International Journal of Solids and Structures最新文献

{"title":"A computationally efficient hybrid formulation for viscoelastic–viscoplastic polymer solids and structures under large numbers of loading cycles","authors":"Darith Anthony Hun ,&nbsp;Mohamed Haddad ,&nbsp;Issam Doghri ,&nbsp;Georgios Tsilimidos ,&nbsp;Michael Lackner ,&nbsp;Zoltan Major ,&nbsp;Leonhard Doppelbauer ,&nbsp;Sara Haouala","doi":"10.1016/j.ijsolstr.2025.113290","DOIUrl":"10.1016/j.ijsolstr.2025.113290","url":null,"abstract":"<div><div>The numerical simulation of the high cycle response of solids and structures made of thermoplastic polymers is challenging because those materials exhibit a complex viscoelastic–viscoplastic (VEVP) behavior and even under large numbers of loading cycles, they continue to dissipate energy and feature a frequency dependent response. On the one hand classical simplified methods based on linear elasticity are not applicable, and on the other hand direct structural analyses with VEVP material models are so computationally prohibitive that they are not possible in practice. In this article, a computationally efficient hybrid formulation is proposed. The structure is first computed as being purely VE, using a recently proposed formulation based on Laplace-Carson transform (LCT) and its numerical inversion, and enabling to compute accurate strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the VEVP solution at any points of interest is computed with a time homogenization formulation which uses fast and slow time scales and asymptotic time expansions to compute complete solutions at extremely limited cost. An experimentally identified TPU material and a 3D lattice are used for the numerical simulations. Predictions of the hybrid formulation are compared against reference VEVP solutions and their accuracy verified. Numerical simulations for one million cycles are presented and the low computational cost of the hybrid formulation illustrated. The underlying assumptions of the hybrid formulation linking the VE results with the VEVP calculations are discussed. The proposal lays the foundation for the time and space multiscale modeling and simulation of the high cycle fatigue of thermoplastic solids and structures.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113290"},"PeriodicalIF":3.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611477","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":"Unified finite element limit analysis for solid reinforced concrete structures","authors":"Peter Noe Poulsen,&nbsp;John Forbes Olesen","doi":"10.1016/j.ijsolstr.2025.113307","DOIUrl":"10.1016/j.ijsolstr.2025.113307","url":null,"abstract":"<div><div>The application of Limit Analysis is effective in the pursuit of the collapse load of a structure. So far, whether it is an analytical model or a numerical model, the choice has been to apply either the lower or the upper bound theorem. Here, a unified approach for solid Finite Element models has eliminated this distinction and there is only one shared optimal solution. The unified solution is based on the two theorems by applying coinciding constitutive points for the fulfilment of the yield criteria together with weak forms of the equilibrium and the compatibility demands in the lower and upper bound formulation, respectively. This approach applies to any 3D stress state which may be formulated as a Semidefinite Program. Models based on either the lower or the upper bound theorem often give an indistinct result for the dual solution, interpreted as the displacements or the stresses, respectively. The present unified mixed solution renders accurate results for both stresses, displacements and load levels which in general are more accurate than the corresponding strict lower and upper bound solutions. A tetrahedral solid element with a linear stress variation and a quadratic displacement interpolation is presented along with a compatible embedded bar element. The effectiveness of this implementation is shown in three examples with regards to stresses, displacements, plastic work and the load capacity of reinforced concrete structures.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113307"},"PeriodicalIF":3.4,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600792","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":"Fracture swarm formation during shut-in driven by pore pressure waves","authors":"Cexuan Liu ,&nbsp;Egor Dontsov ,&nbsp;Manchao He ,&nbsp;Fengshou Zhang","doi":"10.1016/j.ijsolstr.2025.113320","DOIUrl":"10.1016/j.ijsolstr.2025.113320","url":null,"abstract":"<div><div>Hydraulic fracturing involves injecting a high-pressure fluid mixture to create fractures in underground rock formations, thereby enhancing hydrocarbon flow. Recent field observations, such as those from the Hydraulic Fracture Test Site (HFTS) project and tests in the Eagle Ford, have revealed surprising complexity of hydraulic fractures, including the presence of densely distributed fracture swarms. These findings challenge conventional expectations and necessitate a deeper understanding of fracture mechanisms. Existing studies have explored the propagation, connectivity, and implications of multiple fractures, but questions remain about the mechanisms behind the formation of fracture swarms, particularly the distribution of these secondary fractures. Our research introduces an alternative mechanism, proposing that secondary fractures result from a pore-pressure wave in which the pore pressure exceeds the compressive stress. This hypothesis suggests that pore-pressure variations within the rock and fluid exchange between the fracture and rock after shut-in can initiate secondary fractures. Through theoretical modeling and scaling, we have identified the governing dimensionless parameters that determine the number and distribution of secondary fractures. Numerical simulations enabled us to construct the parametric space for these parameters. Finally, we propose a procedure to interpret field observations of fracture swarms. Our approach provides new insights into predicting fracture swarms and using the observed fracture swarms to constrain some parameters that are relevant to hydraulic fracturing.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113320"},"PeriodicalIF":3.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143591569","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":"Discrete mechanical modeling of planar structures subjected to out-of-plane loading","authors":"Q. Zhang ,&nbsp;A. Fascetti ,&nbsp;M.A. Perez-Lara ,&nbsp;J.E. Bolander","doi":"10.1016/j.ijsolstr.2025.113321","DOIUrl":"10.1016/j.ijsolstr.2025.113321","url":null,"abstract":"<div><div>Many applications of planar concrete structures and other thin laminated cement-based composites involve the potential for out-of-plane loading. For such loading cases, structural response is highly sensitive to the positioning of reinforcement within the narrow cross-section. Herein, a novel extension of the Voronoi-cell lattice model (VCLM), which is a particle-type lattice model, is proposed to simulate the behavior of planar structural elements subjected to out-of-plane loading. Based on a two-dimensional network of nodes, a layered assembly of the element cross-sections provides a three-dimensional description of section behavior, while accommodating general forms of loading. The associated reduction in computational expense greatly extends the range of potential modeling applications. The efficacy of this layered Voronoi-cell lattice model (L-VCLM) is demonstrated through elastic stress analysis, plastic limit analysis and simulations of ferrocement panels under flexural loading. For this last case, influences of anchoring efficiency and positioning of the reinforcement within the narrow cross-section are directly simulated. Envisaged applications to other thin structural elements, including those containing textile reinforcement, are described.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113321"},"PeriodicalIF":3.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592131","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":"Forced vibration analysis of a spinning Timoshenko beam under axial loads by means of the three-dimensional Green’s functions","authors":"Long Wang ,&nbsp;Mingze Yuan ,&nbsp;Xiang Zhao ,&nbsp;Weidong Zhu","doi":"10.1016/j.ijsolstr.2025.113324","DOIUrl":"10.1016/j.ijsolstr.2025.113324","url":null,"abstract":"<div><div>Vibration of spinning structure is a very important and common problem in rotation machines and oil drilling. This paper studies dynamic responses of a spinning Timoshenko beam (STB) under the combined action of axial force and external excitation, and the three-dimentional (3D) steady-state Green’s function of forced vibration of the spinning beam is derived, in a systematic manner, which are actually constructed by two components i.e. two Green’s functions in two vertical directions. The Hamilton’s principle is used to establish forced vibration equations of the STB. By employing the separation of variables method and Laplace transform method, the 3D Green’s functions of STBs are obtained for different boundary conditions. By setting the shear correction factor <em>k</em> to infinity and the moment of inertia <em>γ</em> is set to zero, the present 3D Green’s functions can be reduced to the spinning Rayleigh beam and Euler-Bernoulli beam cases. In numerical section, the present analytical solution is verified by finite element method results, experimental results, and results in references in this work. Influences of the cross-section shape, such as circle, square, and ring, to the present solutions are discussed, and influences of some important geometric and physical parameters, such as the spinning speed and axial force, to the present solutions are also discussed.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"315 ","pages":"Article 113324"},"PeriodicalIF":3.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697809","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":"Investigation of fracture behaviour of a complex interface crack using a modified interaction energy integral method under thermal shock loading","authors":"Yanyan Zhang ,&nbsp;Zengtao Chen ,&nbsp;Zewei Li ,&nbsp;Fengnan Guo ,&nbsp;Hao Ran","doi":"10.1016/j.ijsolstr.2025.113317","DOIUrl":"10.1016/j.ijsolstr.2025.113317","url":null,"abstract":"<div><div>The fracture behavior of advanced materials with complex interfaces is a critical concern in material design and manufacture. In this article, a novel method is proposed to capture fracture parameters of a crack in multiphase materials with complex interfaces under thermal shock loading. With the help of the designed auxiliary fields, the interaction energy integral method (IEIM), which is complicated by both the complex interface structure and the thermal shock loading, is simplified, making it applicable to various types of multiphase materials and the thermal shock conditions. Using this method, the crack growth in the complex interface structure of advanced multiphase material under transient, thermal shock loading is investigated. The evolution of the complex thermal stress intensity factors (CTSIFs) of mixed-mode around the interface crack tip is presented during the process of thermal shock loading, and the corresponding influence caused by the complex interface is examined from multiple perspectives. First, the relationship between the transient values of each CTSIF and the corresponding crack length is established during the thermal shock process. Both <em>K</em>₁ and <em>K</em>₂ exhibit distinct changes when the crack reaches the interface, which intersects its propagation path in all three multiphase materials. Next, from the variation of the peak values of each CTSIF, a potential well and a sharp variation in the slope of <em>K</em>₂ are identified in the process of thermal shock, which are attributed to the presence of the complex interface structure. These founds suggest that specific interface types within the complex interface structure can influence the CTSIF of the interface crack under thermal shock. Additionally, the strain energy release rate is computed and analysed. Based on its variation, the process of the interface crack growth under thermal shock is classified into the unstable and the stable growth. Those findings, along with the proposed IEIM provide valuable insights for the design, evaluation, and engineering applications of complex thermal interfaces in advanced materials.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113317"},"PeriodicalIF":3.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143591570","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":"Shock induced damage and failure mechanisms of magnesium aluminate spinel based on an atomistically calibrated bond-based peridynamic model","authors":"Junwei Huang ,&nbsp;Lanxi Feng ,&nbsp;Xiaoqing Zhang ,&nbsp;Run Zhang ,&nbsp;Longhui Zhang ,&nbsp;Xiaohu Yao","doi":"10.1016/j.ijsolstr.2025.113316","DOIUrl":"10.1016/j.ijsolstr.2025.113316","url":null,"abstract":"<div><div>Understanding the dynamic mechanical properties and failure behavior of polycrystalline magnesium aluminate spinel MgAl₂O₄ is an important task for the development and design of transparent ceramic armor. However, the lack of the consideration of the microstructural characteristics in existing investigations leads to difficulties in accurately explaining the relationship between microcrack propagation and macroscopic damage evolution. To further explore the influence of the microstructure on the dynamic mechanical behavior of MgAl₂O₄ spinel, in this study, we propose a modified peridynamic (PD) model which take into account the fracture properties of grain boundaries and a compressive failure criterion with a residual post-failure bond strength. Fracture parameters of grain boundaries in PD model are extracted from molecular dynamics (MD) modeling. Meanwhile, planar impact experiments are performed to calibrate the PD simulations. In addition to the observed pullback signal indicating spall, the reload signal representing failure wave is also captured in experiments. The numerical predictions agree well with present experimental results, and provide new insight into the damage characteristics and failure mechanisms in both spall and failure wave events. With the increase of grain size, the ultimate spall strength decreases, while the failure wave velocity increases. Moreover, the velocity transition interval between the spall fracture and the failure wave is obtained, and the appearance of the third recompression phenomenon is interpreted.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113316"},"PeriodicalIF":3.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577873","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":"Additively manufactured kerf structures: Flexibility, energy absorption, and load-bearing behaviors","authors":"Aryabhat Darnal ,&nbsp;Kanak Mantri ,&nbsp;Ali Farajmandi ,&nbsp;Negar Kalantar ,&nbsp;Erfan Rezaei Azari ,&nbsp;Anastasia Muliana","doi":"10.1016/j.ijsolstr.2025.113331","DOIUrl":"10.1016/j.ijsolstr.2025.113331","url":null,"abstract":"<div><div>We introduce a new design of flexible structures that draws inspiration from the kerfing method used in wood shaping. The kerf structures, which consist of top and bottom cells linked by connectors and gaps between cells, enable the construction of freeform geometries. The kerf topology can lead to structural reconfigurations, i.e., connector buckling and densification, under compression and locking mechanism under bending, which contributes to energy absorption and alters stiffness and load bearing of kerf structures as they deform. We investigate the compressive and bending responses of 3D-printed kerf structures through experiments and simulations. We consider two kerf topologies, namely hexagon-triangle and square patterns, printed out of brittle Polylactic Acid (PLA), compliant thermoplastic polyurethane (TPU), and ductile Onyx composite consisting of nylon and carbon fiber. We study the interplay of kerf topology and the mechanical behavior of the material in controlling the flexibility, load-bearing capacity, energy absorption, and bend-locking characteristics. Using brittle PLA with hexagon kerf topology results in high load bearing, energy absorption, and bend-locking due to good load resistance of the connectors, better packing ability of hexagon cells, and high strength of PLA. The use of ductile Onyx composite shows an interplay between connector buckling, densification, and inelastic material deformation, contributing to high energy dissipation and energy absorption, as well as good load bearing. Although no failure occurs in the compliant TPU kerf structures, their high flexibility results in low load bearing and low energy absorption.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113331"},"PeriodicalIF":3.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611475","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":"Multiaxial yield behavior of transversely isotropic closed-cell aluminum foams","authors":"Erdong Wang ,&nbsp;Jingjing Cai ,&nbsp;Xintao Huo ,&nbsp;Xiao Guo","doi":"10.1016/j.ijsolstr.2025.113322","DOIUrl":"10.1016/j.ijsolstr.2025.113322","url":null,"abstract":"<div><div>Mechanical properties of metallic foams will exhibit direction-dependency when the cell shape anisotropy is generated during the manufacturing process. To provide effective design and analysis for the foam-based structures in engineering applications, it is essential to gain a robust understanding of the multiaxial yield properties of anisotropic foams. High-fidelity Voronoi foam model is constructed based on the statistical microstructure information that are measured using micro-CT technique. Transversely isotropic Voronoi foams are generated and adopted to conduct virtual multiaxial experiments. Numerical results show that large plastic deformation is mainly concentrated nearby the rigid platens in uniaxial, biaxial and triaxial compression, while a shear-like deformation localization bands is formed in the compression-shear loading. Sufficient yield points are determined in multiaxial loadings as per a total dissipation energy-based criterion. Numerical isotropic yield surfaces are plotted in the mean-effective stress plane and expand with increasing relative density, which can be well fitted using Zhang yield criteria. For transversely isotropic foams, the dispersion degree of yield points in the mean-effective stress plane is increased with increasing geometric stretch factor. The transversely isotropic yield surfaces are scaled proportionally with the uniaxial yield strength along transverse direction. The extended Hill’s anisotropic yield criterion can generally capture initial yielding behavior of transversely isotropic foams with different anisotropy coefficients and relative densities, outperforming other isotropic yield criteria.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113322"},"PeriodicalIF":3.4,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551626","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":"An anisotropic constitutive relationship by a series of 8 chain models","authors":"Libin Yang ,&nbsp;Teng Long ,&nbsp;Lixiang Yang","doi":"10.1016/j.ijsolstr.2025.113288","DOIUrl":"10.1016/j.ijsolstr.2025.113288","url":null,"abstract":"<div><div>Hyperelastic models have been widely used to model polymers and soft tissues. However, most hyperelastic models are phenomenological material models. Based on statistical mechanics and molecular chain configuration, the 8 chain model or Arruda-Boyce model is a physical model which can be used to understand how microstructures of chains affect macroscopic mechanical properties of polymers and soft tissues. Mechanical properties of many polymers and soft tissues are directional dependent. Polymer matrix can be reinforced by fibers. For soft tissues, ligaments and tendons will lead to anisotropic properties. Since matrix and reinforcements are composed of similar microstructural molecular chains, they can be modeled by using the same mathematical model. In this paper, a series of 8 chain models is used to understand composite properties. That is, an isotropic 8 chain model will be used to model matrix and anisotropic 8 chain models will be used to model fibers. Replacing <span><math><mrow><msub><mi>I</mi><mn>1</mn></msub></mrow></math></span> in isotropic 8 chain model with <span><math><mrow><msub><mi>I</mi><mn>4</mn></msub></mrow></math></span> in anisotropic 8 chain model is physically corresponding to changing representative 8 chain cubic cell to 8 chain slender cell. This treatment not only simplifies exist anisotropic mathematical structures but also keeps microscopic physics of the 8 chain model unchanged.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113288"},"PeriodicalIF":3.4,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552350","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}