{"title":"Unsteady thermoelastic-diffusive vibrations of a Bernoulli-Euler beam on an elastic foundation","authors":"Andrei V. Zemskov , Le Van Hao","doi":"10.1016/j.euromechsol.2025.105707","DOIUrl":"10.1016/j.euromechsol.2025.105707","url":null,"abstract":"<div><div>This paper addresses the problem of unsteady vibrations of a Bernoulli–Euler beam, taking into account the relaxation effects in thermal and diffusion processes. The original mathematical model comprises a system of equations describing unsteady bending vibrations, incorporating both heat and mass transfer. These equations are derived from the general model of thermoelastic diffusion in a continuum, using the variational D'Alembert principle. As an example, a simply supported three-component beam composed of an alloy of zinc, copper, and aluminum is considered. The interaction among the mechanical, thermal, and diffusion fields in the beam is investigated under a mechanical load distributed along its length. The influence of relaxation effects on the kinetics of heat and mass transfer is analyzed. The solution is presented both in analytical form and as spatiotemporal 3D graphs of displacement, temperature increment, and concentration increment fields.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105707"},"PeriodicalIF":4.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Awantika Mishra, Aquib Ahmad Siddiqui, Sushma Santapuri
{"title":"Computational analysis of limit point instability in circular magnetoelastic membranes","authors":"Awantika Mishra, Aquib Ahmad Siddiqui, Sushma Santapuri","doi":"10.1016/j.euromechsol.2025.105686","DOIUrl":"10.1016/j.euromechsol.2025.105686","url":null,"abstract":"<div><div>Membranes made of soft materials are prone to limit point instability, characterized by a loss of monotonicity in pressure-deflection relationship. In soft active materials that respond to external fields (e.g. magneto-/electro-elastic materials), onset of this instability can be controlled using the external field. In this work, limit point instability in magnetoelastic circular membranes is analyzed in the presence of magnetic field and transverse pressure. Forces and deformation in the membrane are studied for a weakly magnetizable material medium under axisymmetric loading and transverse magnetic field while incorporating material nonlinearity, Maxwell stress, and pre-stretch effects. An <span><math><mi>h</mi></math></span>-order membrane theory is presented and the resulting nonlinear system of ordinary differential equations are solved using a boundary value problem (BVP) solver in MATLAB. BVP solvers are prone to convergence issues for nonlinear problems and exhibit a high sensitivity to the initial guesses, particularly in the unstable regime. An iterative computational scheme is proposed here to alleviate this issue by improving the initial guesses provided to the solver. The results are validated with existing literature for special cases and several parametric studies are performed to understand the response of a magnetoelastic membrane actuator under combined magnetomechanical loading. Improved convergence for a wide range of input values is observed, allowing a more comprehensive study of soft magnetoelastic membrane actuators. The computational framework presented in this work can be applied towards device design in soft robotics.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105686"},"PeriodicalIF":4.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdoul Magid Amadou Sanoko , Simon Essongue , Lionel Gélébart , Lucas Lapostolle , Léo Morin , Joseph Paux
{"title":"A FFT-based numerical scheme for the transient conductivity of heterogeneous materials with non-periodic boundary conditions","authors":"Abdoul Magid Amadou Sanoko , Simon Essongue , Lionel Gélébart , Lucas Lapostolle , Léo Morin , Joseph Paux","doi":"10.1016/j.euromechsol.2025.105680","DOIUrl":"10.1016/j.euromechsol.2025.105680","url":null,"abstract":"<div><div>The aim of this work is to develop FFT-based solvers for transient diffusion in heterogeneous materials subjected to non-periodic (Dirichlet/Neumann) boundary conditions. We focus on a problem of thermal conductivity and derive a theta-method which includes an implicit solver for transient thermal conductivity in heterogeneous materials. The method is based on a fixed-point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space based on mixed sine–cosine series. The solution field is decomposed as a known term verifying the boundary conditions and a fluctuation (unknown) term described by appropriate sine–cosine series. The solution of the auxiliary problem involves discrete sine–cosine transforms, of type I and III, which makes the solver rely on the computational complexity of fast Fourier transforms. The method is applied to the prediction of transient thermal fields in a composite material subjected to non periodic boundary conditions.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105680"},"PeriodicalIF":4.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143916463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dilek Atilla Yolcu , Berkan Öztürk , Gözde Sarı , Buket Okutan Baba
{"title":"Free vibration response of sandwich composites with auxetic chiral core","authors":"Dilek Atilla Yolcu , Berkan Öztürk , Gözde Sarı , Buket Okutan Baba","doi":"10.1016/j.euromechsol.2025.105700","DOIUrl":"10.1016/j.euromechsol.2025.105700","url":null,"abstract":"<div><div>The aim of this study was to investigate the influence of auxetic core structure pattern and boundary conditions on the vibration behavior of square flat sandwich panels. The sandwich composite panels consist of three layers, with the top and bottom skins of orthotropic E-glass/epoxy laminates and the central auxetic core layer of chiral structures with negative Poisson's ratio using the isotropic PLA material. The core structures consist of tetrachiral, anti-tetrachiral, and hexachiral auxetic cells with constant ligament length and node diameter. The face sheets were produced by the hand-layup method and a three-dimensional printing technique was utilized to create auxetic cores. In order to find natural frequencies and the mode shapes of sandwich panels with different auxetic cores, the numerical analyses were performed for the sandwich panels under free-free (F–F), simply supported (S–S) and clamped (C–C) boundary conditions using ANSYS software. Additionally, the finite element analysis results were compared with vibration test results that were conducted on sandwich panels under only the freely boundary condition to confirm the accuracy and efficiency of the finite element analysis. The results obtained from the simulation suggest that the auxetic chiral cores have promising properties for dynamic performance. In particular, hexachiral cores were shown to effectively increase the natural frequency compared to anti-tetrachiral and tetrachiral cores. Although the use of auxetic core structure in sandwich structures significantly increases the natural frequency, the natural frequencies of sandwich panels with different core patterns are close to each other.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105700"},"PeriodicalIF":4.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A systematic finite element procedure for flexoelectric piezoelectric nanobeams using the asymptotic numerical method","authors":"S. Abdelkhalek , F. Najar","doi":"10.1016/j.euromechsol.2025.105679","DOIUrl":"10.1016/j.euromechsol.2025.105679","url":null,"abstract":"<div><div>Analysis of small-scale beam structures under the combined effects of flexoelectric and piezoelectric responses is of interest in this work. The problem is tackled by the derivation of a mixed finite element model accounting for geometric nonlinearity and large strains through a total Lagrangian representation, so that the von Karman strain can be considered. In addition, a Penalty method is introduced to account for higher order stress tensors. The asymptotic numerical method (ANM) is implemented for the first time in this context to deal with nonlinearities. To avoid tedious manual calculation of the ANM power series terms, a systematic procedure is proposed in this work with an application to a clamped–clamped nanobeam. The obtained model is applied for different flexoelectric-piezoelectric materials, and the results indicate that the applied electric voltage can lead to buckling of the beam. However, this instability is observed for negative voltages for some materials, and positive voltages for others, depending on a combination of flexoelectric and piezoelectric coefficients of the material.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105679"},"PeriodicalIF":4.4,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Anisotropic elastic metamaterials for novel wave manipulation: a review","authors":"Jeseung Lee , Yoon Young Kim","doi":"10.1016/j.euromechsol.2025.105696","DOIUrl":"10.1016/j.euromechsol.2025.105696","url":null,"abstract":"<div><div>Elastic waves are crucial in non-destructive testing and evaluation across industrial and medical fields. While elastic metamaterials have been extensively studied for elaborate wave manipulation, those exhibiting isotropic or orthotropic behavior often fail to achieve certain elastic wave phenomena involving coupled normal and shear deformations. Therefore, their applicability is limited in many practical contexts. To overcome these limitations, elastic metamaterials with extraordinary anisotropy—exhibiting properties not found in nature—have emerged as a promising solution. This paper elucidates the fundamental design principles of anisotropic elastic metamaterials and their applications for unconventional wave manipulation.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105696"},"PeriodicalIF":4.4,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deep Malu , Dongjing He , Wenting Shi , M.G. Finn , Yuhang Hu
{"title":"Statistical chain-based model for predicting drug release from degradable hydrogels","authors":"Deep Malu , Dongjing He , Wenting Shi , M.G. Finn , Yuhang Hu","doi":"10.1016/j.euromechsol.2025.105699","DOIUrl":"10.1016/j.euromechsol.2025.105699","url":null,"abstract":"<div><div>Hydrogel-based drug delivery systems have emerged as promising platforms for controlled cargo release due to their tunable degradation and swelling properties. These systems can trap drug particles within their polymeric network, releasing them gradually as the network degrades and swells. This study presents a statistical chain-based multiphysics model that integrates degradation, swelling, and diffusion to predict drug release profiles from degradable hydrogels. The model, calibrated using a recently developed degradable hydrogel, incorporates the interplay between chain-level degradation, dynamic mesh size changes, and evolving cargo diffusivity. Experimental validation demonstrates the model's accuracy, and parametric studies highlight the impact of various design parameters such as cargo size, gel geometry, and crosslinker functionality on release profiles. This framework provides insights into hydrogel design for tailored drug release, addressing limitations in current phenomenological approaches.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105699"},"PeriodicalIF":4.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A semi-analytical method for determining homogenized relaxation times and moduli in Prony series of a heterogeneous viscoelastic material","authors":"Huilin Jia , Zifeng Yuan","doi":"10.1016/j.euromechsol.2025.105683","DOIUrl":"10.1016/j.euromechsol.2025.105683","url":null,"abstract":"<div><div>This work introduces a semi-analytical method to obtain homogenized relaxation times and moduli in terms of Prony series of a heterogeneous viscoelastic material. This can be treated as an extension of linear homogenization theory which calculates homogenized elastic properties of a heterogeneous elastic material. The heterogeneous viscoelastic material is consist of multiple phases where each phase is assumed as a standard-solid viscoelastic material. The idea of so-called reduced-order-homogenization method is introduced to propose a set of residual-free governing equations with respect to the averaged strains and eigenstrains of all the phases. The set of governing equations can be rewritten as a set of ordinary differential equations (ODEs), which can be solved analytically to obtain relationship between the phase strains and the macroscopic strains. The solution of the ODEs stems from an eigenvalue problem, where the eigenvalues are the homogenized relaxation times. In addition, the relaxation moduli can be evaluated through the ODEs as well. Accordingly, a homogenized viscoelastic material in term of Prony series can be determined. Four sets of numerical tests are proposed to verify the semi-analytical method: unit cell tests, tension tests on a plate with a hole, pure bending tests, and torsion tests. The results from these tests demonstrate a strong agreement between the homogenized model and direct numerical simulations. Additionally, we compared our model against experimental measurements, further confirming the accuracy and reliability of our proposed approach.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105683"},"PeriodicalIF":4.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bending mechanics of biomimetic scale plates","authors":"Pranta Rahman Sarkar , Hossein Ebrahimi , Md Shahjahan Hossain , Hessein Ali , Ranajay Ghosh","doi":"10.1016/j.euromechsol.2025.105664","DOIUrl":"10.1016/j.euromechsol.2025.105664","url":null,"abstract":"<div><div>Dermal scale-inspired structures are a unique class of multi-material systems that can exhibit significant nonlinearity and evolving anisotropy, even in small strains. In this work, architecture–property relationships are derived for both synclastic and anticlastic curvatures of the plate using analytical modeling, finite elements, and experiments. The developed model outlines analytical relationships between geometry, deformation, and bending response of the system. The results show that, as the scales engage, both synclastic and anticlastic deformations show non-linear scale contact kinematics and cross-curvature sensitivity of moments, resulting in strong curvature-dependent elastic nonlinearity and emergent anisotropy. The anisotropy of bending rigidities and their evolution with curvatures are affected by both the direction and magnitude of bending, as well as scale geometry parameters, and their distribution on the substrate. Similar to earlier beam-like substrates, kinematic locked states were found to occur; however, their existence and evolution are also strongly determined by scale geometry and imposed cross-curvatures. This validated model helps us to quantify bending response, locking behavior, and their geometric dependence, paving the way for a deeper understanding of the nature of nonlinearity and anisotropy of these systems.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105664"},"PeriodicalIF":4.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jacopo Ciambella , Giovanni Lancioni , Nico Stortini
{"title":"A finite viscoelastic phase-field model for prediction of crack propagation speed in elastomers","authors":"Jacopo Ciambella , Giovanni Lancioni , Nico Stortini","doi":"10.1016/j.euromechsol.2025.105678","DOIUrl":"10.1016/j.euromechsol.2025.105678","url":null,"abstract":"<div><div>Crack propagation in soft viscoelastic solids is crucial in many applications, yet accurate modeling of their fracture behavior, particularly the rate-dependent fracture toughness, remains a challenge. We address this by proposing a thermodynamically consistent phase-field fracture model for viscoelastic materials. The model incorporates both equilibrium and non-equilibrium elastic energies, along with distinct dissipation mechanisms for viscous losses and irreversible damage processes. Importantly, two characteristic time scales are introduced, reflecting the distinct nature of viscous relaxation and damage evolution, both of which significantly influence crack propagation dynamics. Numerical simulations are performed to investigate the impact of the different energy contributions on the fracture propagation in elastomeric membranes, accompanied by comparisons to experimental results.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"113 ","pages":"Article 105678"},"PeriodicalIF":4.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}