International Journal of Engineering Science最新文献

{"title":"A spectral dislocation-based framework for 3D internal fracture in layered transversely isotropic half-spaces with imperfect interfaces","authors":"A. Vattré ,&nbsp;Z. Zhang ,&nbsp;E. Pan","doi":"10.1016/j.ijengsci.2025.104404","DOIUrl":"10.1016/j.ijengsci.2025.104404","url":null,"abstract":"<div><div>A unified dislocation-based framework is developed for the three-dimensional analysis of internal and horizontal penny-shaped cracks embedded in multilayered transversely isotropic half-spaces. The proposed formulation covers all three classical fracture modes I, II, and III, while accounting for elastic mismatch, crack depth, and imperfect interfacial contact within arbitrary layup stacking sequences. The fundamental Green’s solutions, corresponding to the elastic response induced by continuous distributions of unit-concentrated dislocation sources, are expanded using a Fourier–Bessel series system of vector functions composed of longitudinal, gradient-type meridional, and curl-type torsional modal fields. This modal decomposition establishes a canonical correspondence between fracture modes and basis components, thereby enabling mixed-mode representations by linear superposition. The displacement field is represented by spectral Love-type expansion coefficients, where the Love numbers are computed only once. The unknown displacement discontinuity is discretized using a ring-wise collocation method and subsequently determined to satisfy the prescribed crack-face loading for each fracture mode. By means of the dual-variable and position technique, recursive layer-by-layer propagation schemes are constructed to ensure internal continuity conditions and to incorporate imperfect contact through normal and tangential interfacial springs, leading to stable and fast convergence for multilayered structures. Stress intensity factors and energy release rates are extracted by matching the near-tip asymptotic behavior of the displacement discontinuity, showing excellent agreement with benchmark reference solutions, and further extending to depth-dependent mode I, II, III, and mixed-mode fracture in layered configurations. The capabilities of the formulation are illustrated by examining titanium-based multilayer systems under mode I loading. The contrast between stiff and soft gradient-layered configurations reveals how stiffness variation and interfacial compliance modulate both stress concentration and crack-face separation. The soft gradient architecture, while producing a greater crack opening, yields a reduced normalized mode I stress intensity factor compared to the stiff layered configuration. The analysis emphasizes symmetry deviations, fracture-mode-dependent discontinuities, and the localized nature of displacement and stress fields. The results provide insight into internal fracture phenomena in coated structures, layered ceramics, and stratified functional materials, and support the design of multilayer systems with improved durability and damage tolerance.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"218 ","pages":"Article 104404"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145427962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Static bending of micromorphic Timoshenko beams","authors":"S. El-Borgi ,&nbsp;M. Trabelssi ,&nbsp;N. Challamel ,&nbsp;J.N. Reddy","doi":"10.1016/j.ijengsci.2025.104403","DOIUrl":"10.1016/j.ijengsci.2025.104403","url":null,"abstract":"<div><div>This study develops a rigorous analytical framework for investigating the static bending behavior of micromorphic and nonlocal strain gradient Timoshenko beams, with particular emphasis on capturing size-dependent effects in micro- and nano-scale structural elements. The model is derived using a variational principle and it consists of a set of governing equations and boundary conditions that incorporate two distinct internal length-scales, one associated with nonlocal stress gradients and the other with strain gradient effects. The obtained system of two coupled differential equations governs the deflection and the rotation of the beam. Uncoupling both equations leads to sixth- and fifth-order differential equations for the deflection and the rotation, respectively. Exact solutions are obtained for standard boundary configurations, including simply-supported, clamped–clamped, and cantilever cases, under both point and distributed loads. The analytical model is shown to be theoretically equivalent to a class of two-length-scale nonlocal strain gradient theories, thereby offering a consistent and unified description of scale-dependent mechanics in microstructured beams. A distinct series-based solution is also constructed to verify the closed-form micromorphic results. Verification against established reference solutions demonstrates the accuracy and generality of the proposed model. A series of parametric studies is conducted to quantify the role of internal length-scales, revealing that the model successfully predicts both stiffening and softening trends, depending on the microstructural configuration. The derived exact solutions provide a reliable benchmark for assessing numerical schemes and serve as a foundation for further studies involving advanced materials with microstructural complexity.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"218 ","pages":"Article 104403"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the construction of a viscoelastic constitutive model for brain tissue maximizing tension–compression asymmetry","authors":"Mani Reddipaga ,&nbsp;K. Kannan","doi":"10.1016/j.ijengsci.2025.104415","DOIUrl":"10.1016/j.ijengsci.2025.104415","url":null,"abstract":"<div><div>Human brain tissue exhibits a nonlinear viscoelastic response characterised by relaxation, creep, and loading-rate dependence. Under quasi-static conditions, its elastic behaviour shows pronounced tension–compression asymmetry and greater shear stiffness in compression than in tension under combined loading. Capturing these features with fewer parameters remains a challenge. To ensure physical consistency, isotropic hyperelastic models are required to satisfy the Baker–Ericksen (B–E) inequalities. Leveraging the physical interpretation of Lode invariants, we construct a stored energy function through a priori analysis of B–E inequalities, achieving maximal tension–compression asymmetry by satisfying these inequalities. The resulting two-parameter stored energy function is benchmarked against existing models using the nonlinear shear modulus and Mooney’s asymmetry function under uniaxial deformation. Among these, the proposed model yields a correct bounded response consistent with experimental brain tissue data. The model is then extended to viscoelasticity using K.R. Rajagopal’s thermodynamic approach, where the viscoelastic constitutive equations are derived from the two scalar functions: the stored energy and the rate of dissipation. The developed stored energy is employed for both equilibrium and non-equilibrium contributions, and a simple quadratic dissipation function is chosen. Constitutive equations are derived by extremizing the rate of dissipation function subject to constraints such as incompressibility and the second law of thermodynamics. Validation against experimental data of Budday et al. (2017) shows that the proposed four-parameter model captures key mechanical features of brain tissue, including tension–compression asymmetry, hysteresis, and relaxation, while showing closer agreement than the six-parameter Budday–Ogden model for shear superposed on tension/compression deformation.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"218 ","pages":"Article 104415"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compression-twist induced 3D mechanical metamaterial with programmable mechanical properties","authors":"Ning Cao ,&nbsp;Tongtong Liu ,&nbsp;Xingchen Chen ,&nbsp;Ying Wu ,&nbsp;Xiang Li","doi":"10.1016/j.ijengsci.2025.104406","DOIUrl":"10.1016/j.ijengsci.2025.104406","url":null,"abstract":"<div><div>Mechanical metamaterials have attracted extensive attention for their unconventional mechanical responses. Among them, compression-twist (CT) materials introduce new opportunities for programmable mechanical behavior. However, achieving continuous control of stiffness and Poisson’s ratio over wide ranges remains challenging. While negative Poisson’s ratio (NPR) metamaterials have been widely explored for their auxetic effects, their tunability and multi-physical performance are still limited. Here, we design four three-dimensional (3D) mechanical metamaterials—CT-NPR, CT-positive Poisson’s ratio (CT-PPR), augmented CT (ACT)-NPR, and ACT-PPR—by combining CT and NPR architectures. These structures exhibit tunable Poisson’s ratios and stiffness spanning over an extremely wide range. Numerical simulations and theoretical analysis reveal that CT-NPR and CT-PPR are bending-dominated with low stiffness, whereas ACT-NPR and ACT-PPR are stretching-dominated with high stiffness. Then, the metamaterials are fabricated via 3D printing, and their mechanical properties are characterized using quasi-static compression tests. Experimental results are consistent with theoretical predictions, confirming NPR behavior in CT-NPR and ACT-NPR, and positive Poisson’s ratio behavior in CT-PPR and ACT-PPR. Additionally, CT-PPR exhibits a distinctive two-step deformation process without self-contact, while energy absorption studies show that ACT-NPR achieves superior energy dissipation and CT-PPR maintains a stable deformation mode. This work provides a new framework for designing programmable mechanical metamaterials with potential applications in shape-morphing devices, energy absorbers, medical instruments, smart actuators, and crashworthy structures.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"218 ","pages":"Article 104406"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145448081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homogenization of architected materials incorporating shearable beams","authors":"Matteo Franzoi,&nbsp;Davide Bigoni,&nbsp;Andrea Piccolroaz","doi":"10.1016/j.ijengsci.2025.104397","DOIUrl":"10.1016/j.ijengsci.2025.104397","url":null,"abstract":"<div><div>Two-dimensional architected materials are often realized as periodic grids of elastic beams. Conventional homogenization methods represent these structures as equivalent elastic solids but neglect shear deformation in the constituent beams. This article addresses this limitation by incorporating shear deformability through Timoshenko beam theory, enabling accurate modeling of stubby beams. Moreover, shearable beams with extreme mechanical characteristics can be obtained through the design of appropriate microstructures. Introducing shearable beams into the grid expands the design space, allowing, for instance, the control of the effective Poisson’s ratio beyond the limits achievable with slender beams.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"218 ","pages":"Article 104397"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145360522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Torsional vibration of a coupled cylinder","authors":"Igor Istenes ,&nbsp;Daniel Peck ,&nbsp;Yuriy Protserov ,&nbsp;Natalya Vaysfeld ,&nbsp;Zinaida Zhuravlova","doi":"10.1016/j.ijengsci.2025.104374","DOIUrl":"10.1016/j.ijengsci.2025.104374","url":null,"abstract":"<div><div>The torsion loading of a coupled cylinder, comprising distinct upper and lower cylindrical sections potentially made of different materials, is considered. The bottom of the cylinder is fixed in place, and induces the cylinder vibration. The torsion is applied via an arbitrary loading on the upper face. Three forms of coupling condition between the upper and lower cylinders are outlined: ideal, soft (weak), and rigid (hard/ stiff) contact. The resulting displacements and tangential stresses are obtained using the finite Hankel transform, and a Green’s function representation of the displacement. Numerical results are provided, and the impact of the differing coupling conditions investigated for a range of cylinder geometries, material properties and vibration rates. The resonance frequencies of the coupled cylinder are determined. A method for using the coupled cylinder model to approximate the displacement of a cylinder containing a damaged region via a weak interfacial layer is outlined. The properties of the weak interface layer needed for this approximation are determined, and the advantages of its use in non-destructive testing are discussed.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104374"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Creep fracture entropy: A thermomechanical damage-based failure index","authors":"Asghar Zajkani ,&nbsp;Michael Khonsari","doi":"10.1016/j.ijengsci.2025.104376","DOIUrl":"10.1016/j.ijengsci.2025.104376","url":null,"abstract":"<div><div>This paper presents an analytical framework for thermodynamical modeling of creep damage and fracture in materials through the lens of entropy production. Building on the second law of thermodynamics and principles of irreversible processes, the study establishes a unified coupling between a phenomenological damage law and continuum damage mechanics. The model links creep deformation to internal entropy generation and introduces a process-dependent damage exponent to ensure physically consistent and mathematically robust damage evolution. A key contribution is to introduce Creep Fracture Entropy (CFE)—a novel, material-specific thermodynamic index that serves as a reliable predictor of creep failure. By deriving time-dependent expressions for strain, strain rate, and entropy production, the model captures the full progression of creep behavior, without requiring empirical stage segmentation. The model is validated against a range of experimental data from various alloys, manifesting strong agreement with the observed strain and entropy trends. Notably, the calculated CFE values remain confined within a narrow range for each material, highlighting their intrinsic nature of constancy and reliability as fracture indicators. The thermodynamic formulation presented here enhances predictive accuracy for creep life assessment, emphasizing entropy as a pivotal damage variable in irreversible thermodynamics.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104376"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hadamard compatibility conditions for Rivlin–Ericksen tensors on weak singular surfaces","authors":"Markus Kaczvinszki,&nbsp;Wei Wu","doi":"10.1016/j.ijengsci.2025.104382","DOIUrl":"10.1016/j.ijengsci.2025.104382","url":null,"abstract":"<div><div>We consider weak singular surfaces in the sense of Hadamard and Thomas. The jump condition for the velocity gradient across such singular surfaces is well established and often used in the bifurcation analysis of localized deformation. In this paper, we present the jump conditions for the Rivlin–Ericksen tensors for the first time. With regards to a material motion, the jump conditions are derived for both propagating and standing singular surfaces. We showcase the geometric structure of strain acceleration discontinuities and the additional restrictions posed by incompressibility. It turns out, for standing (i.e. material) discontinuities the jumps of all higher-order Rivlin–Ericksen tensors depend nonlinearly on the jump of the velocity gradient. This enables a simple setting for the description of discontinuities in certain non-Newtonian constitutive models.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104382"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global limit points behaviour and multistable thresholds in electrostatically actuated double micro-beam structures","authors":"Arava R. Korakh,&nbsp;Lior Medina","doi":"10.1016/j.ijengsci.2025.104387","DOIUrl":"10.1016/j.ijengsci.2025.104387","url":null,"abstract":"<div><div>The study presents a rigorous global stability analysis of a weakly coupled and electrostatically actuated double micro-beam structure. The analysis is conducted using a reduced-order (RO) model, from which an eigenvalue analysis is carried, to determine stable and unstable points along a given equilibrium curve, thus providing stable and unstable branches, that are differentiated by limit points. Under such an analysis, it is found that unlike classical structures, limit points will not necesserally coincide with extremum points in a given curve. In the current study, the analysis is extended to a range of parameters to create a global stability analysis, prompting global limit points maps, used to determine their evolution, as well as determine various stability thrsholds. The study is carried out in two stages. First, it is studied when the structure is mechanically loaded, solidifying the analysis paradigm while also serving as a preliminary validation tool, where a finite element (FE) model serves as the reference. The analysis then moves to study the effect of electrostatic load, where direct solutions of finite differences (FD) were used as the reference, after establishing their merit at the previous stage. It is shown that while a double micro-beam can become bistable when mechanically loaded, it will transform under electrostatic load to include hitherto unknown complex limit point maps, prompting tri-, quad- and quintstability, alongside new dynamic configurations, as well as unorthodox branch formations. It is shown that the model can project stability shifts of the structure and be used as a design tool for compact tristable actuators.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104387"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approaching and overcoming the limitations of the multiscale Capriccio method for simulating the mechanical behavior of amorphous materials","authors":"Lukas Laubert ,&nbsp;Felix Weber ,&nbsp;Fabrice Detrez ,&nbsp;Sebastian Pfaller","doi":"10.1016/j.ijengsci.2025.104317","DOIUrl":"10.1016/j.ijengsci.2025.104317","url":null,"abstract":"<div><div>The Capriccio method is a computational technique for coupling finite element (FE) and molecular dynamics (MD) domains to bridge their length scales and to provide boundary conditions typically employed in large-scale engineering applications. Earlier studies showed that strain inconsistencies between the coupled domains are caused by the coupling region’s (bridging domain, BD) resistance to spatial motion. Thus, this work examines influences of coupling parameters on strain convergence in Capriccio-coupled setups to study the mechanical behavior of solid amorphous materials. To this end, we employ a linear elastic 1D setup, imitating essential features of the Capriccio method, including force-transmitting anchor points (AP), which couple the domains via linear elastic springs. To assess the effect of more complex interactions in 3D models versus 1D results, we use an interdimensional mapping scheme, allowing qualitative and quantitative comparisons. For validation, we employ both an inelastic polystyrene MD model and a predominantly elastic silica glass MD model, each coupled to a corresponding FE material description. Our 1D results demonstrate that decreasing the conventionally high AP stiffness, along with other less significant measures, diminishes this motion resistance, revealing an optimal ratio between the material stiffness of the coupled domains and the cumulative AP stiffness. The 3D silica setup confirms that these measures ensure decent domain adherence and sufficiently low strain incompatibilities to study the mechanical behavior of elastic models. However, these measures turn out limited and may not ensure sufficient accuracy for studying the deformation and fracture behavior of Capriccio-coupled inelastic models. To overcome this, we employ a modified coupling approach, revising the Capriccio method’s AP concept by introducing a much lower so-called molecular statics stiffness during the FE calculation and a higher AP stiffness during only the MD calculation. Initial results on the 1D setup indicate that essential coupling limitations can be overcome, albeit with the risk of oscillatory strain amplifications depending on the BD’s design. This novel approach may enable a more accurate analysis of the mechanical behavior of coupled inelastic amorphous materials. We recommend evaluating its performance in 3D alongside additional methodological extensions. Overall, our results outline the current limitations of the Capriccio method and lay the groundwork for its targeted extension to study the mechanical behavior and, in particular, fracture phenomena in inelastic amorphous materials.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104317"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}