{"title":"Dynamics of a beam on a displacement-driven nonlocal foundation under a moving load","authors":"F.M.F. Simões, A. Pinto da Costa","doi":"10.1016/j.ijsolstr.2026.113877","DOIUrl":"10.1016/j.ijsolstr.2026.113877","url":null,"abstract":"<div><div>This paper studies the dynamic response of an infinite Euler–Bernoulli elastic beam on a displacement-driven nonlocal elastic foundation, under the action of a concentrated load moving at constant velocity. The steady-state response of the system is analytically obtained and explicitly solved. In particular, we show that, in the limit when the foundation characteristic length vanishes, the steady-state formulation of the local foundation problem is recovered. Furthermore, it is shown that increasing the foundation’s characteristic length reduces the critical velocity of the moving load. These findings are confirmed through an analysis of the dynamic response of a finite beam, on the same foundation and subjected to identical loading conditions, using the finite element method.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113877"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chenglong Wu , Xiaoxia Zhen , Chang He , Guiyuan Liu , Rui Rao , Qinhe Li
{"title":"Semi-active suppression of cable 1/2-order subharmonic resonance in a cable–beam coupled system using time-delayed velocity feedback","authors":"Chenglong Wu , Xiaoxia Zhen , Chang He , Guiyuan Liu , Rui Rao , Qinhe Li","doi":"10.1016/j.ijsolstr.2026.113880","DOIUrl":"10.1016/j.ijsolstr.2026.113880","url":null,"abstract":"<div><div>Cable–beam coupled systems in long-span bridges may exhibit strong 1/2-order subharmonic resonance of the cable when the beam is excited near twice the cable’s natural frequency. This cross-component 2:1 excitation mechanism, where the external load is applied to the beam but the nonlinear response emerges in the cable, has rarely been examined despite its potential to trigger large-amplitude cable vibration. To address this problem, a reduced-order cable–beam coupled model is formulated using Hamilton’s principle, retaining the essential quadratic and cubic coupling terms responsible for nonlinear energy transfer. The method of multiple scales is employed to analytically reveal the formation mechanism and amplitude–frequency characteristics of the cable’s 1/2-order subharmonic response. To suppress this nonlinear vibration, a time-delayed velocity feedback strategy is introduced into the cable equation. Furthermore, a semi-active control scheme based on a magnetorheological (MR) damper is developed, where a mapping algorithm is adopted to reproduce the desired delayed control force. Numerical simulations demonstrate that the proposed control method effectively eliminates subharmonic resonance and stabilizes the cable response. The findings provide new theoretical insight into nonlinear coupling-induced subharmonic vibration and offer practical guidance for vibration control in long-span cable-supported bridges.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113880"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-material FE model for the flexible and extensible sliding sleeve problem","authors":"Stefan Ramsauer, Yury Vetyukov","doi":"10.1016/j.ijsolstr.2026.113867","DOIUrl":"10.1016/j.ijsolstr.2026.113867","url":null,"abstract":"<div><div>A novel finite element model is proposed for the static problem of a rod that slides without friction in a sleeve, with both components considered flexible and extensible. The tensional compliance gives access to internal axial forces and allows for a direct computation of the tangential contact forces that result from the variability of the contact length. Two configurational parameters are introduced to characterize the horizontal position and extent of the insertion. Upon each of the system’s segments, a Eulerian parametrization is used, followed by an individual normalization. Based on this kinematic description, a finite element discretization is applied featuring elements that neither stick with the material nor remain at their initial spatial position. The discretized model is employed to simulate the system’s response under external loading conditions. Being directly accessible due to the extensibility, the Hamiltonian is numerically shown to retain a constant value for each component even across domains with and without contact. Following an analytic approach, a formula for the tangential contact force is proposed, which also takes precurvature into account. Equipped with the new finite element model, simulations are run that strongly support the suggested relation.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113867"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prediction of rupture instability during deep drawing using Gated Recurrent units based on conditional sequence generation","authors":"Yingjian Guo , Lihua Wang , Magd Abdel Wahab","doi":"10.1016/j.ijsolstr.2026.113874","DOIUrl":"10.1016/j.ijsolstr.2026.113874","url":null,"abstract":"<div><div>This study proposes a hybrid method for predicting the forming limit of cylindrical cup deep drawing by integrating analytical modeling, Finite Element Method (FEM), and Gated Recurrent Units (GRUs). First, an analytical model is established to describe the theoretical forming load-bearing capacity during the sheet metal drawing process. FEM is then used to obtain forming force–displacement curves under various process parameter conditions. By identifying the intersection between the simulated forming force curves and the theoretical limit load curve, the fracture height, representing the maximum drawing limit, is determined and validated against experimental data from literature, confirming the accuracy and effectiveness of the proposed approach. Building upon this, a comprehensive dataset of forming forces is generated using FEM under a wide range of process conditions, including variations in the coefficient of friction, die radius, punch radius and blank holder force. This dataset is used to train a GRU neural network model to enable rapid prediction of the drawing force. Finally, by combining the GRU-predicted force curves with the analytically derived load-bearing capacity, the maximum punch displacement under arbitrary process parameters was efficiently obtained. The findings indicate that the proposed approach delivers accurate predictions and exhibits robust generalization performance, while significantly reducing the computational cost associated with process parameter optimization. This work provides an efficient and reliable surrogate modeling framework for the intelligent design of deep drawing processes.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113874"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 electro-mechanical-orientational coupling deformation of dielectric nematic elastomers: Modeling and analysis","authors":"Yiwei Xu , Shenxin Gong","doi":"10.1016/j.ijsolstr.2026.113876","DOIUrl":"10.1016/j.ijsolstr.2026.113876","url":null,"abstract":"<div><div>Dielectric nematic elastomers (DNEs) exhibit electroactive deformations arising from the intrinsic coupling among mechanical deformation, electric fields, and reorientation of the nematic director, which serves as the local material axis. In most existing electro-mechanical-orientational (EMO) coupling models for DNEs, the mechanical elastic contribution is formulated based on the neo-classical ideal-soft or semi-soft elastic energy densities, which fail to capture the transversely isotropic elasticity observed experimentally and omit the strain-stiffening of polymer networks. As a result, these models are unable to accurately predict certain qualitative electroactive deformation behaviors, including electromechanical instability. To address this limitation, this work develops a mechanical elastic constitutive description within an EMO coupling framework by incorporating both transversely isotropic elasticity and strain stiffening. The resulting model is used to investigate homogeneous anisotropic electroactive deformations and associated instability behaviors of monodomain DNE films, and 3D finite element simulations are further performed to study inhomogeneous electroactive deformations with spatially varying director orientations. The results highlight the critical roles of elastic anisotropy, strain stiffening, and director reorientation in governing the electroactive responses of DNEs.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113876"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhen Dai , Fei Xu , Qiuzu Yang , Jiayi Wang , Wei Feng
{"title":"Adhesion strength prediction of cold spray particle via smoothed particle hydrodynamics","authors":"Zhen Dai , Fei Xu , Qiuzu Yang , Jiayi Wang , Wei Feng","doi":"10.1016/j.ijsolstr.2026.113875","DOIUrl":"10.1016/j.ijsolstr.2026.113875","url":null,"abstract":"<div><div>Adhesion strength is a key indicator determining the integrity and service performance of cold spray coatings. However, traditional evaluation methods (such as pull-off tests) are not only constrained by adhesive strength but also involve time-consuming and costly processes. Consequently, developing reliable numerical prediction methods hold significant scientific and engineering value. This paper establishes a Smoothed Particle Hydrodynamics (SPH) model integrated with a physical interface interaction model to predict the adhesion strength of cold spray particles. The model simulates the formation of metal-to-metal connections between particle and substrate and utilizes the stable attractive forces generated post-bonding to enable direct numerical prediction of adhesion strength. The results indicate that adhesion strength increases nonlinearly with impact velocity, with the rate of increase gradually slowing, which is closely linked to jetting and inward curling behavior at the particle periphery. The predictions show good agreement with experimental data, validating the model’s effectiveness. Furthermore, applying this method to deposition processes under various process parameters (spray angle, particle size, and initial temperature) systematically reveals quantitative relationships between these parameters and adhesion strength, demonstrating the model’s potential for optimizing process windows and tailoring performance. Overall, this study provides a physics-based numerical tool for understanding and enhancing the bonding performance of cold spray coatings.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"330 ","pages":"Article 113875"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Formulating a constitutive model for anisotropic sand using stress probing analysis","authors":"D. Liao, Z.X. Yang","doi":"10.1016/j.ijsolstr.2025.113819","DOIUrl":"10.1016/j.ijsolstr.2025.113819","url":null,"abstract":"<div><div>Natural sands often possess anisotropic fabric that significantly influences their mechanical behaviour. This study examines the incremental stress–strain relationship of anisotropic sand through stress probing tests conducted via discrete element simulations. The tests apply incremental stress in various directions to identical soil samples, yielding corresponding strain increments. Numerical probing tests under various initial states were conducted to assess the effects of fabric anisotropy on the incremental response of sand. Based on the test results, explicit formulations for the yield surface, plastic flow direction, and plastic modulus were derived, facilitating the development of an anisotropic constitutive model within the framework of anisotropic critical state theory. The proposed model can accurately capture the behaviour of anisotropic sand under varying initial states and loading conditions.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113819"},"PeriodicalIF":3.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boundary element method for normal contacts of poroelastic layers","authors":"Jean-Emmanuel Leroy, Valentin L. Popov","doi":"10.1016/j.ijsolstr.2026.113866","DOIUrl":"10.1016/j.ijsolstr.2026.113866","url":null,"abstract":"<div><div>The paper builds upon a method previously developed and introduced by the authors for the normal contact of a rigid smooth indenter with a poroelastic half-space extending it to a single layer. Fundamental solutions in the Fourier and Laplace space for two types of the layer support, bonded and unbonded, are presented. It is shown how using these solutions discrete kernels can be constructed, enabling FFT-accelerated computation of the layer response to applied pressure distributions in both space and time, and therefore efficient solution of contact problems with indenters of arbitrary shape.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113866"},"PeriodicalIF":3.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theoretical modeling of out-of-plane crashworthiness of a wavy tri-chiral honeycomb","authors":"Yilin Zhu , Miao Zhou , Xue Rui , Chao Yu , Yifeng Zhong , Chuanzeng Zhang","doi":"10.1016/j.ijsolstr.2026.113873","DOIUrl":"10.1016/j.ijsolstr.2026.113873","url":null,"abstract":"<div><div>Chiral honeycombs are demonstrated to exhibit exceptional out–of–plane mechanical properties owing to their distinctive chirality. However, systematic investigations, particularly theoretical studies, remain limited. In this work, a comprehensive study is conducted on the out‑of‑plane crashworthiness of a prototypical chiral topology, namely the wavy tri‑chiral honeycomb (WTCH). The configuration of the WTCH can be interpreted as a transformation of the conventional hexagonal honeycomb (CHH), achieved by substituting its straight cell walls with curved segments. Finite element (FE) simulations are first performed to elucidate the out-of-plane crashworthiness and underlying deformation mechanism of the WTCH. Under quasi-static loading condition, three distinct collapse modes, i.e., progressive folding, concertina-like buckling, and global bending, are identified, governed by a trade-off between wave slope and cell wall slenderness ratio. The latter two modes are characterized by significantly elevated peak stresses, rendering them unfavorable for energy-absorbing applications. In contrast, under dynamic loading conditions, all WTCH configurations exhibit a progressive folding collapse mode. Based on the identified deformation mechanism, theoretical models for predicting the plateau stresses of the WTCH undergoing progressive folding collapse are developed using the Simplified Super Folding Element (SSFE) theory and validated against numerical simulations, showing strong agreement. Finally, a quantitative comparison with the CHH demonstrates that the WTCH achieves at least a 47 % improvement in specific energy absorption under identical cell size and relative density, along with consistently higher crush force efficiency. These findings provide valuable insights for the structural optimization and engineering applications of wavy chiral honeycombs in crash protection and safety contexts.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113873"},"PeriodicalIF":3.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear vibrations and dynamic instability analysis of a two-directional functionally graded conical shell under parametric and external excitations","authors":"Amin Rezaeezadeh , Babak Mirzaei Moghaddam , Ali Mohammadi , Arash Eftekhari","doi":"10.1016/j.ijsolstr.2025.113826","DOIUrl":"10.1016/j.ijsolstr.2025.113826","url":null,"abstract":"<div><div>This paper analyzes the nonlinear vibrations and dynamic instability of two-directional functionally graded (2DFG) conical shells. To this end, the shell dynamic model is derived using the first-order shear deformation theory (FSDT) and nonlinear strain–displacement relations. The shell is subjected to a time-varying axial parametric force and harmonic external transverse excitation. In this article, a new hybrid solution method is used. Specifically, the generalized differential quadrature method (GDQM) is applied to solve the eigenvalue problem and obtain the mode shape vectors. These mode shapes are then used to discretize the equations using the Galerkin method. The multiple time scale method (MTSM) is used to analyze the nonlinear dynamics of the system. Initially, the shell’s nonlinear frequency response is obtained from steady-state motion, followed by an evaluation of the system’s nonlinear dynamic behavior in two resonance regions: primary and parametric. Finally, the effects of conical shell parameters such as the amplitude of the parametric and external excitation, detuning parameter, structural damping, FG power indices, semi-vertex angle, thickness-to-length ratio, and boundary conditions on the maximum amplitude and hardening behavior of the frequency response at primary resonance, as well as the dynamic instability of the shell, are investigated.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113826"},"PeriodicalIF":3.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}