Pub Date : 2026-02-09DOI: 10.1016/j.ijengsci.2026.104497
P.Q. Li, K.F. Wang, B.L. Wang
Multistable systems, characterized by their ability to undergo discrete phase transitions, underpin a broad range of phenomena and applications from snapping metamaterials to protein unfolding. However, the foundational assumption of homogeneity in conventional bistable chain models restricts them to predicting only uniformly propagating phase transitions, thereby overlooking the sequential, path-dependent behaviors that are characteristic of real-world heterogeneous systems. To address this limitation, we develop a semi-analytical heterogeneous bistable chain model composed of dissimilar bistable elements. Each element is described by trilinear force-displacement relation with distinct phase transition thresholds. The two limiting pathways, the minimum energy (thermodynamic equilibrium) and maximum hysteresis (athermal) paths, are generalized to account for heterogeneity. They provide the theoretical envelope that contains all possible mechanical responses. Furthermore, through heterogeneous bistable chain model, we analytically reveal the mechanism of coupled phase transitions: a cooperative phenomenon unique to heterogeneous multistable systems where the phase transition of one element can induce phase transitions in others. The predictive capability of the proposed framework is validated through the design of gradient multistable metamaterials, where theoretical predictions show excellent agreement with finite element simulations and experimental measurements. This work provides both a fundamental understanding of discrete phase transitions in heterogeneous systems and an efficient reduced-order modeling tool for structural design with programmable phase transition pathways.
{"title":"Heterogeneity-dominated discrete phase transitions in multistable systems: A unified bistable chain framework","authors":"P.Q. Li, K.F. Wang, B.L. Wang","doi":"10.1016/j.ijengsci.2026.104497","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2026.104497","url":null,"abstract":"Multistable systems, characterized by their ability to undergo discrete phase transitions, underpin a broad range of phenomena and applications from snapping metamaterials to protein unfolding. However, the foundational assumption of homogeneity in conventional bistable chain models restricts them to predicting only uniformly propagating phase transitions, thereby overlooking the sequential, path-dependent behaviors that are characteristic of real-world heterogeneous systems. To address this limitation, we develop a semi-analytical heterogeneous bistable chain model composed of dissimilar bistable elements. Each element is described by trilinear force-displacement relation with distinct phase transition thresholds. The two limiting pathways, the minimum energy (thermodynamic equilibrium) and maximum hysteresis (athermal) paths, are generalized to account for heterogeneity. They provide the theoretical envelope that contains all possible mechanical responses. Furthermore, through heterogeneous bistable chain model, we analytically reveal the mechanism of coupled phase transitions: a cooperative phenomenon unique to heterogeneous multistable systems where the phase transition of one element can induce phase transitions in others. The predictive capability of the proposed framework is validated through the design of gradient multistable metamaterials, where theoretical predictions show excellent agreement with finite element simulations and experimental measurements. This work provides both a fundamental understanding of discrete phase transitions in heterogeneous systems and an efficient reduced-order modeling tool for structural design with programmable phase transition pathways.","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"16 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146146593","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}
Pub Date : 2026-02-03DOI: 10.1016/j.ijengsci.2026.104496
PMS Almeida, D Garcia, AMP Afonso, A Akhavan-Safar, RJC Carbas, EAS Marques, J Hrachova, H Leenders, LFM da Silva
{"title":"Numerical modeling and experimental validation of adhesive squeeze flow in confined geometries","authors":"PMS Almeida, D Garcia, AMP Afonso, A Akhavan-Safar, RJC Carbas, EAS Marques, J Hrachova, H Leenders, LFM da Silva","doi":"10.1016/j.ijengsci.2026.104496","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2026.104496","url":null,"abstract":"","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"24 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146109812","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}
Pub Date : 2026-02-02DOI: 10.1016/j.ijengsci.2026.104491
Takashi Arima, Tommaso Ruggeri
{"title":"A symmetric hyperbolic non-isothermal model for viscoelastic solids and non-Newtonian fluids","authors":"Takashi Arima, Tommaso Ruggeri","doi":"10.1016/j.ijengsci.2026.104491","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2026.104491","url":null,"abstract":"","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"275 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146109818","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}
Pub Date : 2026-02-02DOI: 10.1016/j.ijengsci.2026.104495
Valeriy A. Buryachenko
{"title":"Additive general integral equations in thermoelastic micromechanics of composites","authors":"Valeriy A. Buryachenko","doi":"10.1016/j.ijengsci.2026.104495","DOIUrl":"https://doi.org/10.1016/j.ijengsci.2026.104495","url":null,"abstract":"","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"127 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146109817","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}
Pub Date : 2026-01-30DOI: 10.1016/j.ijengsci.2026.104481
Chengxiang Zheng , Tao Wu , Danming Zhong , Zichen Deng , Shaoxing Qu
In this paper, the chemically coupled elastic theory is proposed for hydrogel, based on statistical mechanics foundations, with particular emphasis on the critical yet overlooked role of hydrostatic modulus. We propose a comprehensive free energy density formulation that systematically integrates chemical interactions with both linear and nonlinear elastic moduli. Through analysis of isotropic swelling of hydrogel, a calibration protocol is developed for the chemically coupled elastic moduli, and the explicit relationship is derived between elastic moduli and environmental parameters. These analytical expressions facilitate direct determination and dynamic monitoring of instantaneous elastic moduli, including the hydrostatic modulus, linear constants, and second-order coefficients, under varying environmental conditions through measurable material properties.
Notably, our theoretical framework reveals the significant influence of hydrostatic modulus on hydrogel shear response, a previously unrecognized mechanism. As a demonstration, shear of a rectangular hydrogel block is investigated with the statistically-based phenomenological elastic theory, elucidating the impact of hydrostatic modulus and nonlinear properties through both linear and second-order nonlinear simulations. Under linear approximation, our model recovers the classical infinitesimal deformation theory, while second-order instantaneous elastic moduli prove essential for capturing finite deformation effects such as the negative Poynting effect, wherein shear induces axial contraction. Furthermore, the direct connection is established between internal micro-physical parameters and macroscopic deformation. The effects of chemical potential, Flory parameter, crosslinking degree, and related factors on shear deformation are analytically investigated and quantified for their contributions to material response.
Through systematic analysis, this work advances hydrogel mechanics understanding through a unified energy formulation that bridges statistical physics with continuum mechanics. And the results obtained here may provide a comprehensive guide for analysis of complex phenomena and design of soft materials.
{"title":"Physically based elastic theory of hydrogel with application to shear accounting for the effect of hydrostatic modulus","authors":"Chengxiang Zheng , Tao Wu , Danming Zhong , Zichen Deng , Shaoxing Qu","doi":"10.1016/j.ijengsci.2026.104481","DOIUrl":"10.1016/j.ijengsci.2026.104481","url":null,"abstract":"<div><div>In this paper, the chemically coupled elastic theory is proposed for hydrogel, based on statistical mechanics foundations, with particular emphasis on the critical yet overlooked role of hydrostatic modulus. We propose a comprehensive free energy density formulation that systematically integrates chemical interactions with both linear and nonlinear elastic moduli. Through analysis of isotropic swelling of hydrogel, a calibration protocol is developed for the chemically coupled elastic moduli, and the explicit relationship is derived between elastic moduli and environmental parameters. These analytical expressions facilitate direct determination and dynamic monitoring of instantaneous elastic moduli, including the hydrostatic modulus, linear constants, and second-order coefficients, under varying environmental conditions through measurable material properties.</div><div>Notably, our theoretical framework reveals the significant influence of hydrostatic modulus on hydrogel shear response, a previously unrecognized mechanism. As a demonstration, shear of a rectangular hydrogel block is investigated with the statistically-based phenomenological elastic theory, elucidating the impact of hydrostatic modulus and nonlinear properties through both linear and second-order nonlinear simulations. Under linear approximation, our model recovers the classical infinitesimal deformation theory, while second-order instantaneous elastic moduli prove essential for capturing finite deformation effects such as the negative Poynting effect, wherein shear induces axial contraction. Furthermore, the direct connection is established between internal micro-physical parameters and macroscopic deformation. The effects of chemical potential, Flory parameter, crosslinking degree, and related factors on shear deformation are analytically investigated and quantified for their contributions to material response.</div><div>Through systematic analysis, this work advances hydrogel mechanics understanding through a unified energy formulation that bridges statistical physics with continuum mechanics. And the results obtained here may provide a comprehensive guide for analysis of complex phenomena and design of soft materials.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"222 ","pages":"Article 104481"},"PeriodicalIF":5.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076848","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}
Pub Date : 2026-01-30DOI: 10.1016/j.ijengsci.2026.104480
Anjan Mukherjee , Biswanath Banerjee
A strain-gradient single-crystal plasticity framework is developed to capture size-dependent strengthening and gradient-induced hardening effects. The constitutive equations are derived from a constrained minimization of a dual dissipative potential, with positive plastic dissipation imposed to ensure thermodynamic consistency. The plastic slip gradient is decomposed into recoverable and unrecoverable components, rather than decomposing the higher-order stresses. The constrained minimization results in the higher-order stress of each slip plane evolving nonlinearly, similar to the Armstrong-Frederick type backstress model. The evolution equation includes strain gradient hardening along with a relaxation term. In the absence of the relaxation term, the formulation produces purely gradient-induced linear kinematic hardening without additional plastic dissipation. The inclusion of the relaxation term enhances dissipation and gives rise to an higher-order isotropic-type hardening effect associated with the plastic slip gradient. As cumulative plastic flow progresses due to evolution, the higher-order stress attains saturation. Both size-dependent kinematic and isotropic hardening also reach saturation when the recoverable part of the slip gradient saturates. Conversely, the unrecoverable slip gradient continues to rise with the plastic flow. Numerical simulations are performed to assess the effect of the relaxation coefficient on a single-crystal infinite shear layer subjected to monotonic, cyclic, and non-proportional loading conditions, with responses compared to the dislocation dynamic study. Two-dimensional polycrystalline tension with a hard interface illustrates the effect of grain size on macroscopic yield stress. It is observed that size-dependent long-range interactions are active near the grain interface and exhibit a saturating behavior. Finally, the proposed methodology is assessed against recent experimental investigations.
{"title":"Strain gradient crystal plasticity model with strengthening and kinematic hardening due to plastic slip gradient","authors":"Anjan Mukherjee , Biswanath Banerjee","doi":"10.1016/j.ijengsci.2026.104480","DOIUrl":"10.1016/j.ijengsci.2026.104480","url":null,"abstract":"<div><div>A strain-gradient single-crystal plasticity framework is developed to capture size-dependent strengthening and gradient-induced hardening effects. The constitutive equations are derived from a constrained minimization of a dual dissipative potential, with positive plastic dissipation imposed to ensure thermodynamic consistency. The plastic slip gradient is decomposed into recoverable and unrecoverable components, rather than decomposing the higher-order stresses. The constrained minimization results in the higher-order stress of each slip plane evolving nonlinearly, similar to the Armstrong-Frederick type backstress model. The evolution equation includes strain gradient hardening along with a relaxation term. In the absence of the relaxation term, the formulation produces purely gradient-induced linear kinematic hardening without additional plastic dissipation. The inclusion of the relaxation term enhances dissipation and gives rise to an higher-order isotropic-type hardening effect associated with the plastic slip gradient. As cumulative plastic flow progresses due to evolution, the higher-order stress attains saturation. Both size-dependent kinematic and isotropic hardening also reach saturation when the recoverable part of the slip gradient saturates. Conversely, the unrecoverable slip gradient continues to rise with the plastic flow. Numerical simulations are performed to assess the effect of the relaxation coefficient on a single-crystal infinite shear layer subjected to monotonic, cyclic, and non-proportional loading conditions, with responses compared to the dislocation dynamic study. Two-dimensional polycrystalline tension with a hard interface illustrates the effect of grain size on macroscopic yield stress. It is observed that size-dependent long-range interactions are active near the grain interface and exhibit a saturating behavior. Finally, the proposed methodology is assessed against recent experimental investigations.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"222 ","pages":"Article 104480"},"PeriodicalIF":5.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070911","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}
Pub Date : 2026-01-30DOI: 10.1016/j.ijengsci.2026.104479
Xianfeng Yang , Leyang Cheng , Hua Liu , Sicong Zhou , Jialing Yang
Ceramic lattices hold promise for structural and functional applications due to its lightweight and high specific strength. However, the brittle fracture of ceramic lattices under quasi-static or dynamic loading significantly limits the applications in energy absorption. To address this challenge, this study proposes a chain-lattice composite energy absorber inspired by the mortise and tenon joint. The chain structure operates as a generalizable mechanical principle by transforming tensile loads into confined axial compression within an internal energy-absorbing core, thereby suppressing the development of tensile strain in non-loading directions. This boundary confinement strategy effectively delayed global failure and enhanced energy absorption through controlled damage progression and stress redistribution. Quasi-static compression tests on various ceramic lattices revealed distinct deformation modes and failure mechanisms under unconstrained loading. Furthermore, quasi-static and dynamic tensile experiments on chain structure filled with lattices provided insights into constrained failure behavior and energy absorption characteristics under constrained loading. The results demonstrate that ceramic lattices within chain structure can absorb kinetic energy even after brittle fractures occur. Compared to unconstrained situations, the effective displacement of lattices under constraint can be increased by at least 19 times and the specific energy absorption can be increased by over 17 times. Notably, the BCC lattice-based chain absorber exhibits a stress plateau and large effective displacement, highlighting its ability to delay failure through progressive densification. This study provides a novel design strategy for enhancing the energy absorption capacity and delaying global failure in brittle materials, bridging core mechanical principles with practical applications in impact protection.
{"title":"Chain structure for ceramic lattices with improved energy absorption and delayed failure","authors":"Xianfeng Yang , Leyang Cheng , Hua Liu , Sicong Zhou , Jialing Yang","doi":"10.1016/j.ijengsci.2026.104479","DOIUrl":"10.1016/j.ijengsci.2026.104479","url":null,"abstract":"<div><div>Ceramic lattices hold promise for structural and functional applications due to its lightweight and high specific strength. However, the brittle fracture of ceramic lattices under quasi-static or dynamic loading significantly limits the applications in energy absorption. To address this challenge, this study proposes a chain-lattice composite energy absorber inspired by the mortise and tenon joint. The chain structure operates as a generalizable mechanical principle by transforming tensile loads into confined axial compression within an internal energy-absorbing core, thereby suppressing the development of tensile strain in non-loading directions. This boundary confinement strategy effectively delayed global failure and enhanced energy absorption through controlled damage progression and stress redistribution. Quasi-static compression tests on various ceramic lattices revealed distinct deformation modes and failure mechanisms under unconstrained loading. Furthermore, quasi-static and dynamic tensile experiments on chain structure filled with lattices provided insights into constrained failure behavior and energy absorption characteristics under constrained loading. The results demonstrate that ceramic lattices within chain structure can absorb kinetic energy even after brittle fractures occur. Compared to unconstrained situations, the effective displacement of lattices under constraint can be increased by at least 19 times and the specific energy absorption can be increased by over 17 times. Notably, the BCC lattice-based chain absorber exhibits a stress plateau and large effective displacement, highlighting its ability to delay failure through progressive densification. This study provides a novel design strategy for enhancing the energy absorption capacity and delaying global failure in brittle materials, bridging core mechanical principles with practical applications in impact protection.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"222 ","pages":"Article 104479"},"PeriodicalIF":5.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070912","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}
Pub Date : 2026-01-29DOI: 10.1016/j.ijengsci.2025.104433
Paolo Badino , Federico Bosi , Andrea Bacigalupo
A high-fidelity continualization framework is introduced for the accurate modeling of smart chiral lattice metamaterials aimed at controlling elastic wave propagation. The proposed approach yields convergent, multiband continuum models that are spectrally consistent with the underlying discrete Lagrangian formulation. It is readily extendable to both block- and beam-type periodic lattices, and naturally accommodates the inclusion of shunted piezoelectric resonators for active band-gap tuning. Thermodynamic consistency is ensured by embedding nonlocal effects into the inertial terms of the field equations through a regularization kernel that accurately captures dispersive behavior in all propagation directions, thus overcoming the intrinsic limitations of classical continualization methods. The integral-form continuum model, spectrally equivalent to the discrete one at the band-structure level, is simplified via Taylor expansions of the kernel, leading to systematic higher-order gradient models. Within the same framework, a rigorous downscaling map is introduced that, by means of an inverse Z-transform and a relabeling of the degrees of freedom, reconstructs the discrete kinematics from the continuum fields, thereby establishing explicit bridging relations between discrete and continuous descriptions. In parallel, the discrete Lagrangian formulation is developed with special emphasis on the shunted piezoelectric inertial resonator, modeled through an equivalent stiffness matrix obtained from numerically identified strain localization tensors, ensuring compliance with the pseudo-macro-homogeneity condition. Parametric analyses and numerical simulations of wave propagation confirm the spectral and kinematic consistency between the two formulations and demonstrate the capability of the high-fidelity continuum model to support the design of adaptive acoustic metamaterials for intelligent wave-guiding applications.
{"title":"Bridging Scales in Smart Chiral Metamaterials: A Convergent Multiband Continualization Yielding Spectrally Consistent Continua","authors":"Paolo Badino , Federico Bosi , Andrea Bacigalupo","doi":"10.1016/j.ijengsci.2025.104433","DOIUrl":"10.1016/j.ijengsci.2025.104433","url":null,"abstract":"<div><div>A high-fidelity continualization framework is introduced for the accurate modeling of smart chiral lattice metamaterials aimed at controlling elastic wave propagation. The proposed approach yields convergent, multiband continuum models that are spectrally consistent with the underlying discrete Lagrangian formulation. It is readily extendable to both block- and beam-type periodic lattices, and naturally accommodates the inclusion of shunted piezoelectric resonators for active band-gap tuning. Thermodynamic consistency is ensured by embedding nonlocal effects into the inertial terms of the field equations through a regularization kernel that accurately captures dispersive behavior in all propagation directions, thus overcoming the intrinsic limitations of classical continualization methods. The integral-form continuum model, spectrally equivalent to the discrete one at the band-structure level, is simplified via Taylor expansions of the kernel, leading to systematic higher-order gradient models. Within the same framework, a rigorous downscaling map is introduced that, by means of an inverse Z-transform and a relabeling of the degrees of freedom, reconstructs the discrete kinematics from the continuum fields, thereby establishing explicit bridging relations between discrete and continuous descriptions. In parallel, the discrete Lagrangian formulation is developed with special emphasis on the shunted piezoelectric inertial resonator, modeled through an equivalent stiffness matrix obtained from numerically identified strain localization tensors, ensuring compliance with the pseudo-macro-homogeneity condition. Parametric analyses and numerical simulations of wave propagation confirm the spectral and kinematic consistency between the two formulations and demonstrate the capability of the high-fidelity continuum model to support the design of adaptive acoustic metamaterials for intelligent wave-guiding applications.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"222 ","pages":"Article 104433"},"PeriodicalIF":5.7,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070910","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}
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