Pub Date : 2025-12-01Epub Date: 2025-08-18DOI: 10.1016/j.ijnonlinmec.2025.105238
Sounak Chakraborty, Santanu Das
Soft-impact and Gent models are analysed and a Duffing like approximation corresponding to the Gent model is derived to obtain a connection between them. The approximate model highlights the underlying nature of the nonlinearity present in the system and establishes a relationship between the Gent and the soft-impact model. Using the approximate non-composite model, the membrane parameters corresponding to the soft-impact model are calculated analytically. The calculated parameters are used to compare the dynamical responses, membrane voltage variation and the harvested power corresponding to the Gent, the approximate and the soft-impact models. A series of bifurcation studies, of and around the period-1 oscillations, with respect to the excitation parameters are performed by employing the approximate model. The effect of energy harvesting on bifurcation structure is also studied. In conclusion, the applicability and the limitations of the hard-impact, the soft-impact and approximate models are analysed taking the stress based Gent model as the standard.
{"title":"Comparative analysis of soft-impact and Gent models used in dielectric membrane based vibro-impact energy harvesting","authors":"Sounak Chakraborty, Santanu Das","doi":"10.1016/j.ijnonlinmec.2025.105238","DOIUrl":"10.1016/j.ijnonlinmec.2025.105238","url":null,"abstract":"<div><div>Soft-impact and Gent models are analysed and a Duffing like approximation corresponding to the Gent model is derived to obtain a connection between them. The approximate model highlights the underlying nature of the nonlinearity present in the system and establishes a relationship between the Gent and the soft-impact model. Using the approximate non-composite model, the membrane parameters corresponding to the soft-impact model are calculated analytically. The calculated parameters are used to compare the dynamical responses, membrane voltage variation and the harvested power corresponding to the Gent, the approximate and the soft-impact models. A series of bifurcation studies, of and around the period-1 oscillations, with respect to the excitation parameters are performed by employing the approximate model. The effect of energy harvesting on bifurcation structure is also studied. In conclusion, the applicability and the limitations of the hard-impact, the soft-impact and approximate models are analysed taking the stress based Gent model as the standard.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105238"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887464","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}
Pub Date : 2025-12-01Epub Date: 2025-08-22DOI: 10.1016/j.ijnonlinmec.2025.105243
Yuntian Zhang, Xiuting Sun, Jian Xu
The vibration isolation performance of a combined vibration isolation (CVI) system incorporating triple quasi-zero stiffness (TQZS) and a dynamic vibration absorber (DVA) is investigated in this paper. The influences of mass ratio and static characteristics on the CVI system are analyzed, and the superior isolation performances of the CVI system compared to both the basic TQZS system and the QZS-DVA system are validated. The coupled effects of enhanced vibration absorption and weakened achievable optimal static characteristics, resulting from increased mass ratio, on the CVI system’s isolation performance are explored. Significant advantages of the CVI system are observed, not only compared to traditional QZS-DVA systems, but also compared to high-order single QZS-DVA systems at larger excitation amplitudes. Greater robustness in the tuning frequency is demonstrated by the CVI system when compared to the QZS-DVA system, leading to effective adaptation across a wider range of excitation amplitudes and reducing the reliance on adaptive tuning. An upward shift of the Pareto frontiers is observed with increasing mass ratio, resulting in a degradation of the achievable static characteristics of the CVI system. Improved robustness can be maintained by ensuring a low restoring force at the zero-stiffness point located away from the equilibrium, when the TQZS characteristics are selected from the Pareto frontiers.
{"title":"Isolation performances of combined system with large amplitude nonlinearity and dynamic vibration absorber","authors":"Yuntian Zhang, Xiuting Sun, Jian Xu","doi":"10.1016/j.ijnonlinmec.2025.105243","DOIUrl":"10.1016/j.ijnonlinmec.2025.105243","url":null,"abstract":"<div><div>The vibration isolation performance of a combined vibration isolation (CVI) system incorporating triple quasi-zero stiffness (TQZS) and a dynamic vibration absorber (DVA) is investigated in this paper. The influences of mass ratio and static characteristics on the CVI system are analyzed, and the superior isolation performances of the CVI system compared to both the basic TQZS system and the QZS-DVA system are validated. The coupled effects of enhanced vibration absorption and weakened achievable optimal static characteristics, resulting from increased mass ratio, on the CVI system’s isolation performance are explored. Significant advantages of the CVI system are observed, not only compared to traditional QZS-DVA systems, but also compared to high-order single QZS-DVA systems at larger excitation amplitudes. Greater robustness in the tuning frequency is demonstrated by the CVI system when compared to the QZS-DVA system, leading to effective adaptation across a wider range of excitation amplitudes and reducing the reliance on adaptive tuning. An upward shift of the Pareto frontiers is observed with increasing mass ratio, resulting in a degradation of the achievable static characteristics of the CVI system. Improved robustness can be maintained by ensuring a low restoring force at the zero-stiffness point located away from the equilibrium, when the TQZS characteristics are selected from the Pareto frontiers.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105243"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894995","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}
Pub Date : 2025-12-01Epub Date: 2025-06-10DOI: 10.1016/j.ijnonlinmec.2025.105188
Wen Zhang , Yuan Yue , Pengcheng Miao , Xin Wu
In this paper, a dynamic model of wheelset system on curved tracks is established, and its hunting stability, hysteresis behavior, and generalized Hopf bifurcation are studied. The Newton-Raphson method and Hurwitz stability criterion are used to determine critical speed for instability of the system, and the saddle-node bifurcation point is located based on Floquet multipliers. The type of Hopf bifurcation (i.e. supercritical or subcritical) is determined by the sign of the first Lyapunov coefficient which is obtained by the projection method and central manifold theory. The influence of key parameters on the uncertainty and hysteresis regions generated by supercritical and subcritical Hopf bifurcations is studied. The results show that when the system undergoes subcritical Hopf bifurcation, the degree of uncertainty increases with increasing curvature radius. When the system undergoes supercritical Hopf bifurcation, changes from negative to positive with the increase of the primary longitudinal stiffness, and then increases with increasing primary longitudinal stiffness. The length of the hysteresis region also increases with the increase of primary longitudinal stiffness. Furthermore, the degenerated Hopf bifurcation is studied when the value of the first Lyapunov coefficient is zero. By calculating the expression of the second Lyapunov coefficient, the topological structure near the degenerated Hopf bifurcation and the motion state in the corresponding parameter region are studied in detail. Finally, the influences of key parameters of the wheelset system on Hopf bifurcation type, critical speed of Bautin bifurcation, second Lyapunov coefficient, and the displacement of the instability point are discussed.
{"title":"Hysteresis dynamics and generalized Hopf bifurcation analysis of wheelset system on curved tracks","authors":"Wen Zhang , Yuan Yue , Pengcheng Miao , Xin Wu","doi":"10.1016/j.ijnonlinmec.2025.105188","DOIUrl":"10.1016/j.ijnonlinmec.2025.105188","url":null,"abstract":"<div><div>In this paper, a dynamic model of wheelset system on curved tracks is established, and its hunting stability, hysteresis behavior, and generalized Hopf bifurcation are studied. The Newton-Raphson method and Hurwitz stability criterion are used to determine critical speed for instability of the system, and the saddle-node bifurcation point is located based on Floquet multipliers. The type of Hopf bifurcation (i.e. supercritical or subcritical) is determined by the sign of the first Lyapunov coefficient which is obtained by the projection method and central manifold theory. The influence of key parameters on the uncertainty and hysteresis regions generated by supercritical and subcritical Hopf bifurcations is studied. The results show that when the system undergoes subcritical Hopf bifurcation, the degree of uncertainty <span><math><mrow><msub><mi>v</mi><mrow><mi>u</mi><mi>n</mi></mrow></msub></mrow></math></span> increases with increasing curvature radius. When the system undergoes supercritical Hopf bifurcation, <span><math><mrow><msub><mi>v</mi><mrow><mi>u</mi><mi>n</mi></mrow></msub></mrow></math></span> changes from negative to positive with the increase of the primary longitudinal stiffness, and then increases with increasing primary longitudinal stiffness. The length of the hysteresis region <span><math><mrow><mo>Δ</mo><mi>v</mi></mrow></math></span> also increases with the increase of primary longitudinal stiffness. Furthermore, the degenerated Hopf bifurcation is studied when the value of the first Lyapunov coefficient is zero. By calculating the expression of the second Lyapunov coefficient, the topological structure near the degenerated Hopf bifurcation and the motion state in the corresponding parameter region are studied in detail. Finally, the influences of key parameters of the wheelset system on Hopf bifurcation type, critical speed of Bautin bifurcation, second Lyapunov coefficient, and the displacement of the instability point are discussed.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105188"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048356","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}
Pub Date : 2025-12-01Epub Date: 2025-08-11DOI: 10.1016/j.ijnonlinmec.2025.105215
Trung-Dung Tran , Canh V. Le , Phuc L.H. Ho , Duc-Chinh Pham
This paper presents a novel extension of the kinematic limit analysis framework by incorporating hydrostatic stress effects into the plastic dissipation function, enabling the modeling of pressure-sensitive failure mechanisms. The associated dissipation function is reformulated to relax the plastic incompressibility constraint, resulting in a generalized optimization problem amenable to second-order cone programming (SOCP). To address volumetric locking in low-order elements, the node-based smoothed finite element method (NS-FEM) is employed, enhancing numerical accuracy and convergence. The proposed formulation is validated through several benchmark problems, including structures with stress concentrations and pressure-dominant states. Results demonstrate the method’s ability to capture both global and localized collapse mechanisms, offering a robust and efficient alternative to classical approaches in the analysis of pressure-sensitive materials and porous structures.
{"title":"Three-dimensional kinematic plastic limit analysis with plastic incompressibility and conic programming","authors":"Trung-Dung Tran , Canh V. Le , Phuc L.H. Ho , Duc-Chinh Pham","doi":"10.1016/j.ijnonlinmec.2025.105215","DOIUrl":"10.1016/j.ijnonlinmec.2025.105215","url":null,"abstract":"<div><div>This paper presents a novel extension of the kinematic limit analysis framework by incorporating hydrostatic stress effects into the plastic dissipation function, enabling the modeling of pressure-sensitive failure mechanisms. The associated dissipation function is reformulated to relax the plastic incompressibility constraint, resulting in a generalized optimization problem amenable to second-order cone programming (SOCP). To address volumetric locking in low-order elements, the node-based smoothed finite element method (NS-FEM) is employed, enhancing numerical accuracy and convergence. The proposed formulation is validated through several benchmark problems, including structures with stress concentrations and pressure-dominant states. Results demonstrate the method’s ability to capture both global and localized collapse mechanisms, offering a robust and efficient alternative to classical approaches in the analysis of pressure-sensitive materials and porous structures.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105215"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829887","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}
Pub Date : 2025-12-01Epub Date: 2025-08-28DOI: 10.1016/j.ijnonlinmec.2025.105236
Abhik Mukherjee , Anurag
The Mathieu equation serves as a foundational model in the study of parametrically excited systems and has been extensively analyzed using both analytical and numerical techniques. Motivated by its relevance to various physical and engineering systems, we investigate its nonlinear extension – the Mathieu cubic–quintic Duffing equation – which includes both cubic and quintic stiffness terms. This nonlinear variant exhibits rich dynamical behavior including complex stability transitions and bifurcations. To explore these phenomena, we employ the Lindstedt–Poincaré method, which allows us to analytically capture both pitchfork bifurcations (subcritical and supercritical) near unstable parametric resonance tongues and subharmonic bifurcations at higher values of excitation frequencies. The analytical predictions are validated using numerical simulations based on Poincaré sections. Our results reveal the emergence of two distinct unstable tongues centered around and , as well as two subharmonic bifurcations located at and . We construct a comprehensive global bifurcation diagram in the parametric frequency–excitation strength space, showing transitions in equilibrium stability and the birth of multiple stable and unstable equilibrium points. Notably, the transition through each bifurcation boundary results in a specific number of stable and unstable equilibrium points alternatively. These findings not only extend the known behavior of the Mathieu and Mathieu–Duffing systems but also offer deeper insight into the complex dynamics induced by higher-order nonlinearities.
{"title":"Comprehending stability and bifurcations in Mathieu cubic–quintic Duffing system using Lindstedt–Poincaré methodology","authors":"Abhik Mukherjee , Anurag","doi":"10.1016/j.ijnonlinmec.2025.105236","DOIUrl":"10.1016/j.ijnonlinmec.2025.105236","url":null,"abstract":"<div><div>The Mathieu equation serves as a foundational model in the study of parametrically excited systems and has been extensively analyzed using both analytical and numerical techniques. Motivated by its relevance to various physical and engineering systems, we investigate its nonlinear extension – the Mathieu cubic–quintic Duffing equation – which includes both cubic and quintic stiffness terms. This nonlinear variant exhibits rich dynamical behavior including complex stability transitions and bifurcations. To explore these phenomena, we employ the Lindstedt–Poincaré method, which allows us to analytically capture both pitchfork bifurcations (subcritical and supercritical) near unstable parametric resonance tongues and subharmonic bifurcations at higher values of excitation frequencies. The analytical predictions are validated using numerical simulations based on Poincaré sections. Our results reveal the emergence of two distinct unstable tongues centered around <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>2</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, as well as two subharmonic bifurcations located at <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>4</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>6</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>. We construct a comprehensive global bifurcation diagram in the parametric frequency–excitation strength space, showing transitions in equilibrium stability and the birth of multiple stable and unstable equilibrium points. Notably, the transition through each bifurcation boundary results in a specific number of stable and unstable equilibrium points alternatively. These findings not only extend the known behavior of the Mathieu and Mathieu–Duffing systems but also offer deeper insight into the complex dynamics induced by higher-order nonlinearities.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105236"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921168","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}
Pub Date : 2025-12-01Epub Date: 2025-08-06DOI: 10.1016/j.ijnonlinmec.2025.105234
Jun Wang, Yu Wang, Kai Wu, Jun Ni, Han Zheng, Yu Sun
To investigate the electromechanical coupling between the main transmission system, the permanent magnet synchronous motor (PMSM), and the gear system of a servo press, this study focuses on a crank-type servo press. Firstly, the servo press structure is analyzed, and a control model for the PMSM under the id = 0 control strategy is established. Secondly, a dynamic model of the gear transmission–crank–slider mechanism is then developed using the Lagrange method, in which time-varying meshing stiffness is considered in the gear system. Finally, by introducing the electromagnetic torque relationship, the electromechanical coupling dynamic model of the servo press is constructed and implemented in Simulink for coupled simulation. Simulation results show that under no-load conditions, the angular velocity error of gear Ⅱ decreases with increasing PMSM speed, with a maximum error of -0.231 %. Meanwhile, the maximum slider speed error increases, and the peak errors occur near crank angles of 462.74°, 625.59°, and 455.47°, respectively. Frequency-domain analysis of the angular acceleration of gear Ⅱ and the slider acceleration indicates that the dominant spectral amplitudes are concentrated around the gear meshing frequency and its harmonics. Under impact load, all responses exhibit abrupt fluctuations, followed by gradual stabilization after the load is released. The spectral amplitudes in this case are significantly higher than those under no-load conditions. No-load experiments conducted on a prototype crank-type servo press show good agreement with the simulation results. This study provides a theoretical foundation for electromechanical coupling modeling and key parameter selection in PMSM–gear–crank–slider systems, offering valuable insights for the design and dynamic optimization of servo press.
{"title":"Electromechanical coupling dynamic modeling and dynamic response analysis of servo press","authors":"Jun Wang, Yu Wang, Kai Wu, Jun Ni, Han Zheng, Yu Sun","doi":"10.1016/j.ijnonlinmec.2025.105234","DOIUrl":"10.1016/j.ijnonlinmec.2025.105234","url":null,"abstract":"<div><div>To investigate the electromechanical coupling between the main transmission system, the permanent magnet synchronous motor (PMSM), and the gear system of a servo press, this study focuses on a crank-type servo press. Firstly, the servo press structure is analyzed, and a control model for the PMSM under the <em>i</em><sub>d</sub> = 0 control strategy is established. Secondly, a dynamic model of the gear transmission–crank–slider mechanism is then developed using the Lagrange method, in which time-varying meshing stiffness is considered in the gear system. Finally, by introducing the electromagnetic torque relationship, the electromechanical coupling dynamic model of the servo press is constructed and implemented in Simulink for coupled simulation. Simulation results show that under no-load conditions, the angular velocity error of gear Ⅱ decreases with increasing PMSM speed, with a maximum error of -0.231 %. Meanwhile, the maximum slider speed error increases, and the peak errors occur near crank angles of 462.74°, 625.59°, and 455.47°, respectively. Frequency-domain analysis of the angular acceleration of gear Ⅱ and the slider acceleration indicates that the dominant spectral amplitudes are concentrated around the gear meshing frequency and its harmonics. Under impact load, all responses exhibit abrupt fluctuations, followed by gradual stabilization after the load is released. The spectral amplitudes in this case are significantly higher than those under no-load conditions. No-load experiments conducted on a prototype crank-type servo press show good agreement with the simulation results. This study provides a theoretical foundation for electromechanical coupling modeling and key parameter selection in PMSM–gear–crank–slider systems, offering valuable insights for the design and dynamic optimization of servo press.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105234"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144841685","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}
Pub Date : 2025-12-01Epub Date: 2025-08-05DOI: 10.1016/j.ijnonlinmec.2025.105223
Krishna Kamdi , S.P. Atul Narayan , Kumbakonam R. Rajagopal
A mixture of granular ice and water exhibits complex behavior because of the compressible nature of granular ice and its tendency to expand in volume when subjected to shear. This can lead to spatial variations in the density of ice, even in simple shear flows. A model was developed in this study to capture such mechanical behavior using the mixture theory approach. Granular ice was taken to be compressible and capable of exhibiting dilatant behavior in shear, whereas water was taken to be incompressible. The model was developed in a Helmholtz-potential-based thermodynamic framework by making constitutive assumptions for the Helmholtz potential and the rate of dissipation and appealing to the principle of maximization of the rate of dissipation. Constitutive relations were developed for two different conditions — one where there is a volume additivity constraint between the volume fractions of the two components and another where there is no such constraint. The capabilities of the model were then evaluated by solving a modified form of Stokes’ first problem — the mixture being sandwiched between two parallel plates and moving one of the plates at a constant velocity. Under this deformation, the volume fractions of both ice and water were observed to vary spatially, with the volume fraction of ice increasing near the fixed plate and the volume fraction of water increasing near the moving plate. The extent of dilatancy of ice could be controlled by a model parameter.
{"title":"A model for the compressible and dilatant behavior of mixtures of water and granular ice","authors":"Krishna Kamdi , S.P. Atul Narayan , Kumbakonam R. Rajagopal","doi":"10.1016/j.ijnonlinmec.2025.105223","DOIUrl":"10.1016/j.ijnonlinmec.2025.105223","url":null,"abstract":"<div><div>A mixture of granular ice and water exhibits complex behavior because of the compressible nature of granular ice and its tendency to expand in volume when subjected to shear. This can lead to spatial variations in the density of ice, even in simple shear flows. A model was developed in this study to capture such mechanical behavior using the mixture theory approach. Granular ice was taken to be compressible and capable of exhibiting dilatant behavior in shear, whereas water was taken to be incompressible. The model was developed in a Helmholtz-potential-based thermodynamic framework by making constitutive assumptions for the Helmholtz potential and the rate of dissipation and appealing to the principle of maximization of the rate of dissipation. Constitutive relations were developed for two different conditions — one where there is a volume additivity constraint between the volume fractions of the two components and another where there is no such constraint. The capabilities of the model were then evaluated by solving a modified form of Stokes’ first problem — the mixture being sandwiched between two parallel plates and moving one of the plates at a constant velocity. Under this deformation, the volume fractions of both ice and water were observed to vary spatially, with the volume fraction of ice increasing near the fixed plate and the volume fraction of water increasing near the moving plate. The extent of dilatancy of ice could be controlled by a model parameter.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105223"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829884","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}
Pub Date : 2025-12-01Epub Date: 2025-08-20DOI: 10.1016/j.ijnonlinmec.2025.105241
Alexander Chesnokov , Valery Liapidevskii , Alexander Kazakov
We apply a one-dimensional nonlinear long-wave Boussinesq-type model, supplemented with friction/force terms, to describe the evolution of internal waves in a three-layer fluid filling a closed reservoir. The model takes into account the effects of dispersion and turbulent mixing. The outer homogeneous layers of the fluid are governed by the Green–Naghdi-type equations. The depth-averaged shallow water equations describe the flow in the intermediate hydrostatic layer. A simple law of vertical mixing governs the interaction of these layers during the development of the Kelvin–Helmholtz instability. We model internal seiches and their transformation into nonlinear wave trains in a quasi-two-layer fluid generated by a tilted tank suddenly returned to the untilted configuration. Comparison of the calculation results for different ratios of layer thicknesses and tank tilt angles shows good agreement with known experimental data. We also consider the evolution of wind-driven internal waves and show that the results obtained from the model align with direct numerical simulations.
{"title":"Nonlinear internal waves and turbulent mixing in a three-layer stratified fluid in a closed reservoir","authors":"Alexander Chesnokov , Valery Liapidevskii , Alexander Kazakov","doi":"10.1016/j.ijnonlinmec.2025.105241","DOIUrl":"10.1016/j.ijnonlinmec.2025.105241","url":null,"abstract":"<div><div>We apply a one-dimensional nonlinear long-wave Boussinesq-type model, supplemented with friction/force terms, to describe the evolution of internal waves in a three-layer fluid filling a closed reservoir. The model takes into account the effects of dispersion and turbulent mixing. The outer homogeneous layers of the fluid are governed by the Green–Naghdi-type equations. The depth-averaged shallow water equations describe the flow in the intermediate hydrostatic layer. A simple law of vertical mixing governs the interaction of these layers during the development of the Kelvin–Helmholtz instability. We model internal seiches and their transformation into nonlinear wave trains in a quasi-two-layer fluid generated by a tilted tank suddenly returned to the untilted configuration. Comparison of the calculation results for different ratios of layer thicknesses and tank tilt angles shows good agreement with known experimental data. We also consider the evolution of wind-driven internal waves and show that the results obtained from the model align with direct numerical simulations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105241"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879498","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}
Pub Date : 2025-11-01Epub Date: 2025-06-27DOI: 10.1016/j.ijnonlinmec.2025.105182
Afshin Anssari-Benam , Fahmi Zaïri
In Part I we presented the application of the hyperinelasticity modelling approach to the large elastic and inelastic deformations of semi-crystalline polymers. In this sequel we extend the application of this model to the finite strains of amorphous polymers, by studying Poly(methyl methacrylate), i.e., PMMA, and rubber-toughened PMMA (RT-PMMA) polymer systems. The effects of variation in rubber particle content, temperature and deformation rate on the elastic and inelastic mechanical behaviour of the specimens will be examined and modelled, under large uniaxial compression. The core model will be calibrated using base-line behaviours (i.e., quasi-static deformation, zero particle content, ambient temperature etc.), and the augmented model will be shown to favourably capture the effects of the foregoing inelasticity-inducing factors on the deformation behaviour of the samples. The augmentation of the core model is achieved by considering a linear evolution of the core model parameters, as the function of, e.g., particle content, deformation rate, temperature etc. Predictions of the elastic and inelastic behaviours at intermediary values of temperature/rubber content etc will also be made, and will be verified against experimental data to demonstrate the close match between the two. Given the success of the modelling approach in these applications and in Part I, this two-part contribution concludes a unified modelling tool for application across various thermoplastic polymers, from semi-crystalline to amorphous polymer types. Such a model allows exploration and prediction of the shift in the material response of semi-crystalline polymers from a thermoplastic-like to a rubber-like behaviour, and the reshaping of the amorphous matrix response in the presence of inelasticity-inducing effects for amorphous polymers, using a unified modelling approach.
{"title":"Modelling the finite deformation of thermoplastic polymers via hyperinelasticity, Part II: An amorphous polymer with varying rubber content-, rate- and temperature-dependency","authors":"Afshin Anssari-Benam , Fahmi Zaïri","doi":"10.1016/j.ijnonlinmec.2025.105182","DOIUrl":"10.1016/j.ijnonlinmec.2025.105182","url":null,"abstract":"<div><div>In Part I we presented the application of the <em>hyperinelasticity</em> modelling approach to the large elastic and inelastic deformations of semi-crystalline polymers. In this sequel we extend the application of this model to the finite strains of amorphous polymers, by studying Poly(methyl methacrylate), i.e., PMMA, and rubber-toughened PMMA (RT-PMMA) polymer systems. The effects of variation in rubber particle content, temperature and deformation rate on the elastic and inelastic mechanical behaviour of the specimens will be examined and modelled, under large uniaxial compression. The <em>core</em> model will be calibrated using base-line behaviours (i.e., quasi-static deformation, zero particle content, ambient temperature etc.), and the <em>augmented</em> model will be shown to favourably capture the effects of the foregoing inelasticity-inducing factors on the deformation behaviour of the samples. The augmentation of the core model is achieved by considering a linear evolution of the core model parameters, as the function of, e.g., particle content, deformation rate, temperature etc. <em>Predictions</em> of the elastic and inelastic behaviours at intermediary values of temperature/rubber content etc will also be made, and will be verified against experimental data to demonstrate the close match between the two. Given the success of the modelling approach in these applications and in Part I, this two-part contribution concludes a <em>unified</em> modelling tool for application across various thermoplastic polymers, from semi-crystalline to amorphous polymer types. Such a model allows exploration and prediction of the shift in the material response of semi-crystalline polymers from a thermoplastic-like to a rubber-like behaviour, and the reshaping of the amorphous matrix response in the presence of inelasticity-inducing effects for amorphous polymers, using a unified modelling approach.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105182"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557422","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}
Pub Date : 2025-11-01Epub Date: 2025-06-06DOI: 10.1016/j.ijnonlinmec.2025.105170
Robert Eberlein , Claus Wrana
This study presents a numerical implementation concept for elastomeric components under cyclic loading conditions at finite strains. Initial material damage is considered that is widely known as Mullins effect. A comprehensive quasi-static model is introduced and prepared for finite element implementation, covering both initial and subsequent loading cycles, converging to equilibrium. The combination of a non-linear relaxation-based hyperelastic model with selected damage functions allows for an accurate quantitative description of arbitrary elastomeric components. The study demonstrates the integration of the relaxed Modified Extended Tube Model (METM) in combination with Advanced Mullins Damage Modeling (AMDM) into a 3D finite element framework. Parameter studies and a relevant example from engineering practise prove the robustness of the finite element implementation and the applicability of the material modeling concept for virtually optimizing customized rubber compounds based on predefined elastomeric component properties.
{"title":"Non-linear finite element damage modeling after multiple cyclic loading of rubberlike materials","authors":"Robert Eberlein , Claus Wrana","doi":"10.1016/j.ijnonlinmec.2025.105170","DOIUrl":"10.1016/j.ijnonlinmec.2025.105170","url":null,"abstract":"<div><div>This study presents a numerical implementation concept for elastomeric components under cyclic loading conditions at finite strains. Initial material damage is considered that is widely known as Mullins effect. A comprehensive quasi-static model is introduced and prepared for finite element implementation, covering both initial and subsequent loading cycles, converging to equilibrium. The combination of a non-linear relaxation-based hyperelastic model with selected damage functions allows for an accurate quantitative description of arbitrary elastomeric components. The study demonstrates the integration of the relaxed Modified Extended Tube Model (METM) in combination with Advanced Mullins Damage Modeling (AMDM) into a 3D finite element framework. Parameter studies and a relevant example from engineering practise prove the robustness of the finite element implementation and the applicability of the material modeling concept for virtually optimizing customized rubber compounds based on predefined elastomeric component properties.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105170"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307956","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}
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