International Journal of Solids and Structures最新文献

{"title":"Sixteen refined theories of longitudinal vibration of Rods: A Review, from Lord Rayleigh to Modernity","authors":"Isaac Elishakoff,&nbsp;Janak Kumar Tharu","doi":"10.1016/j.ijsolstr.2026.113881","DOIUrl":"10.1016/j.ijsolstr.2026.113881","url":null,"abstract":"<div><div>In this review paper, we discuss sixteen available refined theories, to the best of our knowledge, on longitudinal vibration of rods, starting nearly 150 years ago with Rayleigh-Love theory. We herewith try to remain as faithful as possible to the derivations of the original developers of the theories at hand. Finally, the solutions provided by all the above theories are compared with the exact solution of Pochhammer’s and Chree’s derivation from the three-dimensional equations of the theory of elasticity.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113881"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386049","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":"Mechanics informatics-driven topology optimization for test specimen design and single-test material characterization: A Gaussian random field approach","authors":"Royal C. Ihuaenyi,&nbsp;Juner Zhu","doi":"10.1016/j.ijsolstr.2026.113894","DOIUrl":"10.1016/j.ijsolstr.2026.113894","url":null,"abstract":"<div><div>Characterizing materials through conventional testing protocols often requires multiple separate tests, making it resource-intensive and introducing inter-specimen variability. This work presents an informatics-enabled approach that frames material characterization as an information utilization problem rather than a standardized testing problem. Instead of adapting specimen design to multiple simple tests, we adapt tests to a single complex, informative specimen, optimally designed to maximize stress state entropy, a quantitative measure of mechanical information. The specimen design methodology employs Gaussian random fields with Karhunen–Loève expansion as the generative basis for topology optimization, where eigenvalue configurations are tuned via Bayesian optimization to maximize stress state entropy. Applied to orthotropic elasticity and anisotropic plasticity, the framework generates specimens approaching theoretical entropy limits that simultaneously activate all stress states required for accurate characterization within a single uniaxial tension test. To validate this framework, we introduce a physics-informed neural network approach using an Input Convex architecture for learning orthotropic elasticity directly from full-field data while preserving thermodynamic consistency. Comparative analysis demonstrates that parameter identification accuracy scales directly with specimen information content, with the most informative specimen design achieving order-of-magnitude improvement in identification accuracy over specimens with low information content. Additionally, a parametric study reveals that void fraction has a significant influence on the information content of the designed specimen. This work establishes a general framework for informatics-driven test specimen design, enabling efficient material characterization across diverse constitutive models.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113894"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386065","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":"Mode I fracture toughness maximization of low-density architected materials","authors":"Markus G. Holm,&nbsp;Konstantinos Poulios,&nbsp;Niels Aage,&nbsp;Christian F. Niordson,&nbsp;Ole Sigmund","doi":"10.1016/j.ijsolstr.2026.113910","DOIUrl":"10.1016/j.ijsolstr.2026.113910","url":null,"abstract":"<div><div>This paper presents a framework for systematically optimizing the fracture toughness of periodic beam lattice materials using topology optimization. We introduce a new normalization factor for fracture toughness based on the unit cell size arguing that it offers a more consistent and unambiguous basis for comparing different lattice microstructures than the conventional beam-length-based normalization. Our analysis demonstrates that the relative performance ranking of lattice topologies is significantly affected by the choice of normalization. Notably, when evaluated using this proposed unit-cell-based normalization, classical triangular and Kagome structures consistently demonstrate remarkably high fracture toughness, outperforming a demi-regular structure that appear superior under conventional beam-length normalization. This reinforces their established efficacy as high-performance lattice designs. The proposed optimization framework is applied to design lattice structures at low (<span><math><mrow><mover><mrow><mi>ρ</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>=</mo><mtext>1</mtext><mspace></mspace><mtext>%</mtext></mrow></math></span>) and moderate (<span><math><mrow><mover><mrow><mi>ρ</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>=</mo><mtext>15</mtext><mspace></mspace><mtext>%</mtext></mrow></math></span>) relative densities. Interestingly, the framework did not yield structures that surpassed the performance of the Kagome or triangular lattices when assessed with the proposed normalization factor. However, it is remarkable that when evaluated using the conventional beam-length-based normalization from the literature, the framework is able to generate a design that significantly outperforms the triangular and Kagome lattices, as well as a tension-dominated demi-regular structure, at moderate relative densities (<span><math><mrow><mtext>5</mtext><mspace></mspace><mtext>%</mtext><mo>&lt;</mo><mover><mrow><mi>ρ</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>&lt;</mo><mtext>20</mtext><mspace></mspace><mtext>%</mtext></mrow></math></span>). This work highlights the critical influence of normalization choices on performance assessment and underscores the inherent efficiency of classical lattice topologies.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113910"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386050","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":"Multiscale modeling and analysis of coupled thermo-electro-structural behavior in heterogeneous materials and structures with direct FE2 method","authors":"Lu Meng ,&nbsp;Ji Qiu ,&nbsp;Pei Li ,&nbsp;Heng Zhang ,&nbsp;Zhe Liu","doi":"10.1016/j.ijsolstr.2026.113895","DOIUrl":"10.1016/j.ijsolstr.2026.113895","url":null,"abstract":"<div><div>The coupled thermo-electro-structural effect is a key factor affecting the performance and reliability of electrical devices. As the number of coupled physical fields increases, the computational complexity grows nonlinearly, rendering existing methods inadequate for achieving concurrent multiscale modeling of tri-field coupling, which severely constrains the optimal design for multiscale electrical devices under complex operating conditions. To this end, a coupled thermal-electro-structural direct finite element square (D-FE²) method is developed to perform full coupled multiphysics concurrent multiscale computation in heterogeneous materials and structures. Numerical results show that the proposed method not only accurately captures the Joule heating-induced thermal expansion phenomena in three-dimensional heterogeneous materials and structures under various temperature fields (i.e., steady-state and transient) and electrical excitations (i.e., direct current and alternating current), but also achieves over 91% reduction in intrinsic computational workload and above 95% savings in practical resource consumption compared to conventional direct numerical simulation (DNS) methods. This study provides a breakthrough solution for concurrent multiscale modeling and optimization of complex coupled multiphysics systems in large-scale electrical devices.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113895"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154252","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":"Modelling of magneto-mechanically coupled soft thin shells","authors":"Abhishek Ghosh ,&nbsp;Andrew McBride ,&nbsp;Zhaowei Liu ,&nbsp;Luca Heltai ,&nbsp;Paul Steinmann ,&nbsp;Prashant Saxena","doi":"10.1016/j.ijsolstr.2026.113851","DOIUrl":"10.1016/j.ijsolstr.2026.113851","url":null,"abstract":"<div><div>A geometrically exact, dimensionally reduced model is developed to describe the nonlinear deformation of thin magnetoelastic shells. The classical Kirchhoff–Love assumptions for the mechanical fields are extended to the magnetic variables, yielding a consistent two-dimensional theory derived rigorously through a variational framework. Unlike traditional approaches that rely on mid-surface kinematics, the full deformation map is adopted as the primary variable, and the influence of the surrounding free space due to the Maxwell stress on the shell’s upper and lower surfaces is accommodated through a novel application of Green’s theorem. The governing equations are solved in closed form for the canonical case of a hyperelastic thin flat plate and for an infinite cylindrical magnetoelastic shell, to illustrate the capabilities of the model and elucidate the non-standard variables arising in the modified variational formulation.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113851"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386009","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":"A convexity identification model beyond existing geometric analysis methods—Understanding the effect of non-convex yield surfaces on finite element simulations","authors":"Liang Sun ,&nbsp;Kai Du ,&nbsp;Yanqiang Ren ,&nbsp;Liang Zhang ,&nbsp;Li Dong ,&nbsp;Liying Song ,&nbsp;Jing Guo ,&nbsp;Xiaoguang Yuan","doi":"10.1016/j.ijsolstr.2026.113883","DOIUrl":"10.1016/j.ijsolstr.2026.113883","url":null,"abstract":"<div><div>The yield criterion must strictly satisfy the convexity requirement to ensure the physical rationality, mathematical solvability, and consistency with the actual material deformation behavior in finite element simulations. A new high-accuracy convexity identification method (HACI2026) has been developed to concisely and efficiently verify the convexity of the yield function. The new method is embedded with incremental coefficients, size coefficient, and precision coefficient that can be flexibly adjusted as needed. The Hessian matrix, GINCA, E-GINCA, and HACI2026 methods were applied to several different types of yield criteria, such as the Drucker, CB2004, and Cazacu2018 established within the framework of stress invariants, the higher-order polynomial-type Poly4 and Poly6, and the coupled-type CQN_Chen and Poly4*Hosford yield criteria. The range of material parameters satisfying convexity was examined for each criterion based on the single-variable principle. Furthermore, numerical simulations of cup drawing were conducted using both convex and non-convex yield surfaces to investigate the impact of non-convex yield surfaces on the simulation results. The results show that HACI2026 achieves good identification accuracy and computational efficiency without the need to solve partial derivative information. Its inspection results for any category of yield criteria are highly consistent with those of the Hessian matrix method. The new method can be flexibly adjusted according to the function. The precision coefficient is recommended to be set at 2 or 50 for structurally simple or complex coupled yield criteria, respectively. The presence of significant concavities in the yield surface is one of the important reasons why numerical simulation techniques fail to obtain simulation results. Even if slight concavity exists in the yield surface, certain iterative methods can still forcefully compute and obtain results, which may mislead researchers into considering them correct. Therefore, before applying yield criteria, it is necessary to conduct rigorous verification using high-precision convexity identification methods.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113883"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386048","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":"Polymer-based architected materials and structures: Geometry, experiments, constitutive modeling, and advanced simulations","authors":"Ke Ma ,&nbsp;Abhishek Gupta ,&nbsp;Vikas Srivastava,&nbsp;Pradeep Guduru,&nbsp;Yuri Bazilevs","doi":"10.1016/j.ijsolstr.2026.113911","DOIUrl":"10.1016/j.ijsolstr.2026.113911","url":null,"abstract":"<div><div>Architected materials and structures achieve superior performance beyond the limits of their bulk counterparts by exploiting the topology. Among these, triply periodic minimal surface (TPMS)-based designs are especially promising owing to their smooth geometry, high connectivity, and tunability. When constructed using polymers, they offer low density, environmental stability, biocompatibility, and expanded design flexibility. However, predictive modeling is challenged by complex geometry, fabrication variability, and, in particular, the nonlinear, strain-rate dependent constitutive behavior of polymers. This work addresses these challenges with a proposed rate-dependent viscoplastic constitutive model with multiple internal mechanisms. Material characterization, calibration, and experimental validation are hierarchically performed using dog-bone, unit-cell, and lattice specimens produced via stereolithography (SLA). Efficient large-deformation computations are enabled by Isogeometric Kirchhoff–Love (KL) thin-shell analysis. The comprehensive constitutive model demonstrates robust predictive capability in capturing the full spectrum of mechanical behavior at the material-point level: pseudo-elasticity at small strains, strain softening after “yielding”, strain hardening at large strains, and strain-rate dependence across a full deformation spectrum. Our work elevates the level of modeling and simulation and provides better pathways for reliable design of lightweight, tunable polymeric architected materials and structures.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113911"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386117","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":"A variationally consistent chemo-elastic theory for special Cosserat rods","authors":"Asutosh Parida,&nbsp;Prakhar Gupta","doi":"10.1016/j.ijsolstr.2026.113912","DOIUrl":"10.1016/j.ijsolstr.2026.113912","url":null,"abstract":"<div><div>We develop a variationally consistent framework for chemo-elastic special Cosserat rods that incorporates a two-way chemo-mechanical coupling to accurately model large deformations in slender rods. This two-way coupling is particularly important to model stress-assisted diffusion for various metamaterial-based battery electrodes and soft robotics applications. Using the virtual power and energy minimization approach, we first derive coupled equilibrium equations in Lagrangian formulation applicable to three-dimensional chemo-elastic solids. Upon utilizing these equations, we subsequently establish one-dimensional equilibrium equations for the chemo-elastic special Cosserat rod through dimensional reduction. Later, we formulate the constitutive relations and determine work conjugates for chemo-elastic rods coherent with our dimensional reduction approach. Using these constitutive relations, we develop closed-form solutions for the chemo-elastic rod subjected to extension. We present a benchmark result from our theoretical model that shows an excellent agreement with experimental observations for the stress-assisted diffusion case, wherein the concentration increases with the applied load. Such a phenomenon is important in lithium-ion batteries, wherein stress alters lithium diffusion patterns, and this can be captured by our two-way coupling model. Finally, the nonlinear coupled differential equations for chemo-elastic rods are solved numerically, and interestingly, we found the contrasting chemo-mechanical response under displacement and force boundary conditions for varying concentration and concentration gradient.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113912"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386008","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":"Probabilistic damage modeling of hybrid composites with load sharing and multifragmentation","authors":"E. Polyzos ,&nbsp;S. Malefaki ,&nbsp;I.A. Rodrigues Lopes ,&nbsp;P.P. Camanho ,&nbsp;D. Van Hemelrijck ,&nbsp;L. Pyl","doi":"10.1016/j.ijsolstr.2026.113909","DOIUrl":"10.1016/j.ijsolstr.2026.113909","url":null,"abstract":"<div><div>This study introduces a novel analytical probabilistic progressive damage model for multiphase composites and applies it to predict the damage behavior of hybrid composites. The model uses effective field methods in order to express the elastic fields of the fibers and the matrix and to predict the damage of the composite. In particular, the weakest link theory and Weibull statistics are used to express the fiber damage. Multifragmentation phenomena are considered to address fiber segments that continue to contribute to the stiffness of the composite after the first damage event. A novel framework for capturing local load sharing phenomena is introduced to derive explicit solutions expressing the average (over the volume of the composite) overloading of surviving fibers. The novel probabilistic progressive damage model is compared to two state-of-the-art models (i) the progressive failure model (PFM) and (ii) the spring element model (SEM). Two types of hybrid composites, a carbon (AS4) - glass (Eglass) and a carbon (M50S) - carbon (AS4) composite, are analyzed and the results demonstrate an excellent agreement.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113909"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386047","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":"Second-order scaling of cracked quasibrittle materials under dynamic loading","authors":"Keith Davey ,&nbsp;Khine Kyaw ,&nbsp;Hamed Sadeghi","doi":"10.1016/j.ijsolstr.2026.113914","DOIUrl":"10.1016/j.ijsolstr.2026.113914","url":null,"abstract":"<div><div>The new scaling theory <em>finite similitude</em> has made possible the design of multiple scaled experiments for the analysis of systems and structures. The theory has brought into existence an unlimited number of new similitude rules and alternative strategies for scaling analysis and experimental design. The recent application of the approach to fracture has revealed that two scaled experiments are sufficient for the capture of defect-size related size effects under quasistatic loading. However, for fracture under <em>dynamic loading</em>, it is shown necessary to invoke the second-order finite similitude rule, which can feature three scaled experiments or additional equations for the purposes of scaling analysis. This is demonstrated in the paper both analytically and numerically using models scaled down to three sizes or involving additional equations housing scale derivatives up to second order. It is confirmed that tests at three scales provide sufficient information for the reconstruction of dynamic fracture at full size. The practicality of the approach is demonstrated through replication of behaviour of a concrete gravity dam damaged during the Koyna earthquake. Showcased is the practical benefit of targeting invariances (e.g., length, gravity, material properties), enabling scaled experiments with unchanged materials under realistic loading. Length invariance under scaling is shown critically to underpin the application of power-law relationships to quasibrittle materials. The presented results confirm that dynamic fracture mechanics at full-scale can be replicated to low single-digit percentage errors at second order, providing improved accuracy on zeroth- and first-order rules.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"331 ","pages":"Article 113914"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386063","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}