Pub Date : 2025-11-01Epub Date: 2025-07-05DOI: 10.1016/j.ijnonlinmec.2025.105204
L. Cveticanin, M. Prica, M. Zukovic
In this paper the truly nonlinear oscillator (TNO) with position dependent mass (PDM) is considered. The TNO has no linear term, and the degree of nonlinearity is any integer or non-integer (fractional) power. Based on the Hamiltonian for TNO the Lagrange differential equation of motion is developed. The obtained mathematical model is a strong nonlinear Liénard equation which has the first integral of energy type. Analyzing the first integral it is obtained that the motion of the system is periodic and with the constant amplitude. In the paper a new procedure for determination of the frequency of vibration is introduced. The method is based on the He’s frequency formalism and on the exact solution of the TNO with constant mass. The significance of the obtained analytical solution lies in the fact that it provides an explicit relationship between the frequency, the oscillation amplitude, the TNO and PDM parameters, offering the possibility of frequency control. Conditions for low frequency vibrations are determined. The theoretical consideration is applied for vibration analyzes of a diatomic molecule with PDM function of exponential type. The obtained results are applicable in refining spectroscopy analysis and also in molecular and structural physics. In addition, due to analogy between mechanical and quantum oscillators this research provides guidance for further development in semi-conductors and quantum mechanics.
{"title":"Truly nonlinear oscillator with position-dependent mass","authors":"L. Cveticanin, M. Prica, M. Zukovic","doi":"10.1016/j.ijnonlinmec.2025.105204","DOIUrl":"10.1016/j.ijnonlinmec.2025.105204","url":null,"abstract":"<div><div>In this paper the truly nonlinear oscillator (TNO) with position dependent mass (PDM) is considered. The TNO has no linear term, and the degree of nonlinearity is any integer or non-integer (fractional) power. Based on the Hamiltonian for TNO the Lagrange differential equation of motion is developed. The obtained mathematical model is a strong nonlinear Liénard equation which has the first integral of energy type. Analyzing the first integral it is obtained that the motion of the system is periodic and with the constant amplitude. In the paper a new procedure for determination of the frequency of vibration is introduced. The method is based on the He’s frequency formalism and on the exact solution of the TNO with constant mass. The significance of the obtained analytical solution lies in the fact that it provides an explicit relationship between the frequency, the oscillation amplitude, the TNO and PDM parameters, offering the possibility of frequency control. Conditions for low frequency vibrations are determined. The theoretical consideration is applied for vibration analyzes of a diatomic molecule with PDM function of exponential type. The obtained results are applicable in refining spectroscopy analysis and also in molecular and structural physics. In addition, due to analogy between mechanical and quantum oscillators this research provides guidance for further development in semi-conductors and quantum mechanics.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105204"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579949","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}
Here we investigate stability of a film of viscous liquid hanging under a large horizontal cylinder. The liquid film is restricted by two straight contact lines; it is hold by the capillary force balancing the action of gravity. However, Rayleigh-Taylor instability of perturbations along the cylinder may destabilize the film and cause liquid dripping. Here we develop quasi-two-dimensional model for growth and propagation of perturbations in such a film. Linear stability analysis is carried out and the dispersion relationships are obtained. It is found that the width of the film is crucial for film stability: when the width is thinner than certain level, the film remains stable. Above this level, Rayleigh-Taylor instability develops. The wavelength of the fastest growth also depends on the film width. The cases of periodic perturbation and nonlinear localized perturbations are considered; in the latter case, the initial perturbation gets deformed into a new signal dominated by the wavelength of maximum growth.
{"title":"Stability of a liquid film hanging underneath a large horizontal cylinder","authors":"Sergey Aktershev, Aleksey Bobylev, Andrey Cherdantsev","doi":"10.1016/j.ijnonlinmec.2025.105189","DOIUrl":"10.1016/j.ijnonlinmec.2025.105189","url":null,"abstract":"<div><div>Here we investigate stability of a film of viscous liquid hanging under a large horizontal cylinder. The liquid film is restricted by two straight contact lines; it is hold by the capillary force balancing the action of gravity. However, Rayleigh-Taylor instability of perturbations along the cylinder may destabilize the film and cause liquid dripping. Here we develop quasi-two-dimensional model for growth and propagation of perturbations in such a film. Linear stability analysis is carried out and the dispersion relationships are obtained. It is found that the width of the film is crucial for film stability: when the width is thinner than certain level, the film remains stable. Above this level, Rayleigh-Taylor instability develops. The wavelength of the fastest growth also depends on the film width. The cases of periodic perturbation and nonlinear localized perturbations are considered; in the latter case, the initial perturbation gets deformed into a new signal dominated by the wavelength of maximum growth.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105189"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279231","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: 2025-07-05DOI: 10.1016/j.ijnonlinmec.2025.105197
Jamel Ferchichi , Houcine Meftahi
In this work, we study non-Newtonian visco-plastic flows in low regularity spaces. We consider the flow of a viscous, incompressible fluid of Norton–Hoff type, coupled with thermal effects and subjected to the action of particles located within the flow domain. Each particle exerts a pointwise force on the fluid, modeled by a Dirac distribution. The primary objective of this contribution is to establish a solvability result in a very weak sense. This solution concept arises from the low regularity induced by the source term. This lack of regularity precludes the use of classical techniques for deriving the desired existence result. To overcome the regularity issue, an appropriate fixed-point approach is applied within an augmented iterative process. To validate the theoretical developments, numerical experiments are conducted using a Newton iterative scheme in conjunction with the Multifrontal Massively Parallel Sparse Direct Solver (MUMPS), highlighting the approach’s effectiveness.
{"title":"Very weak solvability of singular thermo-visco-plastic flows with numerical investigations","authors":"Jamel Ferchichi , Houcine Meftahi","doi":"10.1016/j.ijnonlinmec.2025.105197","DOIUrl":"10.1016/j.ijnonlinmec.2025.105197","url":null,"abstract":"<div><div>In this work, we study non-Newtonian visco-plastic flows in low regularity spaces. We consider the flow of a viscous, incompressible fluid of Norton–Hoff type, coupled with thermal effects and subjected to the action of particles located within the flow domain. Each particle exerts a pointwise force on the fluid, modeled by a Dirac distribution. The primary objective of this contribution is to establish a solvability result in a very weak sense. This solution concept arises from the low regularity induced by the source term. This lack of regularity precludes the use of classical techniques for deriving the desired existence result. To overcome the regularity issue, an appropriate fixed-point approach is applied within an augmented iterative process. To validate the theoretical developments, numerical experiments are conducted using a Newton iterative scheme in conjunction with the Multifrontal Massively Parallel Sparse Direct Solver (MUMPS), highlighting the approach’s effectiveness.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105197"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579948","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}
Nonlinear primary resonance behavior of titanium dioxide (TiO2)/graphene nanoplatelet (GNP)/polymer nanocomposite rectangular plates using a geometrically nonlinear higher-order shear deformable plate model is investigated. The material properties of the hybrid nanocomposite, consisting of a polymer matrix reinforced with TiO2 nanoparticles and GNPs are determined through the finite element-based micromechanical modeling. The representative volume elements (RVEs) account for nanofiller geometry, dispersion patterns, and interphase effects to accurately simulate the mechanical properties of the nanocomposite. The nonlinear governing equations of motion are derived using Reddy's third-order shear deformation theory and von Kármán nonlinearity and are discretized via the generalized differential quadrature (GDQ) method. The equations are solved using a multistage numerical procedure combining the Galerkin approach, time periodic discretization (TPD) scheme, and pseudo-arc length continuation technique to obtain nonlinear frequency-response curves under various boundary conditions. The results highlight the pronounced contribution of GNP reinforcement, which significantly enhances the stiffness and nonlinear hardening behavior of the plates, as evidenced by increased linear and nonlinear frequencies and reduced vibration amplitudes.
{"title":"Geometrically nonlinear higher-order shear deformable model of TiO2/GNP/polymer nanocomposite rectangular plates: A numerical study on mechanical properties and nonlinear primary resonance features","authors":"Raheb Gholami , Reza Ansari , Mohammad Kazem Hassanzadeh-Aghdam , Saeid Sahmani","doi":"10.1016/j.ijnonlinmec.2025.105209","DOIUrl":"10.1016/j.ijnonlinmec.2025.105209","url":null,"abstract":"<div><div>Nonlinear primary resonance behavior of titanium dioxide (TiO<sub>2</sub>)/graphene nanoplatelet (GNP)/polymer nanocomposite rectangular plates using a geometrically nonlinear higher-order shear deformable plate model is investigated. The material properties of the hybrid nanocomposite, consisting of a polymer matrix reinforced with TiO<sub>2</sub> nanoparticles and GNPs are determined through the finite element-based micromechanical modeling. The representative volume elements (RVEs) account for nanofiller geometry, dispersion patterns, and interphase effects to accurately simulate the mechanical properties of the nanocomposite. The nonlinear governing equations of motion are derived using Reddy's third-order shear deformation theory and von Kármán nonlinearity and are discretized via the generalized differential quadrature (GDQ) method. The equations are solved using a multistage numerical procedure combining the Galerkin approach, time periodic discretization (TPD) scheme, and pseudo-arc length continuation technique to obtain nonlinear frequency-response curves under various boundary conditions. The results highlight the pronounced contribution of GNP reinforcement, which significantly enhances the stiffness and nonlinear hardening behavior of the plates, as evidenced by increased linear and nonlinear frequencies and reduced vibration amplitudes.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105209"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655134","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: 2025-07-07DOI: 10.1016/j.ijnonlinmec.2025.105205
Bowen Chen , Junwu Dai , Guibo Nie
To develop a high-performance numerical method for simulating dynamic behaviors of elastomers, it is necessary and urgent to investigate the influences of nonlinearity and thermodynamics-based stability of hyperelastic strain energy density function on the numerical predictions of dynamic properties of elastomers. To this end, this paper proposed a fractional visco-hyperelastic constitutive modeling approach for the dynamic behaviors of elastomers, in which two-parameter Mooney-Rivlin, Stumpf-Marczak and Hoss-Marczak hyperelastic models were harnessed. In this model, dependences of dynamic properties of elastomers on the frequency, dynamic strain amplitude (Payne effect), and prestrain were considered. Stress-strain constitutive relations were derived in the domain of an intrinsic time variable, which satisfies the thermodynamic consistency in the form of Clausius-Duhem inequality. Afterwards, the constitutive model was geometrically linearized in the neighborhood of a temporally constant predeformation. To determine the constitutive parameters, a linear formulation highlighting the prestrain effect was particularized in the derivations of the storage and the loss modulus. An inverse identification procedure was carried out for the experimental data. The prediction results revealed that the model using a nonlinear and thermodynamically stable strain energy density function with merely one fractional Maxwell element could achieve a remarkable accuracy and reliability in representing the dynamic behaviors of different elastomers under different dynamic loading conditions. Projection of constitutive relations in the intrinsic time domain facilitates the constitutive modeling within the dynamic regime. This work could provide a fundamental guidance for the assessment, optimization and design of elastomers with superior vibration isolation performance.
{"title":"Fractional visco-hyperelastic modeling for dynamic behaviors of elastomers","authors":"Bowen Chen , Junwu Dai , Guibo Nie","doi":"10.1016/j.ijnonlinmec.2025.105205","DOIUrl":"10.1016/j.ijnonlinmec.2025.105205","url":null,"abstract":"<div><div>To develop a high-performance numerical method for simulating dynamic behaviors of elastomers, it is necessary and urgent to investigate the influences of nonlinearity and thermodynamics-based stability of hyperelastic strain energy density function on the numerical predictions of dynamic properties of elastomers. To this end, this paper proposed a fractional visco-hyperelastic constitutive modeling approach for the dynamic behaviors of elastomers, in which two-parameter Mooney-Rivlin, Stumpf-Marczak and Hoss-Marczak hyperelastic models were harnessed. In this model, dependences of dynamic properties of elastomers on the frequency, dynamic strain amplitude (Payne effect), and prestrain were considered. Stress-strain constitutive relations were derived in the domain of an intrinsic time variable, which satisfies the thermodynamic consistency in the form of Clausius-Duhem inequality. Afterwards, the constitutive model was geometrically linearized in the neighborhood of a temporally constant predeformation. To determine the constitutive parameters, a linear formulation highlighting the prestrain effect was particularized in the derivations of the storage and the loss modulus. An inverse identification procedure was carried out for the experimental data. The prediction results revealed that the model using a nonlinear and thermodynamically stable strain energy density function with merely one fractional Maxwell element could achieve a remarkable accuracy and reliability in representing the dynamic behaviors of different elastomers under different dynamic loading conditions. Projection of constitutive relations in the intrinsic time domain facilitates the constitutive modeling within the dynamic regime. This work could provide a fundamental guidance for the assessment, optimization and design of elastomers with superior vibration isolation performance.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105205"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596589","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: 2025-05-26DOI: 10.1016/j.ijnonlinmec.2025.105156
C.O. Horgan , J.G. Murphy
A novel approach to the classical problem of axial shear of isotropic incompressible non-linearly elastic materials is proposed here. It is assumed that only the axial first Piola–Kirchhoff shear stress components are not identically zero, instead of the usual semi-inverse assumption on the displacement field of a typical particle. The form of the displacement consistent with this stress formulation is then obtained, assuming that the so-called Empirical Inequalities hold. The classical displacement formulation of axial shear is derived for the class of generalised neo-Hookean materials. The absence of a normal stress effect is noted. The difficulties in solving the corresponding problem in the context of Cauchy stress are highlighted.
{"title":"Cylindrical axial shear generated by an applied Piola–Kirchhoff stress","authors":"C.O. Horgan , J.G. Murphy","doi":"10.1016/j.ijnonlinmec.2025.105156","DOIUrl":"10.1016/j.ijnonlinmec.2025.105156","url":null,"abstract":"<div><div>A novel approach to the classical problem of axial shear of isotropic incompressible non-linearly elastic materials is proposed here. It is assumed that only the axial first Piola–Kirchhoff shear stress components are not identically zero, instead of the usual semi-inverse assumption on the displacement field of a typical particle. The form of the displacement consistent with this stress formulation is then obtained, assuming that the so-called Empirical Inequalities hold. The classical displacement formulation of axial shear is <em>derived</em> for the class of generalised neo-Hookean materials. The absence of a normal stress effect is noted. The difficulties in solving the corresponding problem in the context of Cauchy stress are highlighted.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105156"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185334","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: 2025-06-28DOI: 10.1016/j.ijnonlinmec.2025.105191
Debendra Prasad Panda, Manoj Pandey
This work presents a comprehensive analysis of a one-dimensional nonlinear blood flow model that incorporates a body force term, using both Eulerian and Lagrangian descriptions. By introducing Lagrangian coordinates, the system is reformulated as a single second-order partial differential equation derived from a variational principle. Lie symmetry analysis is performed in both coordinate systems, leading to the construction of one-dimensional optimal systems and exact invariant solutions. Variational symmetries satisfying Noether’s criterion are identified, and the associated conservation laws are obtained using Noether’s theorem. Finally, the evolution of weak discontinuity waves is investigated using an exact solution, revealing important nonlinear effects such as wave steepening and shock formation. The results highlight the role of symmetries and conservation laws in understanding wave behavior in physiological flow models.
{"title":"Lie symmetry and variational analysis of a blood flow model with body forces","authors":"Debendra Prasad Panda, Manoj Pandey","doi":"10.1016/j.ijnonlinmec.2025.105191","DOIUrl":"10.1016/j.ijnonlinmec.2025.105191","url":null,"abstract":"<div><div>This work presents a comprehensive analysis of a one-dimensional nonlinear blood flow model that incorporates a body force term, using both Eulerian and Lagrangian descriptions. By introducing Lagrangian coordinates, the system is reformulated as a single second-order partial differential equation derived from a variational principle. Lie symmetry analysis is performed in both coordinate systems, leading to the construction of one-dimensional optimal systems and exact invariant solutions. Variational symmetries satisfying Noether’s criterion are identified, and the associated conservation laws are obtained using Noether’s theorem. Finally, the evolution of weak discontinuity waves is investigated using an exact solution, revealing important nonlinear effects such as wave steepening and shock formation. The results highlight the role of symmetries and conservation laws in understanding wave behavior in physiological flow models.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105191"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518559","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: 2025-07-14DOI: 10.1016/j.ijnonlinmec.2025.105207
Edtson Emilio Herrera-Valencia , Mayra Luz Sánchez-Villavicencio , Catalina Soriano-Correa , Linda Verónica Campos-Fernández , Joaquín Flores Gerónimo , Luis Alberto Verduzco Mora , Oscar Bautista , Gabriel Ascanio , Vicente Jesús Hernández-Abad , Fausto Calderas
This study explores theoretically how a time-dependent, pulsatile pressure gradient combined with an electric field affects the flow of a structured electro-viscoelastic fluid in an annular space. The fluid's behavior is described using an extend version of the nonlinear viscoelastic constitutive equation with an exponential structure kernel (ESR-S). This updated ESR model incorporates solvent-related forces, resulting in the ESR-S formulation, which captures complex non-Newtonian behaviors such as shear thinning/thickening, thixotropy, yield stress, elasticity and normal stress differences. Dimensionless variables are introduced to characterize the geometry, material properties, and driving forces, In the linear viscoelastic regime, transfer functions are derived using Fourier analysis, revealing resonance behavior at specific frequencies governed by the Womersley and Deborah numbers. In the nonlinear regime, flow enhancement is predicted based on material characteristic and external mechanisms, including electric and thermal effects. The study shows that combination of a pulsatile pressure gradient and an electric field can significantly enhance flow, particularly when specific dimensionless parameters are met. This effect is demonstrated using rheological data from human blood samples with varying cholesterol levels, where high-cholesterol samples exhibited a distinct flow pattern suggesting a potential diagnostic indicator for hypercholesterolemia. The main objective is to theoretically evaluate the extended ESR-S model for predicting coupled flow behavior in both linear and nonlinear regimes.
{"title":"Combined time-pressure gradient and electric field on the electroosmotic flow of a complex fluid (human blood data) in a concentric annular microchannel: Linear and non-linear cases with the exponential structure rheological constitutive equation","authors":"Edtson Emilio Herrera-Valencia , Mayra Luz Sánchez-Villavicencio , Catalina Soriano-Correa , Linda Verónica Campos-Fernández , Joaquín Flores Gerónimo , Luis Alberto Verduzco Mora , Oscar Bautista , Gabriel Ascanio , Vicente Jesús Hernández-Abad , Fausto Calderas","doi":"10.1016/j.ijnonlinmec.2025.105207","DOIUrl":"10.1016/j.ijnonlinmec.2025.105207","url":null,"abstract":"<div><div>This study explores theoretically how a time-dependent, pulsatile pressure gradient combined with an electric field affects the flow of a structured electro-viscoelastic fluid in an annular space. The fluid's behavior is described using an extend version of the nonlinear viscoelastic constitutive equation with an exponential structure kernel (ESR-S). This updated ESR model incorporates solvent-related forces, resulting in the ESR-S formulation, which captures complex non-Newtonian behaviors such as shear thinning/thickening, thixotropy, yield stress, elasticity and normal stress differences. Dimensionless variables are introduced to characterize the geometry, material properties, and driving forces, In the linear viscoelastic regime, transfer functions are derived using Fourier analysis, revealing resonance behavior at specific frequencies governed by the Womersley and Deborah numbers. In the nonlinear regime, flow enhancement is predicted based on material characteristic and external mechanisms, including electric and thermal effects. The study shows that combination of a pulsatile pressure gradient and an electric field can significantly enhance flow, particularly when specific dimensionless parameters are met. This effect is demonstrated using rheological data from human blood samples with varying cholesterol levels, where high-cholesterol samples exhibited a distinct flow pattern suggesting a potential diagnostic indicator for hypercholesterolemia. The main objective is to theoretically evaluate the extended ESR-S model for predicting coupled flow behavior in both linear and nonlinear regimes.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105207"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663511","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: 2025-07-01DOI: 10.1016/j.ijnonlinmec.2025.105200
Md Jamirul Islam , Mohd Abu Bakr , Muhammad Farhan , Md. Maqubool Hosain , S.M.Mozammil Hasnain
This study investigates the behaviour of reinforced concrete (RC) slabs under impact loading using Finite Element Analysis (FEA) in ABAQUS/CAE. A 760 mm × 760 mm × 76 mm RC slab model was developed with material properties calibrated for both linear and nonlinear behaviour using the Drucker-Prager plasticity model. Simulations were conducted across boundary conditions, impact velocities, and reinforcement configurations. Results revealed that maximum displacement occurred in slabs with one side fixed (12.4 mm) compared to fully fixed slabs (6.8 mm). Boundary conditions significantly influenced stress distribution, with maximum von Mises stress recorded at 38.5 MPa for the cantilever case and 25.2 MPa for fully fixed conditions. Increasing impact velocity from 4500 mm/s to 7200 mm/s increased displacement from 8.6 mm to 14.1 mm and stress from 22.4 MPa to 41.7 MPa, stabilizing beyond 6500 mm/s. Replacing traditional reinforcement with a steel plate reduced displacement by 22 % and improved stress distribution, while reducing the steel plate volume by 40 % resulted in a 15 % increase in displacement. These findings underscore the importance of boundary conditions, material non-linearity, and optimized reinforcement design for predicting RC slab responses under dynamic loads, offering key insights for improving structural resilience in high-impact scenarios.
本研究利用ABAQUS/CAE中的有限元分析（FEA）研究了钢筋混凝土（RC）板在冲击载荷下的行为。建立了760 mm × 760 mm × 76 mm RC板模型，并使用Drucker-Prager塑性模型对材料的线性和非线性行为进行了校准。模拟进行了边界条件，冲击速度和加固配置。结果显示，与完全固定的板（6.8 mm）相比，一侧固定的板（12.4 mm）发生最大位移。边界条件对应力分布有显著影响，悬臂工况下最大von Mises应力为38.5 MPa，完全固定工况下最大von Mises应力为25.2 MPa。将冲击速度从4500 mm/s增加到7200 mm/s，位移从8.6 mm增加到14.1 mm，应力从22.4 MPa增加到41.7 MPa，稳定在6500 mm/s以上。用钢板代替传统的钢筋减少了22%的位移，改善了应力分布，而减少40%的钢板体积导致位移增加了15%。这些发现强调了边界条件、材料非线性和优化钢筋设计对于预测RC板在动荷载下的响应的重要性，为提高高冲击情景下的结构弹性提供了关键见解。
{"title":"Impact response and optimization of reinforced concrete slabs under dynamic loading: A finite element analysis study","authors":"Md Jamirul Islam , Mohd Abu Bakr , Muhammad Farhan , Md. Maqubool Hosain , S.M.Mozammil Hasnain","doi":"10.1016/j.ijnonlinmec.2025.105200","DOIUrl":"10.1016/j.ijnonlinmec.2025.105200","url":null,"abstract":"<div><div>This study investigates the behaviour of reinforced concrete (RC) slabs under impact loading using Finite Element Analysis (FEA) in ABAQUS/CAE. A 760 mm × 760 mm × 76 mm RC slab model was developed with material properties calibrated for both linear and nonlinear behaviour using the Drucker-Prager plasticity model. Simulations were conducted across boundary conditions, impact velocities, and reinforcement configurations. Results revealed that maximum displacement occurred in slabs with one side fixed (12.4 mm) compared to fully fixed slabs (6.8 mm). Boundary conditions significantly influenced stress distribution, with maximum von Mises stress recorded at 38.5 MPa for the cantilever case and 25.2 MPa for fully fixed conditions. Increasing impact velocity from 4500 mm/s to 7200 mm/s increased displacement from 8.6 mm to 14.1 mm and stress from 22.4 MPa to 41.7 MPa, stabilizing beyond 6500 mm/s. Replacing traditional reinforcement with a steel plate reduced displacement by 22 % and improved stress distribution, while reducing the steel plate volume by 40 % resulted in a 15 % increase in displacement. These findings underscore the importance of boundary conditions, material non-linearity, and optimized reinforcement design for predicting RC slab responses under dynamic loads, offering key insights for improving structural resilience in high-impact scenarios.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105200"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144535505","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: 2025-06-02DOI: 10.1016/j.ijnonlinmec.2025.105136
Uğurcan Eroğlu , Giuseppe Ruta
The local theory of elasticity (inner forces are sensible at insensible intermolecular distances) faces inconsistencies and limitations when one considers bodies at very small scales, i.e., with characteristic dimensions that are not several orders of magnitude greater than the intermolecular lengths, even in a linear setting. The so-called quasi-continuum models, preserving the principles of kinematics and balance of ordinary continuum mechanics while incorporating a richer description of inner forces at the constitutive level, attempt to mitigate this issue. One such model, well-known and commonly adopted in the last years, is due to Eringen and linearly expresses stress in terms of strain in a differential or integral form, by resorting to the convolution of a kernel function. This model, while successful for infinite media, encounters possible drawbacks when applied to finite domains, necessitating the imposition of “constitutive boundary conditions” of uncertain physical meaning. A series of alternative proposals in the literature try to overcome such difficulty; in the present contribution, we apply a perturbation procedure that circumvents this requirement. We apply this methodology to analyse paradigmatic problems of statics and free dynamics for fully deformable beams, and we present closed-form first-order expressions for benchmark scenarios, avoiding the necessity to use the constitutive boundary conditions. The solutions for purely flexible, Bernoulli–Euler, beams can be attained as a particular case of those provided here.
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