{"title":"Finite element analysis of non-uniform functionally graded multi-cracked Timoshenko beams using an equilibrium-based formulation","authors":"H.A.F.A. Santos , V.V. Silberschmidt","doi":"10.1016/j.euromechsol.2025.106008","DOIUrl":"10.1016/j.euromechsol.2025.106008","url":null,"abstract":"<div><div>A novel finite element formulation is introduced for the static analysis of non-uniform functionally graded multi-cracked Timoshenko beams with small deformations. The cracks, assumed to remain open, are modelled using the so-called discrete spring approach, in which Dirac delta generalized functions are introduced into the bending flexibility of the beams. The formulation is derived on the basis of a complementary variational approach that involves only the elements’ shear forces and bending moments as the fundamental unknown fields. The corresponding element flexibility matrix is obtained in closed-form, with the crack contributions explicitly separated from the standard bending and shear flexibility terms. The numerical solutions produced by the formulation are strictly equilibrated, <em>i.e.</em>, they satisfy all equilibrium conditions of the associated boundary-value problem in strong form. The effectiveness and accuracy of the formulation are numerically assessed through its application to several benchmark problems. The obtained results are analysed and compared, where possible, to exact (or reference) solutions and solutions given by the standard displacement-based finite element formulation, clearly illustrating the capability of the formulation to deliver highly accurate results for both thin and thick beams, even on meshes with only a few degrees-of-freedom.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106008"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884235","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}
Hadi Arvin , Maryam Shahriari-kahkeshi , Hossein Ghahhari , Ömer Civalek
{"title":"Vibration mitigation in piezoelectric sandwiched nanocomposite beam-like structures considering Bouc-Wen hysteresis: An adaptive fuzzy sliding mode control approach","authors":"Hadi Arvin , Maryam Shahriari-kahkeshi , Hossein Ghahhari , Ömer Civalek","doi":"10.1016/j.euromechsol.2025.105961","DOIUrl":"10.1016/j.euromechsol.2025.105961","url":null,"abstract":"<div><div>In this study, an adaptive fuzzy sliding mode controller is proposed to mitigate the vibrations of a hysteretic sandwiched piezoelectric nanocomposite beam regarding system uncertainties, accounting for the intrinsic hysteresis behavior of the actuator layer. The core consists of a graphene sheet-reinforced composite, while the piezoelectric facesheets operate as both sensors and actuators. The actuator's hysteresis is modeled using a Bouc-Wen formulation with uncertain parameters. To compensate for this uncertain nonlinearity and suppress vibrations, an adaptive fuzzy sliding mode controller is developed, with stability guaranteed via Lyapunov's direct method. The results demonstrate the controller's high effectiveness in mitigating mechanical vibrations. The robustness of the proposed controller against parameter uncertainties allows it to manage small variations in structural stiffness and mass resulting from changes in the distribution pattern of the nanocomposite and the piezoelectric thickness ratio. As a result, the controlled deflection of the nanocomposite beam remains unaffected by these two parameters. The most important parameter affecting the controlled response is the type of boundary condition. Decreasing the piezoelectric layer thickness enhances the controller's effort. Due to the hysteresis behavior of the actuator, a steady-state controller effort remains in the system, which is more pronounced for the clamped-clamped nanocomposite beam. The corresponding hysteretic loop shows a similar observation for this boundary condition.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105961"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694498","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}
Chong Gao , Yihui Huang , Qian Sun , Bo Cao , Takeshi Iwamoto , Tsutomu Umeda , Takayuki Kusaka
{"title":"Fracture mechanism in SUS304 during small punch tests","authors":"Chong Gao , Yihui Huang , Qian Sun , Bo Cao , Takeshi Iwamoto , Tsutomu Umeda , Takayuki Kusaka","doi":"10.1016/j.euromechsol.2025.105953","DOIUrl":"10.1016/j.euromechsol.2025.105953","url":null,"abstract":"<div><div>Past experimental result reveals that a region of the fracture initiation in metastable austenitic stainless steel SUS 304 during a small punch test changes from the loading side to free surface with respect to the loading rate. Since a measurement of a time series of the martensite and temperature distribution, which strongly affects the fracture behavior, is difficult to be realized during testing, a precise finite element (FE) analysis is necessary to support further discussions on the mechanism of the loading rate sensitivity. In the current work, the phenomena observed in the tests are precisely reproduced through the FE analyses including the martensitic transformation and the damage evolution modelled by authors. The condition for the onset of crack extension is provided to assist the future works in determining where the initiation occurs. Even though the austenitic phase is dominant for the fracture, a larger damage variable appears in the region where a significant quantity of martensite is distributed. Simultaneously, the work clarifies the influence of reducing the amount of martensite with respect to the loading rate on ductility of the material. In the dynamic loading, it is newly discovered that the thermal softening plays an important role, inducing the fracture from the free surface of the specimen.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105953"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145646042","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}
Zixiang Zhang , Weile Wang , Yuanyuan Liu , Airong Liu , Sritawat Kitipornchai , Shaoyu Zhao
{"title":"Flexural-torsional buckling of circular arches with variable cross-section under uniformly distributed radial loads","authors":"Zixiang Zhang , Weile Wang , Yuanyuan Liu , Airong Liu , Sritawat Kitipornchai , Shaoyu Zhao","doi":"10.1016/j.euromechsol.2025.105995","DOIUrl":"10.1016/j.euromechsol.2025.105995","url":null,"abstract":"<div><div>Variable cross-section design is a common approach in practical engineering to achieve superior structural characteristics and better landscape effects. This strategy, however, produces complex inner forces in the arch axis and affects the structural out-of-plane flexural-torsional behaviors. To explore the buckling mode and reveal their failure mechanism, this paper carries out an in-depth analysis on the out-of-plane elastic buckling of variable cross-section circular arches with a variable in-plane boundary condition under uniformly distributed radial loads. The cross-section is assumed to be linearized tapered, and the in-plane equilibrium equations of the system are built considering an energy principle. By solving the in-plane governing equations via a harmonic differential quadrature (HDQ) algorithm, the pre-buckling cross-sectional inner forces are obtained. Based on the assumption that the out-of-plane flexural-torsional buckling occurs from an adjacent pre-buckling in-plane deformed equilibrium state, the out-of-plane total potential energy is established. The critical buckling load of variable cross-section circular arches is then determined by solving the out-of-plane governing equations corresponding to lateral displacement and twist angle. Effects of in-plane boundary conditions, cross-section shape, included angle, and slenderness ratio on the flexural-torsional behaviors are further explored. It is found that as the cross-section change parameter continues to grow, the out-of-plane critical buckling load of variable cross-section circular arches decreases gradually, the buckling position shifts towards the arch crown.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105995"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797708","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":"Unveiling the role of peak load in the stability and growth of interlaminar fatigue damage in composite structures","authors":"Angela Russo, Rossana Castaldo, Aniello Riccio","doi":"10.1016/j.euromechsol.2025.106001","DOIUrl":"10.1016/j.euromechsol.2025.106001","url":null,"abstract":"<div><div>Understanding the stability of delamination growth is essential for ensuring the reliability of composite structures under compressive fatigue loading. In post-buckling regimes, where crack propagation can become highly unstable and nonlinear, even small variations in the applied load may drastically alter damage evolution and residual strength. Despite its critical role, the stability of interlaminar crack growth under cyclic compression remains poorly understood, demanding refined numerical strategies to capture its complex behaviour. This work addresses this gap by investigating how the peak compressive load influences the stability and progression of delamination in composite structures.</div><div>A dedicated numerical approach has been developed to study these effects. The methodology, named SMART LOOP, couples the Virtual Crack Closure Technique (VCCT) with the Paris Law-based damage accumulation model. Such method employs an adaptive timestep strategy to ensure precise load control and mesh-independent predictions. SMART LOOP transforms force-controlled fatigue simulations into a sequence of displacement-controlled static analyses, where the displacement input is automatically adjusted to reach the target load level. This produces delamination length results that are independent of element size, eliminating the need for mesh refinement strategies.</div><div>A series of simulations has been carried out on an Omega-stiffened composite panel subjected to three different compressive peak loads (25.2, 27.1, and 29.1 kN). The numerical results have been compared with experimental data from the literature to enhance the understanding of the unstable delamination growth phenomenon. This provides additional insights into failure mechanisms and complements the experimental observations.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106001"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840844","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}
J.C. Zhu , M. Ben Bettaieb , F. Abed-Meraim , B. Jia , J. Li
{"title":"Influence of shear stress on ductile failure initiation: a micromechanical analysis of strain localization","authors":"J.C. Zhu , M. Ben Bettaieb , F. Abed-Meraim , B. Jia , J. Li","doi":"10.1016/j.euromechsol.2026.106019","DOIUrl":"10.1016/j.euromechsol.2026.106019","url":null,"abstract":"<div><div>Shear stress is recognized as a critical factor influencing the ductile failure process. In the present work, we investigate ductile failure initiation under shear-dominated loading by identifying the onset of strain localization, which is predicted using a rigorous bifurcation analysis. Micromechanical computations are performed using cubic voided unit cells (UCs) subjected to fully periodic boundary conditions. Proportional stressing is imposed to keep constant stress triaxiality (<em>T</em>) and Lode parameter (<em>L</em>) throughout the deformation history of UCs. In the proportional stressing, two loading configurations are realized to comparatively study the effect of shear stress component for a given pair of <em>T</em> and <em>L</em>: normal stresses (without shear) <em>versus</em> normal stresses combined with one shear stress component. The effects of initial porosity and void configuration (pattern of voids arrangement) are also systematically analyzed. The results show that the influence of shear stress is strongly modulated by the amount of the initial porosity. While shear stress promotes strain localization at low initial porosity, it conversely delays it at high initial porosity within a specific range of Lode parameters. This porosity-dependent trend reversal is rationalized by a transition from a ligament-thinning-dominated failure mode to an intervoid-shearing-dominated failure mode as the stress state varies. Furthermore, for a given overall initial porosity, the void configuration significantly affects the critical strain locus, the extent of which depends on the imposed triaxiality. These findings provide valuable micromechanical insights for refining predictive modeling in engineering applications.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106019"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976834","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}
Yuanpeng Liu , Meixin Ge , Guang Zeng , Kun Chen , Shunxin Liu , Wenjian Tang , Longxin Zhu
{"title":"Mechanical properties, microstructure evolution, and strengthening mechanism of Al-Mg-Si alloy welded joints using double-sided friction stir welding","authors":"Yuanpeng Liu , Meixin Ge , Guang Zeng , Kun Chen , Shunxin Liu , Wenjian Tang , Longxin Zhu","doi":"10.1016/j.euromechsol.2025.105987","DOIUrl":"10.1016/j.euromechsol.2025.105987","url":null,"abstract":"<div><div>As the demand for lightweight materials grows, aluminum alloys are increasingly utilized across various industries. However, conventional fusion welding of medium-thick aluminum plates often results in defects. Friction stir welding (FSW), a solid-state joining process, effectively mitigates these issues. This study investigates double-sided FSW (DS-FSW) and single-sided FSW (SS-FSW) of 6061-T6 aluminum alloy through combined experiments and numerical simulations. The thermal cycles, stress distribution, material flow, microstructure evolution, and mechanical properties of the joints are systematically examined. Results demonstrate that DS-FSW joints exhibit a 31 % higher yield strength (228 MPa) compared to SS-FSW joints (174 MPa), along with superior tensile strength. However, both joint types show lower elongation than the base material, with DS-FSW slightly lower (4.43 %) than SS-FSW (4.87 %). Microhardness distribution is more heterogeneous in DS-FSW, with higher hardness in the heat-affected zone but lower in the nugget zone. Microstructural analysis reveals finer grains, higher dislocation density, and a greater proportion of high-angle grain boundaries in DS-FSW. The study innovatively proposes the hetero-deformation induced (HDI) strengthening mechanism in DS-FSW joints, offering valuable insights for optimizing welding processes for medium-thick aluminum plates in aerospace, automotive, and energy applications.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105987"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749780","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}
D. Ambrosi , A. Favata , R. Paroni , G. Tomassetti
{"title":"Oncogenic transformation of tubular epithelial ducts: How mechanics affects morphology","authors":"D. Ambrosi , A. Favata , R. Paroni , G. Tomassetti","doi":"10.1016/j.euromechsol.2025.105984","DOIUrl":"10.1016/j.euromechsol.2025.105984","url":null,"abstract":"<div><div>We derive a continuum mechanical model to capture the morphological changes occurring at the pre-tumoral stage of epithelial tissues. The mathematical model, derived from first principles, accounts for the competition between the bulk elasticity of the epithelium and the surface tension of the apical and basal boundaries. The variation of the energy functional yields the Euler–Lagrange equations to be numerically integrated. The numerical results reproduce a variety of morphological shapes, from invagination to evagination, depending on the ratio between bulk and surface energy at variance of the length of the section. In particular, using parameters independently measured, we are able to reproduce experimental data reported for a ring partially made of transformed cells.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105984"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694499","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":"Homogenizing elastic lattices with mechanisms","authors":"Basile Audoly , Claire Lestringant , Hussein Nassar","doi":"10.1016/j.euromechsol.2025.105956","DOIUrl":"10.1016/j.euromechsol.2025.105956","url":null,"abstract":"<div><div>We propose an asymptotic method for homogenizing periodic elastic lattices that works in the presence of mechanisms, both of the macroscopic type (strain-producing modes) and of the microscopic type (internal modes). When a microscopic mechanism is present, the unit-cell problem produced by classical homogenization is singular. It can be fixed by including the amplitude <span><math><mrow><mi>θ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> of the mechanism as an additional macroscopic degree of freedom (enrichment variable) contributing to the effective energy via its gradient <span><math><mrow><mo>∇</mo><mi>θ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span>. When a macroscopic mechanism is present, homogenization delivers a degenerate effective energy at leading order, which can be regularized by accounting for the strain gradient. We introduce an asymptotic second-order homogenization scheme that integrates these two features: it delivers an effective energy capturing both the strain-gradient effect <span><math><mrow><mo>∇</mo><mi>ɛ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> relevant to macroscopic mechanisms, and the <span><math><mrow><mo>∇</mo><mi>θ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> regularization relevant to microscopic mechanisms, if any is present. The versatility of the approach is illustrated with a selection of lattices displaying a variety of effective behaviors. It follows a unified pattern that leads to a classification of these effective behaviors. Whereas the procedure delivers known effective models for elastic lattices without mechanisms, it can generate novel effective models for lattices possessing mechanisms.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105956"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748723","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":"The isotropic relaxed micromorphic model in polar coordinates and its application to an elastostatic axisymmetric extension problem","authors":"Esmaeal Ghavanloo , Patrizio Neff","doi":"10.1016/j.euromechsol.2025.105964","DOIUrl":"10.1016/j.euromechsol.2025.105964","url":null,"abstract":"<div><div>In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential equations. To obtain an analytical solution, modified Bessel functions are utilized and closed-form solutions for the displacement and micro-distortion are obtained. We show how certain limit cases (classical linear elasticity), which are naturally included in the relaxed micromorphic model, can be efficiently achieved. Furthermore, numerical results are calculated and the effects of various parameters are examined. The results can be used to calibrate and check corresponding finite element codes.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 105964"},"PeriodicalIF":4.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145646041","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}