Pub Date : 2026-01-01Epub Date: 2025-09-06DOI: 10.1016/j.ijnonlinmec.2025.105255
Leixiao Wu, Wei Cai, Zhouquan Wang, Jie Yang
The mechanical behaviors of glassy polymers, including the viscoelastic and viscoplastic phases, are highly sensitive to temperature and strain rate. In order to describe such complex stress-strain responses, a variable fractional constitutive model considering temperature and strain rate effects is proposed with the order characterized by a biexponential function. Temperature and strain rate dependent criterion are established for both the elastic modulus and relaxation time, which are linearly decreasing functions of temperature. The fractional orders at different temperatures can be described by the same biexponential function, independent of temperature and strain rate, which indicates the same evolution trend during loading. The unloading behavior is subsequently characterized by shifting the order function depending on the reference unload strain. Numerical simulations show that the proposed model well describes and predicts the loading and unloading behaviors of glassy polymers. The physical interpretation of the order evolution is revealed based on the molecular chain mechanism. The validity and applicability of the model is further verified by the application of the model to different glassy polymers.
{"title":"A novel variable fractional constitutive model for complex multistage polymeric behaviors","authors":"Leixiao Wu, Wei Cai, Zhouquan Wang, Jie Yang","doi":"10.1016/j.ijnonlinmec.2025.105255","DOIUrl":"10.1016/j.ijnonlinmec.2025.105255","url":null,"abstract":"<div><div>The mechanical behaviors of glassy polymers, including the viscoelastic and viscoplastic phases, are highly sensitive to temperature and strain rate. In order to describe such complex stress-strain responses, a variable fractional constitutive model considering temperature and strain rate effects is proposed with the order characterized by a biexponential function. Temperature and strain rate dependent criterion are established for both the elastic modulus and relaxation time, which are linearly decreasing functions of temperature. The fractional orders at different temperatures can be described by the same biexponential function, independent of temperature and strain rate, which indicates the same evolution trend during loading. The unloading behavior is subsequently characterized by shifting the order function depending on the reference unload strain. Numerical simulations show that the proposed model well describes and predicts the loading and unloading behaviors of glassy polymers. The physical interpretation of the order evolution is revealed based on the molecular chain mechanism. The validity and applicability of the model is further verified by the application of the model to different glassy polymers.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105255"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020075","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 : 2026-01-01Epub Date: 2025-09-09DOI: 10.1016/j.ijnonlinmec.2025.105254
Yi Yao , Yanbin Lei , Louis Jézéquel , Xingrong Huang
This paper presents a non-iterative approximative nonlinear mode method based on linear modes for systems frictional stick-slip interfaces under the single resonant mode assumption. The proposed method effectively captures the influence of contact states on nonlinear dynamic behavior and addresses the need for efficient predictive analysis in frictionally damped systems. The core idea is to characterize contact states via stick-slip transitions at frictionally damped systems. Nonlinear modes are constructed by interpolating between linear modes associated with piecewise contact states, ranging from fully stuck to fully slipped. Under the weakly nonlinear assumption, interpolation functions for nonlinear modal frequencies are first established for one single frictional interface, and then generalized to multiple contact interfaces. The interpolation leverages linear modes across varying contact states to construct a piecewise function describing the dependency of nonlinear modal frequencies on relative displacement amplitudes on the interface. This non-iterative formulation avoids computationally expensive iterative procedures determining nonlinear frequencies. Moreover, corresponding nonlinear mode shapes are derived using the interpolated frequencies, and damping ratios are computed via an energy-based approach. The accuracy and efficiency of the proposed framework are demonstrated through three academic and one engineering numerical case studies.
{"title":"A non-iterative method for nonlinear modal analysis of frictional systems using contact-state interpolation","authors":"Yi Yao , Yanbin Lei , Louis Jézéquel , Xingrong Huang","doi":"10.1016/j.ijnonlinmec.2025.105254","DOIUrl":"10.1016/j.ijnonlinmec.2025.105254","url":null,"abstract":"<div><div>This paper presents a non-iterative approximative nonlinear mode method based on linear modes for systems frictional stick-slip interfaces under the single resonant mode assumption. The proposed method effectively captures the influence of contact states on nonlinear dynamic behavior and addresses the need for efficient predictive analysis in frictionally damped systems. The core idea is to characterize contact states via stick-slip transitions at frictionally damped systems. Nonlinear modes are constructed by interpolating between linear modes associated with piecewise contact states, ranging from fully stuck to fully slipped. Under the weakly nonlinear assumption, interpolation functions for nonlinear modal frequencies are first established for one single frictional interface, and then generalized to multiple contact interfaces. The interpolation leverages linear modes across varying contact states to construct a piecewise function describing the dependency of nonlinear modal frequencies on relative displacement amplitudes on the interface. This non-iterative formulation avoids computationally expensive iterative procedures determining nonlinear frequencies. Moreover, corresponding nonlinear mode shapes are derived using the interpolated frequencies, and damping ratios are computed via an energy-based approach. The accuracy and efficiency of the proposed framework are demonstrated through three academic and one engineering numerical case studies.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105254"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106002","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 : 2026-01-01Epub Date: 2025-09-08DOI: 10.1016/j.ijnonlinmec.2025.105237
Hugo Heidy Miyasato, Vinícius Gabriel Segala Simionatto, Milton Dias Junior
Mode coupling is a mechanism of friction-induced vibration that is considered one of the most relevant theories for studying brake squeal. This work introduced a negative stiffness effect in one of the contact interfaces from a nonlinear model with two degrees-of-freedom (DOF) and no external sources of damping. The linearized version presented multi-stability, where pure imaginary characteristic roots (i.e., marginal or neutral stability conditions) occurred for two points under specific parameter combinations. Besides, incommensurate natural frequency ratios prevail under those circumstances unless the exact parameter combinations are applied. Thus, an approximated two-frequency solution was developed using the Harmonic Balance Method (HBM) to evaluate which frequencies played the main role on the power exchanged at contact interfaces. The main results show that some of the marginally stable conditions produced quasi-periodic oscillations, where the liquid power exchanged (i.e. due to the oscillation of the system alone) was represented with important contributions of dominant frequency combinations. As a result, the total work exchanged varied in time as a bounded train of pulses.
{"title":"Bounded responses from a nonlinear model with mode-coupling instability and negative stiffness in one of its contact interfaces","authors":"Hugo Heidy Miyasato, Vinícius Gabriel Segala Simionatto, Milton Dias Junior","doi":"10.1016/j.ijnonlinmec.2025.105237","DOIUrl":"10.1016/j.ijnonlinmec.2025.105237","url":null,"abstract":"<div><div>Mode coupling is a mechanism of friction-induced vibration that is considered one of the most relevant theories for studying brake squeal. This work introduced a negative stiffness effect in one of the contact interfaces from a nonlinear model with two degrees-of-freedom (DOF) and no external sources of damping. The linearized version presented multi-stability, where pure imaginary characteristic roots (i.e., marginal or neutral stability conditions) occurred for two points under specific parameter combinations. Besides, incommensurate natural frequency ratios prevail under those circumstances unless the exact parameter combinations are applied. Thus, an approximated two-frequency solution was developed using the Harmonic Balance Method (HBM) to evaluate which frequencies played the main role on the power exchanged at contact interfaces. The main results show that some of the marginally stable conditions produced quasi-periodic oscillations, where the liquid power exchanged (i.e. due to the oscillation of the system alone) was represented with important contributions of dominant frequency combinations. As a result, the total work exchanged varied in time as a bounded train of pulses.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105237"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049700","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 : 2026-01-01Epub Date: 2025-09-15DOI: 10.1016/j.ijnonlinmec.2025.105264
Suo Wang , He Ma , Zhiyuan Li , Houfan Du , Shengxi Zhou
For the dual-beam coupled flexible bistable energy harvester (FBEH) with time-varying potential wells, accurately fitting the magnetic forces in two directions simultaneously using polynomials is difficult, hindering the derivation of the analytical solutions. Therefore, in this study, a semi-analytical method that combines the incremental harmonic balance method (IHBM) and the arc-length method is employed to determine the periodic solutions, with stability assessed by the Floquet theory. Comprehensive analyses of the dynamic responses are conducted, encompassing jump phenomenon, multiple solutions, and bifurcation characteristics. The obtained semi-analytical solutions demonstrate an excellent approximation for the system's periodic responses. Subsequently, the chaotic responses are analyzed via the Lyapunov exponents, and the effect of nonlinear stiffness was investigated. The nonlinear dynamic behaviors and characteristics of the FBEH demonstrate the consistent dynamic response patterns of the FBEH under different initial magnetic spacings, generally following the sequence of periodic intrawell oscillations, chaotic interwell oscillations, multi-orbit asymmetric periodic responses, chaotic responses and symmetric periodic responses. The initial magnetic spacing and nonlinear stiffness coefficients significantly influenced the jump frequency and response amplitude, whereas their impact on the dynamic response patterns was relatively minor. Overall, this study enhances the theoretical understanding of the FBEH in rotational environments by providing valuable insights and references for the design of such complex nonlinear electromechanical coupling systems.
{"title":"Periodic and chaotic responses of flexible bistable energy harvesters in rotational environment","authors":"Suo Wang , He Ma , Zhiyuan Li , Houfan Du , Shengxi Zhou","doi":"10.1016/j.ijnonlinmec.2025.105264","DOIUrl":"10.1016/j.ijnonlinmec.2025.105264","url":null,"abstract":"<div><div>For the dual-beam coupled flexible bistable energy harvester (FBEH) with time-varying potential wells, accurately fitting the magnetic forces in two directions simultaneously using polynomials is difficult, hindering the derivation of the analytical solutions. Therefore, in this study, a semi-analytical method that combines the incremental harmonic balance method (IHBM) and the arc-length method is employed to determine the periodic solutions, with stability assessed by the Floquet theory. Comprehensive analyses of the dynamic responses are conducted, encompassing jump phenomenon, multiple solutions, and bifurcation characteristics. The obtained semi-analytical solutions demonstrate an excellent approximation for the system's periodic responses. Subsequently, the chaotic responses are analyzed via the Lyapunov exponents, and the effect of nonlinear stiffness was investigated. The nonlinear dynamic behaviors and characteristics of the FBEH demonstrate the consistent dynamic response patterns of the FBEH under different initial magnetic spacings, generally following the sequence of periodic intrawell oscillations, chaotic interwell oscillations, multi-orbit asymmetric periodic responses, chaotic responses and symmetric periodic responses. The initial magnetic spacing and nonlinear stiffness coefficients significantly influenced the jump frequency and response amplitude, whereas their impact on the dynamic response patterns was relatively minor. Overall, this study enhances the theoretical understanding of the FBEH in rotational environments by providing valuable insights and references for the design of such complex nonlinear electromechanical coupling systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105264"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106000","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}
The elasto-viscoplastic behavior of semicrystalline polymers is modeled using an implicit finite element framework across three distinct temperature regimes: below, near, and above the glass transition temperature. The study considers varying strain rates under both isothermal and adiabatic conditions. A phenomenological DSGZ (Duan, Saigal, Greif, and Zimmerman) viscoplastic model is developed specifically for semi-crystalline thermoplastics with high thermal and mechanical resistances. To address the challenges of highly nonlinear terms, a novel perturbation-based return-mapping approach is introduced, ensuring stable and efficient stress integration. Additionally, an optimized procedure is seamlessly integrated to facilitate material parameter identification essential for the viscoplasticity model. Simulation results exhibit strong agreement with a wide range of experimental data, highlighting the necessity of temperature-specific parameter sets. Furthermore, a sensitivity analysis is conducted to assess the influence of key parameters on mechanical response. These findings establish a robust computational framework for accurately simulating and designing thermoplastic components subjected to complex thermo-mechanical loading scenarios.
半晶聚合物的弹粘塑性行为采用隐式有限元框架在三种不同的温度范围内建模：低于、接近和高于玻璃化转变温度。该研究考虑了在等温和绝热条件下不同的应变速率。DSGZ （Duan, Saigal, Greif, and Zimmerman）粘塑性模型是专门为具有高热阻和机械阻的半结晶热塑性塑料开发的。为了解决高度非线性项的挑战，引入了一种新的基于微扰的回归映射方法，以确保稳定和有效的应力积分。此外，优化程序无缝集成，以方便粘塑性模型必不可少的材料参数识别。模拟结果与广泛的实验数据表现出强烈的一致性，突出了温度特定参数设置的必要性。此外，还进行了灵敏度分析，以评估关键参数对力学响应的影响。这些发现为精确模拟和设计受复杂热机械载荷情景影响的热塑性部件建立了一个强大的计算框架。
{"title":"Thermo-viscoplastic constitutive modeling of semicrystalline polymers with a novel perturbation-based return-mapping algorithm","authors":"Rahele Vadizadeh , Asghar Zajkani , Mohsen Mirkhalaf","doi":"10.1016/j.ijnonlinmec.2025.105252","DOIUrl":"10.1016/j.ijnonlinmec.2025.105252","url":null,"abstract":"<div><div>The elasto-viscoplastic behavior of semicrystalline polymers is modeled using an implicit finite element framework across three distinct temperature regimes: below, near, and above the glass transition temperature. The study considers varying strain rates under both isothermal and adiabatic conditions. A phenomenological DSGZ (Duan, Saigal, Greif, and Zimmerman) viscoplastic model is developed specifically for semi-crystalline thermoplastics with high thermal and mechanical resistances. To address the challenges of highly nonlinear terms, a novel perturbation-based return-mapping approach is introduced, ensuring stable and efficient stress integration. Additionally, an optimized procedure is seamlessly integrated to facilitate material parameter identification essential for the viscoplasticity model. Simulation results exhibit strong agreement with a wide range of experimental data, highlighting the necessity of temperature-specific parameter sets. Furthermore, a sensitivity analysis is conducted to assess the influence of key parameters on mechanical response. These findings establish a robust computational framework for accurately simulating and designing thermoplastic components subjected to complex thermo-mechanical loading scenarios.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105252"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106001","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 : 2026-01-01Epub Date: 2025-09-16DOI: 10.1016/j.ijnonlinmec.2025.105263
Yong Song , Xiangming Zhan , Zhanlong Li , Yuan Qin , Yao Wang , Yuyuan Mou
Research on improving whole vehicle performance by enhancing suspension performance has much attention all the time. It is found that inerter based on on-off control strategy combined with bionic nonlinear structure can improve the suspension performance in previous study. Due to this, a whole vehicle performance enhancement method is proposed, that is, a suspension with inerter and bionic nonlinear stiffness characteristics (IBS) is introduced into the whole vehicle, and combined with three whole vehicle layout schemes (Scheme-I, Scheme-II and Scheme-III) of the IBS, the continuous relative-velocity relative-acceleration (CR) control strategy and the continuous absolute-velocity relative-acceleration (CA) control strategy are designed to control the IBS to enhance the whole vehicle performance efficiently. The whole vehicle dynamic models of the proposed schemes are established, the whole vehicle performance for the IBS with passive inerter and semi-active inerter are investigated, and the comprehensive evaluation index is constructed to comprehensively evaluate the whole vehicle performance of the IBS with semi-active inerter. The results show that the IBS with passive inerter can only partially improve the whole vehicle performance. The IBS with semi-active inerter can significantly enhance the whole vehicle ride comfort and handling stability, and eliminate the negative effects of the IBS with passive inerter. Comparatively speaking, the Scheme-II under the CR control strategy has the best whole vehicle performance improvement effect, and it has excellent road and speed adaptability under different working conditions. The above results verify the correctness of the proposed idea, the feasibility of the schemes, and the effectiveness of the control strategies.
{"title":"Research on vehicle performance improvement based on nonlinear bionic suspension with inerter and its control strategies","authors":"Yong Song , Xiangming Zhan , Zhanlong Li , Yuan Qin , Yao Wang , Yuyuan Mou","doi":"10.1016/j.ijnonlinmec.2025.105263","DOIUrl":"10.1016/j.ijnonlinmec.2025.105263","url":null,"abstract":"<div><div>Research on improving whole vehicle performance by enhancing suspension performance has much attention all the time. It is found that inerter based on on-off control strategy combined with bionic nonlinear structure can improve the suspension performance in previous study. Due to this, a whole vehicle performance enhancement method is proposed, that is, a suspension with inerter and bionic nonlinear stiffness characteristics (IBS) is introduced into the whole vehicle, and combined with three whole vehicle layout schemes (Scheme-I, Scheme-II and Scheme-III) of the IBS, the continuous relative-velocity relative-acceleration (CR) control strategy and the continuous absolute-velocity relative-acceleration (CA) control strategy are designed to control the IBS to enhance the whole vehicle performance efficiently. The whole vehicle dynamic models of the proposed schemes are established, the whole vehicle performance for the IBS with passive inerter and semi-active inerter are investigated, and the comprehensive evaluation index is constructed to comprehensively evaluate the whole vehicle performance of the IBS with semi-active inerter. The results show that the IBS with passive inerter can only partially improve the whole vehicle performance. The IBS with semi-active inerter can significantly enhance the whole vehicle ride comfort and handling stability, and eliminate the negative effects of the IBS with passive inerter. Comparatively speaking, the Scheme-II under the CR control strategy has the best whole vehicle performance improvement effect, and it has excellent road and speed adaptability under different working conditions. The above results verify the correctness of the proposed idea, the feasibility of the schemes, and the effectiveness of the control strategies.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105263"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109811","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 : 2026-01-01Epub Date: 2025-08-27DOI: 10.1016/j.ijnonlinmec.2025.105249
Chi Zhang , Guotong Zou , Qiong Lu , Yuehan Liu , Tabassam Yasmeen , Christopher Hopper , Lee Aucott , Jun Jiang
In the hot metal forming processes, materials deform viscoplastically and the microstructure changes dynamically, and constitutive equations used to characterize the material flow and microstructure evolution can be complicated. Although different types of constitutive equations have been proposed by many researchers, due to the strong non-linear relationship and interconnectivity between the variables, determining the material constants could be complex, and it lacks a unified optimization method and program for these problems. This work will develop a groundbreaking step-by-step optimization methodology to determine the material constants in constitutive equations effectively and efficiently. Relationships between the variables will be analyzed, and the computational complexity and cost will be reduced by dividing the whole optimization process into several steps and considering only one or several variables in each step. Five different sets of experimental data for different materials and forming conditions will be considered in this work for demonstration, and different constitutive equations will be used to describe the material flow behaviors and microstructure evolution, where the material constants will be determined using the proposed optimization method. Instead of taking days, weeks or even months to accurately determine the large number of material constants, the proposed unified data-based optimization method only took less than 7 min even for the most complex case, using a conventional personal desktop computer. This transformative optimization method will significantly improve the accuracy and efficiency of viscoplastic constitutive models’ development, enabling more complex microstructure behaviors e.g., phase transformation, void reduction, solid welding quality to be incorporated and reliably modelled.
{"title":"A novel unified data-based approach for determining the material constants in complex unified constitutive equations","authors":"Chi Zhang , Guotong Zou , Qiong Lu , Yuehan Liu , Tabassam Yasmeen , Christopher Hopper , Lee Aucott , Jun Jiang","doi":"10.1016/j.ijnonlinmec.2025.105249","DOIUrl":"10.1016/j.ijnonlinmec.2025.105249","url":null,"abstract":"<div><div>In the hot metal forming processes, materials deform viscoplastically and the microstructure changes dynamically, and constitutive equations used to characterize the material flow and microstructure evolution can be complicated. Although different types of constitutive equations have been proposed by many researchers, due to the strong non-linear relationship and interconnectivity between the variables, determining the material constants could be complex, and it lacks a unified optimization method and program for these problems. This work will develop a groundbreaking step-by-step optimization methodology to determine the material constants in constitutive equations effectively and efficiently<strong>.</strong> Relationships between the variables will be analyzed, and the computational complexity and cost will be reduced by dividing the whole optimization process into several steps and considering only one or several variables in each step. Five different sets of experimental data for different materials and forming conditions will be considered in this work for demonstration, and different constitutive equations will be used to describe the material flow behaviors and microstructure evolution, where the material constants will be determined using the proposed optimization method. Instead of taking days, weeks or even months to accurately determine the large number of material constants, the proposed unified data-based optimization method only took less than 7 min even for the most complex case, using a conventional personal desktop computer. This transformative optimization method will significantly improve the accuracy and efficiency of viscoplastic constitutive models’ development, enabling more complex microstructure behaviors e.g., phase transformation, void reduction, solid welding quality to be incorporated and reliably modelled.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105249"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921423","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 : 2026-01-01Epub Date: 2025-09-30DOI: 10.1016/j.ijnonlinmec.2025.105271
Xu Zhang , Jiangtao Wang , Xiangyang Liu , Yuan Zhang , Ningfei Wang , Xiao Hou
Solid propellants are particle-filled polymeric materials exhibiting nonlinear viscoelastic properties. In this study, viscoelastic compression tests are conducted on solid propellants. The compression nominal stress–strain curves exhibit a J shaped. Relaxation time and viscous stress increase with increasing deformation. The Tension–compression asymmetry in viscoelastic behavior is analyzed. Compared with tension, compression induces higher stress, longer relaxation time, and a larger viscous part. The mechanisms of nonlinear relaxation and Tension–compression asymmetry are analyzed through free volume theory and mesoscale simulations. At the microscopic scale, the limited free volume hinders the rearrangement of molecular networks and chain segments under large deformations. Less free volume and more coiled chain segments under compression lead to higher stress and longer relaxation time. At the mesoscopic scale, the patterns of interface debonding and damage evolution differ under tension and compression. The strength disparity between interfaces and particles leads to distinct tension and compression modulus. The micro–mesoscale coupling mechanisms result in Tension–compression asymmetry in the macroscopic viscoelastic mechanical behavior. The methodology and findings provide insights for multiscale investigations of other particle-filled composites.
{"title":"Tension–compression asymmetry in viscoelastic mechanical behavior and micro–mesoscale coupling mechanisms of composite propellant","authors":"Xu Zhang , Jiangtao Wang , Xiangyang Liu , Yuan Zhang , Ningfei Wang , Xiao Hou","doi":"10.1016/j.ijnonlinmec.2025.105271","DOIUrl":"10.1016/j.ijnonlinmec.2025.105271","url":null,"abstract":"<div><div>Solid propellants are particle-filled polymeric materials exhibiting nonlinear viscoelastic properties. In this study, viscoelastic compression tests are conducted on solid propellants. The compression nominal stress–strain curves exhibit a J shaped. Relaxation time and viscous stress increase with increasing deformation. The Tension–compression asymmetry in viscoelastic behavior is analyzed. Compared with tension, compression induces higher stress, longer relaxation time, and a larger viscous part. The mechanisms of nonlinear relaxation and Tension–compression asymmetry are analyzed through free volume theory and mesoscale simulations. At the microscopic scale, the limited free volume hinders the rearrangement of molecular networks and chain segments under large deformations. Less free volume and more coiled chain segments under compression lead to higher stress and longer relaxation time. At the mesoscopic scale, the patterns of interface debonding and damage evolution differ under tension and compression. The strength disparity between interfaces and particles leads to distinct tension and compression modulus. The micro–mesoscale coupling mechanisms result in Tension–compression asymmetry in the macroscopic viscoelastic mechanical behavior. The methodology and findings provide insights for multiscale investigations of other particle-filled composites.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105271"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220260","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: 2025-08-15DOI: 10.1016/j.ijnonlinmec.2025.105239
Mingzhi Lin , Wei Li , Dongmei Huang , Natasa Trisovic
Designing a control strategy to enhance the reliability of mechanical systems under random loads is crucial for maintaining system stability, resilience, performance, and safety. The primary challenge lies in optimizing the controller parameters while determining the reliability indexes. To overcome this difficulty, we have developed a novel intelligent algorithm to estimate optimal reliability of a kind of mechanical systems subjected to random loads by using a time-delay controller. This algorithm integrates a Gaussian Radial Basis Function Neural Network (GRBFNN) into a Genetic Algorithm (GA), taking the reliability function with unknown controlling parameters as the objective function, meanwhile the Backward Kolmogorov (BK) equation governing the reliability function with boundary condition and initial condition as constraints. In this algorithm, the neural network is employed to solve the BK equations at each iteration step of the GA to derive a fitness function, then the GA is utilized to obtain the optimal controlling parameters. Our algorithm enables the simultaneous optimization of implicit objectives and the solution of time-dependent BK equations. The influence of key parameters, such as population size, maximum iteration times in GA and the number of nodes in the neural network, on reliability performance is discussed in detail. The effectiveness of the proposed algorithm is testified through numerical comparisons and Monte Carlo simulations. The control strategy presented in this paper provides theoretical guidance to enhance reliability performance in mechanical engineering and shows great promise for practical applications.
{"title":"Stochastic reliability optimization of a controlled nonlinear energy sink under random excitation using GA-GRBFNN algorithm","authors":"Mingzhi Lin , Wei Li , Dongmei Huang , Natasa Trisovic","doi":"10.1016/j.ijnonlinmec.2025.105239","DOIUrl":"10.1016/j.ijnonlinmec.2025.105239","url":null,"abstract":"<div><div>Designing a control strategy to enhance the reliability of mechanical systems under random loads is crucial for maintaining system stability, resilience, performance, and safety. The primary challenge lies in optimizing the controller parameters while determining the reliability indexes. To overcome this difficulty, we have developed a novel intelligent algorithm to estimate optimal reliability of a kind of mechanical systems subjected to random loads by using a time-delay controller. This algorithm integrates a Gaussian Radial Basis Function Neural Network (GRBFNN) into a Genetic Algorithm (GA), taking the reliability function with unknown controlling parameters as the objective function, meanwhile the Backward Kolmogorov (BK) equation governing the reliability function with boundary condition and initial condition as constraints. In this algorithm, the neural network is employed to solve the BK equations at each iteration step of the GA to derive a fitness function, then the GA is utilized to obtain the optimal controlling parameters. Our algorithm enables the simultaneous optimization of implicit objectives and the solution of time-dependent BK equations. The influence of key parameters, such as population size, maximum iteration times in GA and the number of nodes in the neural network, on reliability performance is discussed in detail. The effectiveness of the proposed algorithm is testified through numerical comparisons and Monte Carlo simulations. The control strategy presented in this paper provides theoretical guidance to enhance reliability performance in mechanical engineering and shows great promise for practical applications.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105239"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144866100","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: 2025-08-09DOI: 10.1016/j.ijnonlinmec.2025.105240
Shrushti Maheshwari , Koushik Chatterjee , Sarthak S. Singh
The increased use of 3D-printed PLA components demands post-processing to improve their mechanical characteristics and address limitations. This study examines the impact of temperature and heat treatment on the progressive unloading and reloading response of 3D-printed PLA samples under compression, a topic currently underexplored from experimental and modeling point of view. The samples were heat-treated (HT) at 75 °C and 90 °C for 120 min. The degree of crystallinity increased from 3 % (for untreated (UT)) to 54 % for HT-90(120) samples. The compressive yield strength improved from 58 MPa (for UT) to 72 MPa in HT-90(120) as the heat-treated-induced crystallinity change reduced chain mobility. The progressive unloading and reloading experiments were conducted at 27 °C, 37 °C, and 47 °C, and to better represent the crystallinity variation, UT, HT-75(120), and HT-90(120) samples were considered. The loading curve showed linear elastic stiffness, followed by nonlinear pre-peak hardening, yielding, strain softening, or strain hardening, whereas the unloading curve showed a nonlinear response, gradually decreasing stiffness as strain recovered. HT-90(120) showed the lowest hysteresis loss ratio across all cycles, indicating the least energy loss due to stable molecular arrangement. A nonlinear microstructure-based viscoplastic constitutive model was developed to predict the viscoplastic deformation behavior of 3D-printed semi-crystalline materials during progressive unloading and reloading. The model, consisting of two parallel molecular networks representing amorphous and crystalline phases, accurately predicted the unloading and reloading responses of UT, HT-75(120), and HT-90(120) under specific temperature ranges.
{"title":"Exploring the influence of heat treatment on the progressive unloading-reloading behavior of 3D-printed polylactic acid through experiments and viscoplastic model","authors":"Shrushti Maheshwari , Koushik Chatterjee , Sarthak S. Singh","doi":"10.1016/j.ijnonlinmec.2025.105240","DOIUrl":"10.1016/j.ijnonlinmec.2025.105240","url":null,"abstract":"<div><div>The increased use of 3D-printed PLA components demands post-processing to improve their mechanical characteristics and address limitations. This study examines the impact of temperature and heat treatment on the progressive unloading and reloading response of 3D-printed PLA samples under compression, a topic currently underexplored from experimental and modeling point of view. The samples were heat-treated (HT) at 75 <sup>°</sup>C and 90 <sup>°</sup>C for 120 min. The degree of crystallinity increased from 3 % (for untreated (UT)) to 54 % for HT-90(120) samples. The compressive yield strength improved from 58 MPa (for UT) to 72 MPa in HT-90(120) as the heat-treated-induced crystallinity change reduced chain mobility. The progressive unloading and reloading experiments were conducted at 27 °C, 37 °C, and 47 °C, and to better represent the crystallinity variation, UT, HT-75(120), and HT-90(120) samples were considered. The loading curve showed linear elastic stiffness, followed by nonlinear pre-peak hardening, yielding, strain softening, or strain hardening, whereas the unloading curve showed a nonlinear response, gradually decreasing stiffness as strain recovered. HT-90(120) showed the lowest hysteresis loss ratio across all cycles, indicating the least energy loss due to stable molecular arrangement. A nonlinear microstructure-based viscoplastic constitutive model was developed to predict the viscoplastic deformation behavior of 3D-printed semi-crystalline materials during progressive unloading and reloading. The model, consisting of two parallel molecular networks representing amorphous and crystalline phases, accurately predicted the unloading and reloading responses of UT, HT-75(120), and HT-90(120) under specific temperature ranges.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105240"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829886","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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