M. A. Salama, Ahmed E. Abouelregal, Fatma H. Galal
{"title":"A generalized coupled biothermoelastic model for human skin based on the Guyer–Krumhansl framework with nonlocal and thermal relaxation effects","authors":"M. A. Salama, Ahmed E. Abouelregal, Fatma H. Galal","doi":"10.1007/s00161-026-01460-w","DOIUrl":"10.1007/s00161-026-01460-w","url":null,"abstract":"<div><p>This study presents a generalized biothermoelastic model for human skin based on the Guyer–Krumhansl (GK) heat conduction equation, incorporating single-phase lag and spatial nonlocal effects. The framework integrates thermal relaxation time, nonlocal length scale, blood perfusion, and metabolic heat generation into a fully coupled thermoelastic system, extending classical Fourier-based models toward formulations that incorporate non-Fourier conduction effects within a coupled thermoelastic framework. The governing equations are derived in closed form in the Laplace domain and numerically inverted using a Fourier series-based method to capture wave-like and size-dependent heat transport characteristics. Parametric investigations highlight the distinct influence of nonlocality and thermal relaxation on temperature distribution, mechanical displacement, and stress evolution under transient thermal loading. The results underscore the importance of accounting for nonlocal and inertial thermal effects when modeling soft biological media. The developed model provides a rigorous theoretical foundation for analyzing biothermomechanical interactions in heterogeneous tissues and contributes to advancing non-Fourier continuum thermomechanics in biological systems.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147287143","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}
{"title":"Experimental and numerical evaluation of temperature-dependent natural frequencies in cylindrical shells using acoustic excitation","authors":"Maisam Parhikhteh, Mahdi Karimi, Reza Ahmadi, Omid Mohammadpour","doi":"10.1007/s00161-026-01454-8","DOIUrl":"10.1007/s00161-026-01454-8","url":null,"abstract":"<div><p>Cylindrical shells are vital structural components across industries, yet the influence of temperature variations on their dynamic behavior remains underexplored, necessitating combined experimental and numerical studies. This study aims to examine the effect of temperature changes, ranging from − 70 °C to 80 °C, on the natural frequencies and vibration modes of steel cylindrical shells. Non-contact experimental methods, including acoustic excitation via loudspeaker and modal hammer testing, are employed to measure natural frequencies of a steel cylindrical shell at ambient and extreme temperatures. Finite element modeling in COMSOL is performed concurrently to simulate the dynamic behavior, incorporating temperature-dependent material properties to validate experimental findings. This research confirms that temperature significantly alters the dynamic behavior of cylindrical shells, and accurate finite element models can predict these effects with acceptable precision, providing a cost-effective strategy for designing temperature-resilient structures.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230709","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}
Imed Kedim, Taoufik Moulahi, Abdelaala Ahmed, E. S. Elidy
{"title":"Analysis of thermoelastic wave behavior in double porous structures induced by laser pulse heating","authors":"Imed Kedim, Taoufik Moulahi, Abdelaala Ahmed, E. S. Elidy","doi":"10.1007/s00161-026-01450-y","DOIUrl":"10.1007/s00161-026-01450-y","url":null,"abstract":"<div><p>This paper investigates the propagation of two-dimensional thermoelastic waves in a semiconductor medium characterized by double porosity and subjected to pulsed laser excitation. The analysis is conducted within the frameworks of the Lord–Shulman (LS) and Green–Lindsay (GL) theories, which incorporate finite thermal wave speeds and relaxation effects. The governing equations describing the temperature, carrier density, and stress fields are analytically solved using the harmonic wave method. The study emphasizes the effects of time variation, thermoelastic coupling, and laser pulse intensity on the evolution of the dynamic fields. Three-dimensional graphical representations demonstrate the combined influence of these parameters on both thermal and mechanical responses. The findings show that an increase in the thermoelastic coupling parameter intensifies the interaction between thermal and elastic fields, while temporal variations and laser energy significantly modify wave amplitude and energy distribution. A comparative assessment of the CD, LS, and GL theories further clarifies the impact of relaxation times on thermoelastic wave propagation in double-porosity semiconductor materials.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230711","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}
Ajay Kumar, Praveen Ailawalia, Jatinder Kaur, Ahmed E. Abouelregal
{"title":"Advanced thermoelastic analysis of bidirectionally graded materials under Moore Gibson Thompson thermoelastic model","authors":"Ajay Kumar, Praveen Ailawalia, Jatinder Kaur, Ahmed E. Abouelregal","doi":"10.1007/s00161-025-01446-0","DOIUrl":"10.1007/s00161-025-01446-0","url":null,"abstract":"<div><p>This study introduces a novel investigation into a thermoelastic response of functionally graded materials (FGMs) by incorporating bidirectional non-homogeneity within the Moore–Gibson–Thompson thermoelasticity framework. The primary innovation lies in analyzing material properties with exponential variation in two directions, advancing beyond the conventional unidirectional gradation prevalent in existing literature. This work contributes a robust formulation and analytical solution of governing equations for this complex bidirectional case, employing the normal mode technique to derive explicit expressions for displacement components, temperature distribution, and stress fields. Numerical simulations, conducted using MATLAB, illustrate the model’s application at a specific time point, offering actionable insights. Results reveal that bidirectional gradation significantly enhances the material stiffness, reducing normal displacement compared to homogeneous or unidirectionally graded materials. Notably, the model achieves a nearly uniform tangential stress distribution, minimizing stress concentrations and bolstering resistance to shear failure. However, it induces a substantial, nonlinear increase in normal stress, which can be leveraged for targeted load-bearing applications. The thermal response is highly tailorable; bidirectional gradation enables a balanced temperature distribution, mitigating both the exponential rise from horizontal gradation and the gradual decrease from vertical gradation. These findings position the proposed model as a powerful engineering tool. By optimizing gradation parameters, engineers can design FGMs with customized thermomechanical properties, ideal for high-performance applications in aerospace, thermal barrier systems, and structural components under extreme conditions.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230861","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}
{"title":"Buckling and near-critical post-buckling of sandwich cylindrical shells with FG-GNP face sheets and an auxetic core under external pressure in a thermal environment: a closed-form approach","authors":"Ahmet Çalık","doi":"10.1007/s00161-026-01453-9","DOIUrl":"10.1007/s00161-026-01453-9","url":null,"abstract":"<div><p>This paper presents a closed-form formulation for the linear buckling and near-critical single-mode post-buckling response of sandwich cylindrical shells with functionally graded graphene nanoplatelet (FG-GNP) reinforced face sheets and an auxetic honeycomb core under external pressure and a thermal environment. The shell kinematics follow First-order Shear Deformation Theory (FSDT). Face-sheet properties are obtained from a temperature-dependent Halpin–Tsai scheme combined with a power-law through-thickness gradation, while the auxetic core is represented by equivalent orthotropic constants. A Winkler–Pasternak foundation is included. A single-harmonic Galerkin reduction yields a <span>(5times 5)</span> generalized eigenproblem for both simply supported (SS) and clamped–clamped (CC) boundary conditions; for CC edges, an energy-equivalent axial wavenumber is used to represent end restraint without introducing numerical mode shapes. For the baseline configuration, the minimum critical pressures are approximately 15.86 MPa at (m,n)=(1,10) for SS and 19.96 MPa at (0,11) for CC. Increasing temperature difference reduces <span>(p_{cr})</span>, whereas the foundation markedly increases it; larger FG index <i>k</i> (less GNP-rich faces) also decreases <span>(p_{cr})</span>. The Koiter single-mode expansion predicts a stable (hardening) post-buckling branch for the cases examined. The model is intended as a fast analytical screening and benchmarking tool under the stated assumptions.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01453-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146204857","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}
A. Zh. Khachatrian, G. P. Vardanyan, O. A. Zadoyan, Y. G. Virabyan
{"title":"Balance equation: local volumetric flow and surface fluxes in the theory OF continual media","authors":"A. Zh. Khachatrian, G. P. Vardanyan, O. A. Zadoyan, Y. G. Virabyan","doi":"10.1007/s00161-026-01455-7","DOIUrl":"10.1007/s00161-026-01455-7","url":null,"abstract":"<div><p>In this paper, using the example of mass balance for a continuous medium, a kinematic approach based on the concept of local volumetric flow is proposed for the transition from a discrete to a continuous description. This approach takes into account the possibility of discontinuities in the flow derivative at the boundaries of an elementary layer and allows one to derive the balance equation in differential form, eliminating the need for integral relations. It is shown that the inequality of jumps in the derivatives at the left and right boundaries is equivalent to the assumption of mass concentration at the layer boundaries. It is established that the coincidence of the sums of the left and right derivatives at both boundaries is a necessary condition for eliminating negative values of the mass density in the continuous limit.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146196475","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}
{"title":"The modified Kachanov method. Evaporation of multiple droplets","authors":"Ivan Argatov","doi":"10.1007/s00161-026-01456-6","DOIUrl":"10.1007/s00161-026-01456-6","url":null,"abstract":"<div><p>Evaporation of multiple sessile droplets deposited on an impermeable flat substrate is considered in the diffusion-limited isothermal regime, with particular emphasis on determining the total quasi-stationary vapor fluxes from the droplet surfaces. The proposed approximate solution is based on Kachanov’s approximation for the vapor concentration field in the semi-infinite air domain, expressed as a linear combination of solutions to single-droplet problems, with the coefficients determined by imposing appropriate Bubnov–Galerkin orthogonality relations to enforce the boundary conditions on the droplet surfaces. A comparison of the proposed modified Kachanov method with other approximate approaches is presented. The case of multiple thin circular sessile droplets is examined in detail.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01456-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146196583","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}
{"title":"An edge dislocation interacting with two circular compressible liquid inclusions","authors":"Xu Wang, Peter Schiavone","doi":"10.1007/s00161-025-01444-2","DOIUrl":"10.1007/s00161-025-01444-2","url":null,"abstract":"<div><p>We study the plane strain problem associated with two circular compressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation located at an arbitrary position. With the aid of the techniques of conformal mapping and analytic continuation, the boundary value problem is ultimately reduced to an infinite system of linear algebraic equations, which, when solved via truncation leads to the elastic field in the matrix and the internal uniform hydrostatic stress fields within the two circular liquid inclusions. In addition, an explicit expression for the image force acting on the edge dislocation is derived using the Peach-Koehler formula. Numerical results are presented to demonstrate the effect of the two liquid inclusions on the mobility and stability of the edge dislocation. The stiffening and hardening effect of the two liquid inclusions can be observed under certain circumstances.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146153359","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}
{"title":"Surface waves in magneto-piezoelectric thermo-microstretch material without energy dissipation","authors":"Sanjay Debnath, S. Sarat Singh, Holm Altenbach","doi":"10.1007/s00161-025-01448-y","DOIUrl":"10.1007/s00161-025-01448-y","url":null,"abstract":"<div><p>The present paper investigates the effects of magnetic and micropolarity on the propagation of Lamb, Rayleigh and flexural waves in generalized magneto-piezoelectric thermo-microstretch material. The thermoelastic theory without energy dissipation is used and the secular equations of the Lamb waves for both symmetric and anti-symmetric modes of vibration in the medium of finite thickness subject to suitable boundary conditions are derived. At short wavelength limits, the secular equations reduce to that of Rayleigh waves due to the nature of a semi-infinite medium. The secular equation of the anti-symmetric vibration reduces to the secular equation of flexural waves for longer wavelengths comparable with thickness of the medium. The phase speeds and attenuation coefficients are computed numerically from these secular equations using Aluminum epoxy material and the results are presented graphically. The numerical results have shown the simultaneous existence of three modes of dispersion and attenuation for Lamb, Rayleigh and flexural waves. The effect of magnetic field intensity and micropolarity on the phase speeds and attenuation of the three modes are noted. The path of particle motion for all three modes of Lamb, Rayleigh and flexural waves are evaluated analytically and numerically at different depths of the medium. Some special cases are reduced from the current formulation to validate our results.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146138511","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}
Lucca N. Schek, Florian Massing, Elena N. Vilchevskaya, Wolfgang H. Müller, Victor A. Eremeyev
{"title":"Deformation measures of micropolar theory in spatial and material description – A review","authors":"Lucca N. Schek, Florian Massing, Elena N. Vilchevskaya, Wolfgang H. Müller, Victor A. Eremeyev","doi":"10.1007/s00161-025-01438-0","DOIUrl":"10.1007/s00161-025-01438-0","url":null,"abstract":"<div><p>In this paper we present a review of some of the foundations of micropolar continua. The focus is initially on the classical representation of fields in spatial or material description. We shall remind the reader that traditionally both are based on the notion of the indestructible material particle. We will give reasons why these traditional concepts may fail, namely if we wish to study more complex processes, such as agglomeration or crushing of matter. As a way out, we will present a suitable extension, which we call <i>true spatial description</i>. We shall also demonstrate that the classical twofold approach can lead to serious misunderstandings that may result in unnecessary scientific controversies. Further attention is paid to the various deformation measures that are encountered in the literature on micropolar materials. It will be discussed under which circumstances which one should preferably be used. In this context the kinetic equation for the microinertia tensor deserves particular attention: it was recently extended by a production term. This additional feature can be used to describe processes in matter associated with micromorphological change, for example during crushing and milling of substances. Here a continuum description in terms of material, indestructible particles is no longer possible, and true spatial notation becomes a must.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01438-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961685","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}