Pub Date : 2026-03-01Epub Date: 2025-12-16DOI: 10.1016/j.ijengsci.2025.104449
Helmut J. Böhm
The Mori–Tanaka method is a micromechanical effective-field model that approximates the local fields acting on any inhomogeneity phase by the corresponding matrix field. This assumption is tested in a case study using finite-element-based periodic homogenization for numerically evaluating the effective-field inhomogeneity concentration tensors of the reinforcement phases for a set of simple three-phase particle reinforced composites. The numerical predictions show a clear dependence of the mechanical and thermal effective fields on the material properties of the particulate phases. Even though this behavior deviates from the assumption underlying the Mori–Tanaka method, the latter provides useful approximations for the macroscopic stiffnesses and conductivities for the set of composites covered by the study.
{"title":"Three-phase particle reinforced composites: Effective fields and the Mori–Tanaka method","authors":"Helmut J. Böhm","doi":"10.1016/j.ijengsci.2025.104449","DOIUrl":"10.1016/j.ijengsci.2025.104449","url":null,"abstract":"<div><div>The Mori–Tanaka method is a micromechanical effective-field model that approximates the local fields acting on any inhomogeneity phase by the corresponding matrix field. This assumption is tested in a case study using finite-element-based periodic homogenization for numerically evaluating the effective-field inhomogeneity concentration tensors of the reinforcement phases for a set of simple three-phase particle reinforced composites. The numerical predictions show a clear dependence of the mechanical and thermal effective fields on the material properties of the particulate phases. Even though this behavior deviates from the assumption underlying the Mori–Tanaka method, the latter provides useful approximations for the macroscopic stiffnesses and conductivities for the set of composites covered by the study.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104449"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-31DOI: 10.1016/j.ijengsci.2025.104461
Ambalika Halder , Sharad Dwivedi , Shruti Dubey
This study presents an analytical investigation of the dynamics of curved domain walls in a bilayer magnetostrictive–piezoelectric heterostructure, using the extended Landau–Lifshitz–Gilbert equation. The system comprises a thin magnetostrictive layer perfectly bonded to the upper surface of a thick piezoelectric layer. We consider a transversely isotropic hexagonal class of magnetostrictive materials that exhibit structural inversion asymmetry. Our analysis accounts for the coupled effects of external magnetic fields, spin-polarized electric currents, magnetoelastic interactions, magnetocrystalline anisotropy, Rashba spin–orbit fields, and nonlinear viscous-dry friction dissipation mechanisms. Employing the reductive perturbation technique, we derive explicit analytical expressions for key dynamic parameters, such as the velocity, mobility, threshold, and breakdown conditions of the domain wall motion in the steady state. Our results reveal the intricate interplay between mean curvature, Rashba field, magnetoelastic coupling, and nonlinear dissipation, which collectively govern the propagation of domain walls in the magnetostrictive layer. Further, we numerically illustrate the analytical results obtained for curved domain walls on constant-curvature surfaces, such as planes, spheres, and cylinders. The results derived here demonstrate good qualitative alignment with recent studies.
{"title":"Dynamics of curved domain walls in hexagonal magnetostrictive materials with nonlinear dissipation and Rashba effects","authors":"Ambalika Halder , Sharad Dwivedi , Shruti Dubey","doi":"10.1016/j.ijengsci.2025.104461","DOIUrl":"10.1016/j.ijengsci.2025.104461","url":null,"abstract":"<div><div>This study presents an analytical investigation of the dynamics of curved domain walls in a bilayer magnetostrictive–piezoelectric heterostructure, using the extended Landau–Lifshitz–Gilbert equation. The system comprises a thin magnetostrictive layer perfectly bonded to the upper surface of a thick piezoelectric layer. We consider a transversely isotropic hexagonal class of magnetostrictive materials that exhibit structural inversion asymmetry. Our analysis accounts for the coupled effects of external magnetic fields, spin-polarized electric currents, magnetoelastic interactions, magnetocrystalline anisotropy, Rashba spin–orbit fields, and nonlinear viscous-dry friction dissipation mechanisms. Employing the reductive perturbation technique, we derive explicit analytical expressions for key dynamic parameters, such as the velocity, mobility, threshold, and breakdown conditions of the domain wall motion in the steady state. Our results reveal the intricate interplay between mean curvature, Rashba field, magnetoelastic coupling, and nonlinear dissipation, which collectively govern the propagation of domain walls in the magnetostrictive layer. Further, we numerically illustrate the analytical results obtained for curved domain walls on constant-curvature surfaces, such as planes, spheres, and cylinders. The results derived here demonstrate good qualitative alignment with recent studies.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104461"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-07DOI: 10.1016/j.ijengsci.2025.104436
Andrea Nobili , Dipendu Pramanik
We study the dynamics of a bistable Single Degree of Freedom mechanism that bifurcates from the trivial straight configuration when subjected to a critical traction force and it is otherwise incompressible. We show that the appearance of “impacts”, in correspondence with the minimum axial extension of the system, merely reflects the adoption of the axial extension as the dependent variable, as opposed to the angular rotation. Within this description, the structure realizes a perfectly elastic obstacle. Next, we construct the continuous limit for a dense chain of such mechanisms and axial strain naturally emerges as the continuous dependent field. Consequently, an unilateral constraint becomes associated with the system. Most importantly, the corresponding Lagrangian problem needs to be supplemented by energy conservation across the impacts to faithfully represent the underlying microstructure. In doing so, we generalize the established procedure to construct the continuous limit of a dense chain of discrete systems to the presence of unilateral constraints. Remarkably, energy conservation allows to apply Hamilton’s principle in the form of a variational equality, in contrast to the inequality format usually encountered when dealing with non-smooth problems. This important result, which greatly simplifies the mathematics, is available provided that variations are extended to accommodate for discontinuities in the variables. Besides, the system dynamics may be now constructed semi-analytically by joining pairs of d’Alembert’s solutions through the conditions obtained from the extended variational principle at the impact time and location (which are obviously unknown). As a result, waves propagating in the system are obtained and they are checked against global energy conservation.
{"title":"Impact-governed dynamics of an axially-incompressible bistable continuous metastructure","authors":"Andrea Nobili , Dipendu Pramanik","doi":"10.1016/j.ijengsci.2025.104436","DOIUrl":"10.1016/j.ijengsci.2025.104436","url":null,"abstract":"<div><div>We study the dynamics of a bistable Single Degree of Freedom mechanism that bifurcates from the trivial straight configuration when subjected to a critical traction force and it is otherwise incompressible. We show that the appearance of “impacts”, in correspondence with the minimum axial extension of the system, merely reflects the adoption of the axial extension as the dependent variable, as opposed to the angular rotation. Within this description, the structure realizes a perfectly elastic obstacle. Next, we construct the continuous limit for a dense chain of such mechanisms and axial strain naturally emerges as the continuous dependent field. Consequently, an unilateral constraint becomes associated with the system. Most importantly, the corresponding Lagrangian problem needs to be supplemented by energy conservation across the impacts to faithfully represent the underlying microstructure. In doing so, we generalize the established procedure to construct the continuous limit of a dense chain of discrete systems to the presence of unilateral constraints. Remarkably, energy conservation allows to apply Hamilton’s principle in the form of a variational <em>equality</em>, in contrast to the inequality format usually encountered when dealing with non-smooth problems. This important result, which greatly simplifies the mathematics, is available provided that variations are extended to accommodate for discontinuities in the variables. Besides, the system dynamics may be now constructed semi-analytically by joining pairs of d’Alembert’s solutions through the conditions obtained from the extended variational principle at the impact time and location (which are obviously unknown). As a result, waves propagating in the system are obtained and they are checked against global energy conservation.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104436"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145697316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-05DOI: 10.1016/j.ijengsci.2025.104437
Domenico De Tommasi, Francesco Trentadue, Gennaro Vitucci
Double-network (DN) hydrogels combine exceptional toughness with tissue-like softness, making them promising materials for biomedical and soft engineering applications. In this work, we present a novel constitutive model for predicting their mechanical response under general multiaxial loading conditions. At the microscopic scale, the two interlaced polymer networks are represented by effective semiflexible (worm-like) chains, capturing the cooperative behavior of the stiff, brittle first network and the soft, extensible second one. Irreversible damage is modeled as a progressive increase in the effective contour length of these chains, enabling the reproduction of the characteristic softening and Mullins effects observed experimentally. The macroscopic behavior is obtained through affine microsphere-based homogenization, ensuring a thermodynamically consistent formulation with a minimal number of material parameters. Despite its simplicity, the model accurately reproduces uniaxial and biaxial responses reported in the literature and demonstrates predictive capability across different loading paths. Furthermore, the identified parameters exhibit systematic trends with varying crosslinking densities, highlighting the potential of the proposed framework for the rational design of DN hydrogels with tailored mechanical properties.
{"title":"A compact anisotropic model for the mechanical response of double network hydrogels","authors":"Domenico De Tommasi, Francesco Trentadue, Gennaro Vitucci","doi":"10.1016/j.ijengsci.2025.104437","DOIUrl":"10.1016/j.ijengsci.2025.104437","url":null,"abstract":"<div><div>Double-network (DN) hydrogels combine exceptional toughness with tissue-like softness, making them promising materials for biomedical and soft engineering applications. In this work, we present a novel constitutive model for predicting their mechanical response under general multiaxial loading conditions. At the microscopic scale, the two interlaced polymer networks are represented by effective semiflexible (worm-like) chains, capturing the cooperative behavior of the stiff, brittle first network and the soft, extensible second one. Irreversible damage is modeled as a progressive increase in the effective contour length of these chains, enabling the reproduction of the characteristic softening and Mullins effects observed experimentally. The macroscopic behavior is obtained through affine microsphere-based homogenization, ensuring a thermodynamically consistent formulation with a minimal number of material parameters. Despite its simplicity, the model accurately reproduces uniaxial and biaxial responses reported in the literature and demonstrates predictive capability across different loading paths. Furthermore, the identified parameters exhibit systematic trends with varying crosslinking densities, highlighting the potential of the proposed framework for the rational design of DN hydrogels with tailored mechanical properties.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104437"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-05DOI: 10.1016/j.ijengsci.2025.104439
Teoman Özer , Martin Kröger
In this first part of our study, we examine the Kirsch problem analytically for a body composed of a homogeneous but anisotropic material from the perspectives of both classical and gradient elasticity theories. As a continuation, the second part will address the Kirsch problem for a body that is isotropic but inhomogeneous. In the model, the plane is assumed anisotropic and, with positive characterizing the degree of anisotropy, we consider a weakly anisotropic material for which the six elastic coefficients deviate slightly from their values in the equivalent isotropic material. The Airy stress function is used to obtain analytical solutions for stress fields. Similarly, a gradient Airy stress function notation is employed to solve the Kirsch problem in gradient elasticity theory. The stress and displacement fields for the anisotropic Kirsch problem are determined analytically within both classical and gradient elasticity frameworks. The analytical solutions from isotropic and classical elasticity are obtained and compared with existing literature. In addition to the classical boundary conditions, the higher-order gradient boundary conditions are also included in the stress field calculations. The differences that emerge within the scope of classical and gradient elasticity theories are also examined, along with a comparative analysis of the graphical representations of the analytical solutions obtained and the size effects in the gradient elasticity theory. Furthermore, based on both classical and gradient elasticity theories, the comparative presentation of the influence of anisotropic material qualities on the solutions is provided. In this study, we represent the analytical solutions for the homogeneous but anisotropic Kirsch problem, using both classical elasticity and gradient elasticity theory for the first time in the literature.
{"title":"Kirsch problem in classical and gradient elasticity. Part I: Anisotropic and homogeneous bodies","authors":"Teoman Özer , Martin Kröger","doi":"10.1016/j.ijengsci.2025.104439","DOIUrl":"10.1016/j.ijengsci.2025.104439","url":null,"abstract":"<div><div>In this first part of our study, we examine the Kirsch problem analytically for a body composed of a homogeneous but anisotropic material from the perspectives of both classical and gradient elasticity theories. As a continuation, the second part will address the Kirsch problem for a body that is isotropic but inhomogeneous. In the model, the plane is assumed anisotropic and, with positive <span><math><mrow><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>≪</mo><mn>1</mn></mrow></math></span> characterizing the degree of anisotropy, we consider a weakly anisotropic material for which the six elastic coefficients deviate slightly from their values in the equivalent isotropic material. The Airy stress function is used to obtain analytical solutions for stress fields. Similarly, a gradient Airy stress function notation is employed to solve the Kirsch problem in gradient elasticity theory. The stress and displacement fields for the anisotropic Kirsch problem are determined analytically within both classical and gradient elasticity frameworks. The analytical solutions from isotropic and classical elasticity are obtained and compared with existing literature. In addition to the classical boundary conditions, the higher-order gradient boundary conditions are also included in the stress field calculations. The differences that emerge within the scope of classical and gradient elasticity theories are also examined, along with a comparative analysis of the graphical representations of the analytical solutions obtained and the size effects in the gradient elasticity theory. Furthermore, based on both classical and gradient elasticity theories, the comparative presentation of the influence of anisotropic material qualities on the solutions is provided. In this study, we represent the analytical solutions for the homogeneous but anisotropic Kirsch problem, using both classical elasticity and gradient elasticity theory for the first time in the literature.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104439"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-04DOI: 10.1016/j.ijengsci.2025.104438
Ziyu Xing , Xiaodong Wang , Xiaoling Hu , Rongguo Zhao
Rubber elasticity is considered the cornerstone of understanding the conformation of rubbery polymer chains. This paper presents a multi-well energy landscape strategy to explore the rubber elasticity of rubber-like polymers that undergo intermolecular interactions. Based on the tube model and Langevin statistics, the proposed constitutive formulation explicitly incorporates the intrinsic heterogeneity of cross-linked networks and topological entanglements, while simultaneously accounting for the coupling effects of intermolecular interactions. The model postulates that intermolecular interactions manifest as localized constraints, which amplify the inherent heterogeneity by inducing variations in tube diameter and effective chain length, thereby modulating the entropic contributions to the free energy density. Furthermore, the framework captures the emergence of a multi-well energy landscape arising from the intermolecular interaction-induced heterogeneity in conformations of polymer chains. The model was validated against comprehensive experimental datasets of rubber-like polymers, including inflation of balloons, uniaxial tension/compression, pure shear deformation, and equi-biaxial tension. The results demonstrate that the proposed model can accurately predict the mechanical behavior of rubber-like polymers across various deformation modes and conditions. Compared to other models like the Anssari-Benam model, Yeoh model, and Pucci-Saccomnadi model, the proposed model shows advantages in capturing the complex mechanical responses of rubbers, particularly in multi-axial stress states. The study enhances the understanding of rubber elasticity and provides a robust tool for predicting the mechanical behavior of soft rubbery materials.
{"title":"A multi-well energy landscape strategy of the rubber-like polymers undergoing intermolecular interactions for exploring rubber elasticity","authors":"Ziyu Xing , Xiaodong Wang , Xiaoling Hu , Rongguo Zhao","doi":"10.1016/j.ijengsci.2025.104438","DOIUrl":"10.1016/j.ijengsci.2025.104438","url":null,"abstract":"<div><div>Rubber elasticity is considered the cornerstone of understanding the conformation of rubbery polymer chains. This paper presents a multi-well energy landscape strategy to explore the rubber elasticity of rubber-like polymers that undergo intermolecular interactions. Based on the tube model and Langevin statistics, the proposed constitutive formulation explicitly incorporates the intrinsic heterogeneity of cross-linked networks and topological entanglements, while simultaneously accounting for the coupling effects of intermolecular interactions. The model postulates that intermolecular interactions manifest as localized constraints, which amplify the inherent heterogeneity by inducing variations in tube diameter and effective chain length, thereby modulating the entropic contributions to the free energy density. Furthermore, the framework captures the emergence of a multi-well energy landscape arising from the intermolecular interaction-induced heterogeneity in conformations of polymer chains. The model was validated against comprehensive experimental datasets of rubber-like polymers, including inflation of balloons, uniaxial tension/compression, pure shear deformation, and equi-biaxial tension. The results demonstrate that the proposed model can accurately predict the mechanical behavior of rubber-like polymers across various deformation modes and conditions. Compared to other models like the Anssari-Benam model, Yeoh model, and Pucci-Saccomnadi model, the proposed model shows advantages in capturing the complex mechanical responses of rubbers, particularly in multi-axial stress states. The study enhances the understanding of rubber elasticity and provides a robust tool for predicting the mechanical behavior of soft rubbery materials.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104438"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.ijengsci.2025.104450
Yuxuan Ma, Zhiwen Ren, Hao-Wen Dong
Elastic metamaterials typically display anisotropic scattering behavior which mainly stems from high-order modes linked to shear and rotation deformations, thus complicating the characterization of the scattering behavior. However, most existing mass-spring models can only describe the coupled in-plane motions of longitudinal and transverse waves, which naturally ignores the essential rotations. Considering the pure translation and coupled-translation-rotation motions, this study proposes two spring-interconnected mass-in-mass models with rotational symmetry, featuring 2-degree-of-freedom (2-DOF) and 3-DOF anisotropic configurations respectively. For an incident longitudinal wave, the scattered transverse wave energy in these models is theoretically demonstrated at a specific rotation angle of spring. The established scattered elastic wave energy theory associating the dynamic response with structural parameters indicates that the higher scattering energy conversion of metamaterials can be achieved if two polarization components of translation and rotation are considered simultaneously. Comparing the scattering energy conversion capabilities of uni-layer and bi-layer models reveals that the bi-layer 3-DOF anisotropic model promotes the higher-efficiency low-frequency scattering energy conversion by reducing the dynamic effective stiffness. Variations in the scattering conversion coefficient with mass and aspect ratio clarify that lightweight components and soft springs are beneficial for efficient scattering energy conversion over a low-frequency broadband range. Furthermore, by investigating damping on energy distribution of 3-DOF anisotropic model, the underlying mechanism for capturing longitudinal wave energy is identified as integrating low-frequency scattering for energy conversion with high-frequency mechanisms for energy dissipation. Consequently, the 3-DOF anisotropic model achieves reflection-free wave energy across a broadband frequency range with a small amount of loss. To validate the proposed theory, model, and the underlying mechanism, anisotropic multiphase metamaterials are inversely designed to simultaneously deliver broadband wave-energy dissipation and high load-bearing capacity. Scattering characteristic analysis indicates that the metamaterials exhibit strong anisotropy and broadband energy conversion capability, with further validation by simulations and experiments. The present study establishes a foundation for high-load-bearing metamaterial-based elastic-wave absorbers and isolators.
{"title":"Coupled-translation-rotation mechanics model and design for broadband wave energy conversion in anisotropic multiphase metamaterials","authors":"Yuxuan Ma, Zhiwen Ren, Hao-Wen Dong","doi":"10.1016/j.ijengsci.2025.104450","DOIUrl":"10.1016/j.ijengsci.2025.104450","url":null,"abstract":"<div><div>Elastic metamaterials typically display anisotropic scattering behavior which mainly stems from high-order modes linked to shear and rotation deformations, thus complicating the characterization of the scattering behavior. However, most existing mass-spring models can only describe the coupled in-plane motions of longitudinal and transverse waves, which naturally ignores the essential rotations. Considering the pure translation and coupled-translation-rotation motions, this study proposes two spring-interconnected mass-in-mass models with rotational symmetry, featuring 2-degree-of-freedom (2-DOF) and 3-DOF anisotropic configurations respectively. For an incident longitudinal wave, the scattered transverse wave energy in these models is theoretically demonstrated at a specific rotation angle of spring. The established scattered elastic wave energy theory associating the dynamic response with structural parameters indicates that the higher scattering energy conversion of metamaterials can be achieved if two polarization components of translation and rotation are considered simultaneously. Comparing the scattering energy conversion capabilities of uni-layer and bi-layer models reveals that the bi-layer 3-DOF anisotropic model promotes the higher-efficiency low-frequency scattering energy conversion by reducing the dynamic effective stiffness. Variations in the scattering conversion coefficient with mass and aspect ratio clarify that lightweight components and soft springs are beneficial for efficient scattering energy conversion over a low-frequency broadband range. Furthermore, by investigating damping on energy distribution of 3-DOF anisotropic model, the underlying mechanism for capturing longitudinal wave energy is identified as integrating low-frequency scattering for energy conversion with high-frequency mechanisms for energy dissipation. Consequently, the 3-DOF anisotropic model achieves reflection-free wave energy across a broadband frequency range with a small amount of loss. To validate the proposed theory, model, and the underlying mechanism, anisotropic multiphase metamaterials are inversely designed to simultaneously deliver broadband wave-energy dissipation and high load-bearing capacity. Scattering characteristic analysis indicates that the metamaterials exhibit strong anisotropy and broadband energy conversion capability, with further validation by simulations and experiments. The present study establishes a foundation for high-load-bearing metamaterial-based elastic-wave absorbers and isolators.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"220 ","pages":"Article 104450"},"PeriodicalIF":5.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145785754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-19DOI: 10.1016/j.ijengsci.2025.104421
Yu Chen, Jianyou Zhou, Zheng Zhong
Soft-hard integrated composites have received much attention owing to their programmable deformation and tunable material properties. In particular, the rotation of hard inclusions in the soft matrix plays a significant role in their mechanical performance and functionality. However, existing studies on particle rotation have mostly been limited to non-porous soft matrix, while porous matrix is ubiquitous in biological materials and composite systems. In this work, a theoretical modeling framework is developed based on the complex potential method and superposition principle to quantitatively characterize the influence of pores on the rotation of elliptic rigid particles embedded in a soft matrix. Integrated with a dimensionless stiffness scale factor, the established model is capable of capturing the effect of pore-pore interactions on particle rotation. In addition, the critical inter-pore distance is established to determine when to consider the interaction among pores on particle rotation. Finite element simulations are also performed to further validate the presented model. It is found that the influence of pores on particle rotation is controlled by the redistribution of stress field induced by the particle-pore interaction. Based on the redistribution of stress field, the concept of “pressure vortex” is proposed to elucidate the tuning mechanism of pores and inclusions on particle rotation. This work is anticipated to provide significant insights into the rotation mechanics of rigid inclusions in soft porous materials and theoretical guidelines for the optimal design of soft-hard integrated flexible devices with engineered pores and porosity.
{"title":"Tuning elliptic-particle rotation in a soft matrix by pores","authors":"Yu Chen, Jianyou Zhou, Zheng Zhong","doi":"10.1016/j.ijengsci.2025.104421","DOIUrl":"10.1016/j.ijengsci.2025.104421","url":null,"abstract":"<div><div>Soft-hard integrated composites have received much attention owing to their programmable deformation and tunable material properties. In particular, the rotation of hard inclusions in the soft matrix plays a significant role in their mechanical performance and functionality. However, existing studies on particle rotation have mostly been limited to non-porous soft matrix, while porous matrix is ubiquitous in biological materials and composite systems. In this work, a theoretical modeling framework is developed based on the complex potential method and superposition principle to quantitatively characterize the influence of pores on the rotation of elliptic rigid particles embedded in a soft matrix. Integrated with a dimensionless stiffness scale factor, the established model is capable of capturing the effect of pore-pore interactions on particle rotation. In addition, the critical inter-pore distance is established to determine when to consider the interaction among pores on particle rotation. Finite element simulations are also performed to further validate the presented model. It is found that the influence of pores on particle rotation is controlled by the redistribution of stress field induced by the particle-pore interaction. Based on the redistribution of stress field, the concept of “pressure vortex” is proposed to elucidate the tuning mechanism of pores and inclusions on particle rotation. This work is anticipated to provide significant insights into the rotation mechanics of rigid inclusions in soft porous materials and theoretical guidelines for the optimal design of soft-hard integrated flexible devices with engineered pores and porosity.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"219 ","pages":"Article 104421"},"PeriodicalIF":5.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145577900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-11DOI: 10.1016/j.ijengsci.2025.104405
Michal Vazana, Mahmood Jabareen
In the present study, an extension of a smooth inelasticity finite-strain model to include softening based on an implicit non-local gradient-enhanced formulation is presented. The non-local formulation includes an intrinsic length-scale parameter that eliminates mesh sensitivity and allows the model to capture the realistic mechanical behavior of materials due to localization associated with strain softening. The constitutive equations are formulated in an Eulerian approach, and the transition from elastic to plastic response is smooth. The damage variable, which gradually degrades the yield strength, is computed as a function of a non-local accumulated plastic strain. A finite element formulation, which incorporates three variational fields for the equilibrium equations and an additional field for the Helmholtz type equation of the gradient-enhanced formulation, is developed. The evolution equations are numerically integrated with a strongly objective integration algorithm, and a linearization of the incremental stress update algorithm is derived. The capabilities of the developed finite element to predict the occurrence of shear bands and to display mesh-insensitivity are demonstrated by a set of numerical examples. Specifically, simulations for the patch test, objectivity test, rate of convergence test, necking of a cylindrical bar, a plate under tension, and plane strain indentation of a rigid plate into a block are presented.
{"title":"An Eulerian finite-deformation framework for a gradient-enhanced material softening model with a smooth elastic–plastic transition","authors":"Michal Vazana, Mahmood Jabareen","doi":"10.1016/j.ijengsci.2025.104405","DOIUrl":"10.1016/j.ijengsci.2025.104405","url":null,"abstract":"<div><div>In the present study, an extension of a smooth inelasticity finite-strain model to include softening based on an implicit non-local gradient-enhanced formulation is presented. The non-local formulation includes an intrinsic length-scale parameter that eliminates mesh sensitivity and allows the model to capture the realistic mechanical behavior of materials due to localization associated with strain softening. The constitutive equations are formulated in an Eulerian approach, and the transition from elastic to plastic response is smooth. The damage variable, which gradually degrades the yield strength, is computed as a function of a non-local accumulated plastic strain. A finite element formulation, which incorporates three variational fields for the equilibrium equations and an additional field for the Helmholtz type equation of the gradient-enhanced formulation, is developed. The evolution equations are numerically integrated with a strongly objective integration algorithm, and a linearization of the incremental stress update algorithm is derived. The capabilities of the developed finite element to predict the occurrence of shear bands and to display mesh-insensitivity are demonstrated by a set of numerical examples. Specifically, simulations for the patch test, objectivity test, rate of convergence test, necking of a cylindrical bar, a plate under tension, and plane strain indentation of a rigid plate into a block are presented.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"219 ","pages":"Article 104405"},"PeriodicalIF":5.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145478835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-20DOI: 10.1016/j.ijengsci.2025.104422
J.R. Fernández , R. Quintanilla
The objective of this article is to study the spatial behavior of solutions in the case of heat conduction in a static cylinder for a mixture of rigid solids. Although this question is an ill-posed problem in the Hadamard sense, since there is no uniqueness of solutions nor continuous dependence on initial data, we focus on the study of decaying solutions. When we restrict to this class of functions, we obtain a well-posed problem. We will show that we can see the solutions through an analytic semigroup structure, for which the long variable acts as the evolution variable. Therefore, we can apply the properties of these semigroups. Finally, we also consider the case in which a certain type of supply terms is introduced, and the solutions are obtained with the help of semigroups theory. A few comments for alternative boundary conditions are also considered.
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