DOIUrl":"10.1007/s00161-024-01356-7","url":null,"abstract":"<div><p>This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with <span>(p = 2)</span> nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this <i>n</i>-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in <i>(n−1)</i> unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in <i>(n−1)</i> unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in <i>(n−1)</i> unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case <span>(p= 1)</span> interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01356-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-30DOI: 10.1007/s00161-025-01358-z
Adam Zakria, Ahmed Yahya, Ahmed E. Abouelregal, Muntasir Suhail
This study investigated the thermoelastic vibration behavior of microbeams supported by a Pasternak foundation, characterized by two elastic parameters: the shear layer modulus and the Winkler modulus. The thermoelastic behavior of the beam was modeled using the Moore–Gibson–Thompson (MGT) heat conduction theory, which accounted for finite thermal wave speeds and included a higher-order time derivative to effectively address heat conduction dynamics in small-scale structures. The governing equations were derived from the coupled theories of generalized thermoelasticity and beam mechanics, integrating the effects of the foundation. The research examined how foundation parameters, thermal relaxation times, and beam geometry influenced vibration frequency, thermal damping, and the stability of the microbeam. Numerical simulations were performed to demonstrate the effects of material properties, foundation stiffness, and thermal loading on the dynamic behavior of the microbeam. The findings offered valuable insights for the design and optimization of microbeams in advanced engineering applications, such as MEMS devices and nanoscale structures, where thermal effects and foundation interactions were crucial
{"title":"Vibration analysis of thermoelastic micro-beams on a Pasternak foundation with two parameters using the Moore–Gibson–Thompson heat conduction model","authors":"Adam Zakria, Ahmed Yahya, Ahmed E. Abouelregal, Muntasir Suhail","doi":"10.1007/s00161-025-01358-z","DOIUrl":"10.1007/s00161-025-01358-z","url":null,"abstract":"<div><p>This study investigated the thermoelastic vibration behavior of microbeams supported by a Pasternak foundation, characterized by two elastic parameters: the shear layer modulus and the Winkler modulus. The thermoelastic behavior of the beam was modeled using the Moore–Gibson–Thompson (MGT) heat conduction theory, which accounted for finite thermal wave speeds and included a higher-order time derivative to effectively address heat conduction dynamics in small-scale structures. The governing equations were derived from the coupled theories of generalized thermoelasticity and beam mechanics, integrating the effects of the foundation. The research examined how foundation parameters, thermal relaxation times, and beam geometry influenced vibration frequency, thermal damping, and the stability of the microbeam. Numerical simulations were performed to demonstrate the effects of material properties, foundation stiffness, and thermal loading on the dynamic behavior of the microbeam. The findings offered valuable insights for the design and optimization of microbeams in advanced engineering applications, such as MEMS devices and nanoscale structures, where thermal effects and foundation interactions were crucial</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056222","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 : 2025-01-24DOI: 10.1007/s00161-025-01357-0
Mircea Bîrsan, Milad Shirani, David J. Steigmann
Detailed derivations of the Legendre-Hadamard necessary conditions for energy-minimizing states of fiber-reinforced three-dimensional solids and two-dimensional shells are presented. The underlying conceptual framework is Cosserat elasticity theory in which the Cosserat rotation field controls the orientation of the embedded fibers. This is partially coupled to the continuum deformation gradient by the requirement that the fibers convect as material curves with respect to the matrix material in which they are embedded. The conditions obtained combine the effects of deformation and rotation and subsume previously obtained decoupled inequalities involving these effects separately.
{"title":"The coupled Legendre-Hadamard condition for fiber-reinforced materials: three-dimensional solids and two-dimensional shells","authors":"Mircea Bîrsan, Milad Shirani, David J. Steigmann","doi":"10.1007/s00161-025-01357-0","DOIUrl":"10.1007/s00161-025-01357-0","url":null,"abstract":"<div><p>Detailed derivations of the Legendre-Hadamard necessary conditions for energy-minimizing states of fiber-reinforced three-dimensional solids and two-dimensional shells are presented. The underlying conceptual framework is Cosserat elasticity theory in which the Cosserat rotation field controls the orientation of the embedded fibers. This is partially coupled to the continuum deformation gradient by the requirement that the fibers convect as material curves with respect to the matrix material in which they are embedded. The conditions obtained combine the effects of deformation and rotation and subsume previously obtained decoupled inequalities involving these effects separately.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01357-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1007/s00161-024-01345-w
S. E. Khader, A. A. Marrouf, M. Khedr
We consider a model of two layers for two cases. In the first case, a viscoelastic upper layer over an elastic half-space. In the second case, an elastic upper layer over a viscoelastic half-space. The upper layer’s surface is taken to be traction-free and is subjected to a constant thermal shock. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. Laplace transform techniques are used. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions. This work may be useful in the design of materials used in thermal insulation, vibration reduction, and applications in microelectronics.
{"title":"A model for elastic half space under a visco-elastic layer in generalized thermoelasticity","authors":"S. E. Khader, A. A. Marrouf, M. Khedr","doi":"10.1007/s00161-024-01345-w","DOIUrl":"10.1007/s00161-024-01345-w","url":null,"abstract":"<div><p>We consider a model of two layers for two cases. In the first case, a viscoelastic upper layer over an elastic half-space. In the second case, an elastic upper layer over a viscoelastic half-space. The upper layer’s surface is taken to be traction-free and is subjected to a constant thermal shock. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. Laplace transform techniques are used. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions. This work may be useful in the design of materials used in thermal insulation, vibration reduction, and applications in microelectronics.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01345-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-14DOI: 10.1007/s00161-025-01359-y
Marin Marin, Andreas Öchsner, Sorin Vlase, Hamid M. Sedighi, Stefan Pirlog
In our study we approach a Cosserat thermoelastic body in which we take into account both the usual temperature and the microtemperature, that is, the temperature of the microparticles of the body. After constructing the mixed problem with initial and boundary values, in this context, we define an appropriate Hilbert space in which we obtain a temporal evolutionary equation which is equivalent to the already constructed mixed problem. With the help of some known results from the theory of contraction semigroups we prove both the existence and the uniqueness of the solution of the evolution equation, therefore of the considered mixed problem. Furthermore, the same semigroup theory allows us to obtain the continuous dependence of the solution of the mixed problem, both with respect to the initial data and with respect to the loading.
{"title":"A study of a thermoelastic body possessing microtemperatures","authors":"Marin Marin, Andreas Öchsner, Sorin Vlase, Hamid M. Sedighi, Stefan Pirlog","doi":"10.1007/s00161-025-01359-y","DOIUrl":"10.1007/s00161-025-01359-y","url":null,"abstract":"<div><p>In our study we approach a Cosserat thermoelastic body in which we take into account both the usual temperature and the microtemperature, that is, the temperature of the microparticles of the body. After constructing the mixed problem with initial and boundary values, in this context, we define an appropriate Hilbert space in which we obtain a temporal evolutionary equation which is equivalent to the already constructed mixed problem. With the help of some known results from the theory of contraction semigroups we prove both the existence and the uniqueness of the solution of the evolution equation, therefore of the considered mixed problem. Furthermore, the same semigroup theory allows us to obtain the continuous dependence of the solution of the mixed problem, both with respect to the initial data and with respect to the loading.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01359-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142975184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}