Pub Date : 2026-01-22DOI: 10.1016/j.ijengsci.2025.104454
E. Radi , M.A. Güler
In this work, we present an analytical solution for the contact problem of a rigid, loaded pin interacting with a circular hole in an infinite plane with microstructure, modelled by the couple-stress elastic theory, assuming frictionless contact with clearance under plane-strain conditions. The solution is constructed by employing the most general trigonometric series representations in polar coordinates for the stress, couple-stress, displacement, and rotation fields admitted by the theory of couple-stress elasticity. Enforcing the contact conditions yields a system of dual series equations for the unknown coefficients, which is subsequently reduced to an infinite linear algebraic system and solved by truncation, following established approaches in related literature. The influence of the material microstructure on the contact angle, as well as on the stress and couple-stress distributions along the hole boundary, is then examined. The results show that increasing the intrinsic material length scale leads to a stiffer mechanical response, thereby clearly highlighting the size-dependent behavior predicted by couple-stress theory. The convergence properties of the trigonometric series solution are also discussed.
{"title":"Effects of microstructure in pin-loaded hole contact with clearance","authors":"E. Radi , M.A. Güler","doi":"10.1016/j.ijengsci.2025.104454","DOIUrl":"10.1016/j.ijengsci.2025.104454","url":null,"abstract":"<div><div>In this work, we present an analytical solution for the contact problem of a rigid, loaded pin interacting with a circular hole in an infinite plane with microstructure, modelled by the couple-stress elastic theory, assuming frictionless contact with clearance under plane-strain conditions. The solution is constructed by employing the most general trigonometric series representations in polar coordinates for the stress, couple-stress, displacement, and rotation fields admitted by the theory of couple-stress elasticity. Enforcing the contact conditions yields a system of dual series equations for the unknown coefficients, which is subsequently reduced to an infinite linear algebraic system and solved by truncation, following established approaches in related literature. The influence of the material microstructure on the contact angle, as well as on the stress and couple-stress distributions along the hole boundary, is then examined. The results show that increasing the intrinsic material length scale leads to a stiffer mechanical response, thereby clearly highlighting the size-dependent behavior predicted by couple-stress theory. The convergence properties of the trigonometric series solution are also discussed.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104454"},"PeriodicalIF":5.7,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.ijengsci.2026.104475
Vito Diana, Alessandro Fortunati, Andrea Bacigalupo
We examine the dispersion behavior and spatial attenuation of generalized oriented peridynamic continua with non-central pair-potential interactions. The free-wave propagation problem is analyzed analytically through integral transform methods, enabling the closed-form derivation of dispersion relations for real-valued wavenumbers. A complementary perturbation approach is proposed to investigate the spatial attenuation behavior, derive the full band structure, and systematically explore the dispersive response of the model for complex wavenumbers, achieving progressively higher accuracy with increasing order of the truncated expansions. The integro-differential nature of the governing equations, together with the enhanced kinematic description and pairwise interaction formalism, provides a natural framework to represent the dynamic behavior of mechanical metamaterials — such as beam- and block-lattice systems — traditionally modeled through discrete Lagrangian formulations. A central result of this study shows that the oriented peridynamic continuum with pairwise potentials — also referred to as a continuum–molecular model, to emphasize its blend of continuous mass distribution and discrete-like kinematics — successfully reproduces both the acoustic and optical branches of the architected material when the horizon approaches the characteristic microstructural lengths, a capability unattainable in conventional peridynamic continua. Furthermore, the microstructure-informed oriented model typically attains higher accuracy than a micropolar continuum derived via standard continualisation of the lattice-like material equations. The theoretical framework is validated, and its physical implications are further illustrated through a case study of forced wave propagation in architected block-lattice materials featuring a hexagonal topology.
{"title":"Dispersive waves in microstructure-informed peridynamic continua","authors":"Vito Diana, Alessandro Fortunati, Andrea Bacigalupo","doi":"10.1016/j.ijengsci.2026.104475","DOIUrl":"10.1016/j.ijengsci.2026.104475","url":null,"abstract":"<div><div>We examine the dispersion behavior and spatial attenuation of generalized oriented peridynamic continua with non-central pair-potential interactions. The free-wave propagation problem is analyzed analytically through integral transform methods, enabling the closed-form derivation of dispersion relations for real-valued wavenumbers. A complementary perturbation approach is proposed to investigate the spatial attenuation behavior, derive the full band structure, and systematically explore the dispersive response of the model for complex wavenumbers, achieving progressively higher accuracy with increasing order of the truncated expansions. The integro-differential nature of the governing equations, together with the enhanced kinematic description and pairwise interaction formalism, provides a natural framework to represent the dynamic behavior of mechanical metamaterials — such as beam- and block-lattice systems — traditionally modeled through discrete Lagrangian formulations. A central result of this study shows that the oriented peridynamic continuum with pairwise potentials — also referred to as a continuum–molecular model, to emphasize its blend of continuous mass distribution and discrete-like kinematics — successfully reproduces both the acoustic and optical branches of the architected material when the horizon approaches the characteristic microstructural lengths, a capability unattainable in conventional peridynamic continua. Furthermore, the microstructure-informed oriented model typically attains higher accuracy than a micropolar continuum derived via standard continualisation of the lattice-like material equations. The theoretical framework is validated, and its physical implications are further illustrated through a case study of forced wave propagation in architected block-lattice materials featuring a hexagonal topology.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104475"},"PeriodicalIF":5.7,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.ijengsci.2026.104474
J. Kozlík , K. Tůma , O. Souček , J. Dobrzański , S. Stupkiewicz
In this paper, we revisit a classical multiwell phase-field model in the context of – phase transformations in titanium alloys. We propose a novel model by adjusting the algebraic part of the traditional interfacial free energy in a way that allows for a relaxation of the standard well-posedness constraints on surface tensions in the total-spreading case. The proposed adjustment effectively prevents the formation of a mixed – state in the resulting phase-field continuum model, aligning with the crystallographic impossibility of such a configuration in reality. We further introduce a chemical energy mixing function that preserves the local stability of purely two-phase – configurations, preventing the spontaneous appearance of additional phases. We illustrate the advantages of the novel model through numerical simulations in one, two and three spatial dimensions and outline a pathway toward a more realistic model of – transition model in titanium alloys.
{"title":"Multiwell phase-field model for arbitrarily strong total-spreading case","authors":"J. Kozlík , K. Tůma , O. Souček , J. Dobrzański , S. Stupkiewicz","doi":"10.1016/j.ijengsci.2026.104474","DOIUrl":"10.1016/j.ijengsci.2026.104474","url":null,"abstract":"<div><div>In this paper, we revisit a classical multiwell phase-field model in the context of <span><math><mi>β</mi></math></span>–<span><math><mi>ω</mi></math></span> phase transformations in titanium alloys. We propose a novel model by adjusting the algebraic part of the traditional interfacial free energy in a way that allows for a relaxation of the standard well-posedness constraints on surface tensions in the total-spreading case. The proposed adjustment effectively prevents the formation of a mixed <span><math><mi>ω</mi></math></span>–<span><math><mi>ω</mi></math></span> state in the resulting phase-field continuum model, aligning with the crystallographic impossibility of such a configuration in reality. We further introduce a chemical energy mixing function that preserves the local stability of purely two-phase <span><math><mi>β</mi></math></span>–<span><math><mi>ω</mi></math></span> configurations, preventing the spontaneous appearance of additional phases. We illustrate the advantages of the novel model through numerical simulations in one, two and three spatial dimensions and outline a pathway toward a more realistic model of <span><math><mi>β</mi></math></span>–<span><math><mi>ω</mi></math></span> transition model in titanium alloys.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104474"},"PeriodicalIF":5.7,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.ijengsci.2026.104476
Nithin Veerendranath Kammara, Anastasia Muliana
Many biological composites rely on interlocking arrangements of brittle (hard) and compliant (soft) constituents, which give rise to diverse load-transfer pathways and, in turn, exceptional resistance to mechanical loading, enhanced crack suppression, and effective energy dissipation under dynamic conditions. In this study, we develop a micromechanical model to explain how microstructural characteristics and mechanical properties of constituents govern the overall deformation of staggered composites. Our analysis examines how platelet (inclusion) geometry, arrangement, and packing density influence load transfer. We find that the size of staggered regions and packing density play more dominant roles than the platelet volume fraction in controlling the elastic moduli and nonlinear inelastic tensile response of the staggered composites. Furthermore, we identify design pathways for achieving high elastic stiffness in composites with low packing density and low platelet volume fraction by increasing the extent of staggered regions and forming connected platelet networks. A noteworthy and somewhat counterintuitive result is that platelet volume fraction has a minor effect on mechanical behavior in staggered architectures, in contrast to non-staggered microstructures, because staggered layouts activate multiple load-transfer mechanisms enabled by tailored platelet geometry and arrangement. We validate the prediction of our mechanical models against experimental data and other models.
{"title":"Microstructural characteristics and its role in load transfer within staggered architectures of brittle and compliant constituents","authors":"Nithin Veerendranath Kammara, Anastasia Muliana","doi":"10.1016/j.ijengsci.2026.104476","DOIUrl":"10.1016/j.ijengsci.2026.104476","url":null,"abstract":"<div><div>Many biological composites rely on interlocking arrangements of brittle (hard) and compliant (soft) constituents, which give rise to diverse load-transfer pathways and, in turn, exceptional resistance to mechanical loading, enhanced crack suppression, and effective energy dissipation under dynamic conditions. In this study, we develop a micromechanical model to explain how microstructural characteristics and mechanical properties of constituents govern the overall deformation of staggered composites. Our analysis examines how platelet (inclusion) geometry, arrangement, and packing density influence load transfer. We find that the size of staggered regions and packing density play more dominant roles than the platelet volume fraction in controlling the elastic moduli and nonlinear inelastic tensile response of the staggered composites. Furthermore, we identify design pathways for achieving high elastic stiffness in composites with low packing density and low platelet volume fraction by increasing the extent of staggered regions and forming connected platelet networks. A noteworthy and somewhat counterintuitive result is that platelet volume fraction has a minor effect on mechanical behavior in staggered architectures, in contrast to non-staggered microstructures, because staggered layouts activate multiple load-transfer mechanisms enabled by tailored platelet geometry and arrangement. We validate the prediction of our mechanical models against experimental data and other models.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104476"},"PeriodicalIF":5.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.ijengsci.2026.104477
Rahul Kumar, K. Arvind, K. Kannan
A realistic description of the transverse strain in uniaxial tension remains a significant limitation of existing angular-integral models (AngI/AngIx) for distributed fibres. These models exhibit a premature perversion point, defined as the point at which the sign reversal of the out-of-plane transverse strain occurs, together with an overprediction of radial thickening. In the limit of unidirectional fibres, they yield identical shear responses in distinct shear modes, diminishing their predictive capability. Although incorporating both invariants, and , could mitigate these issues, the tension–compression switching criterion using the Heaviside function may ultimately counteract these improvements.
An alternative to handling the contribution of compressed fibres within a distribution is to smoothly attenuate it using a vanishing matched invariant constructed from both the and invariants. Although the resulting switchless constitutive relation (VanGOH (Arvind and Kannan, 2025)), based on the averaged matched invariant, mitigates several of the limitations associated with the switching criterion in generalised structure tensor frameworks, its non-integral structure restricts its ability to accurately reproduce both shear and normal stress responses under general in-plane biaxial loading. To overcome these shortcomings, we introduce VanAngI, an angular–integration–based, Heaviside-free model developed within the framework of vanishing matched invariants. VanAngI (1) achieves a 42% reduction in the uniaxial fitting error compared with the AngIx model while correctly capturing the sign of the experimental out-of-plane Poisson’s ratio, (2) accurately resolves the simple shear response, and (3) delivers consistently superior biaxial predictions—all while using at most two fibre families and a minimal set of material parameters.
对于现有的角积分模型（AngI/AngIx）来说，对单轴拉伸下横向应变的真实描述仍然是分布式纤维的一个重大限制。这些模型表现出一个过早的反常点，定义为面外横向应变的符号反转发生的点，以及对径向增厚的过度预测。在单向纤维的极限下，它们在不同的剪切模式下产生相同的剪切响应，从而降低了它们的预测能力。虽然合并两个不变量I4和I5可以缓解这些问题，但使用Heaviside函数的张力-压缩切换准则最终可能会抵消这些改进。处理分布内压缩纤维贡献的另一种方法是使用由I4和I5不变量构建的消失匹配不变量平滑地衰减它。尽管由此产生的基于平均匹配不变量的无切换本构关系（VanGOH (Arvind and Kannan, 2025)）减轻了广义结构张量框架中与切换准则相关的几个限制，但其非积分结构限制了其在一般平面内双轴载荷下准确再现剪切和法向应力响应的能力。为了克服这些缺点，我们引入了VanAngI，这是一种在消失匹配不变量框架内开发的基于角积分的无heaviside模型。与AngIx模型相比，VanAngI(1)在正确捕获实验面外泊松比的符号的同时，实现了单轴拟合误差降低42%，(2)准确地解决了简单的剪切响应，(3)提供了一致的卓越的双轴预测——所有这些都是在最多使用两个纤维族和最小的材料参数集的情况下完成的。
{"title":"Heaviside-free microsphere-based formulation to smoothly attenuate the compression response in arterial tissues","authors":"Rahul Kumar, K. Arvind, K. Kannan","doi":"10.1016/j.ijengsci.2026.104477","DOIUrl":"10.1016/j.ijengsci.2026.104477","url":null,"abstract":"<div><div>A realistic description of the transverse strain in uniaxial tension remains a significant limitation of existing angular-integral models (AngI/AngIx) for distributed fibres. These models exhibit a premature <em>perversion point</em>, defined as the point at which the sign reversal of the out-of-plane transverse strain occurs, together with an overprediction of radial thickening. In the limit of unidirectional fibres, they yield identical shear responses in distinct shear modes, diminishing their predictive capability. Although incorporating both invariants, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span>, could mitigate these issues, the tension–compression switching criterion using the Heaviside function may ultimately counteract these improvements.</div><div>An alternative to handling the contribution of compressed fibres within a distribution is to smoothly attenuate it using a vanishing matched invariant constructed from both the <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> invariants. Although the resulting switchless constitutive relation (VanGOH (Arvind and Kannan, 2025)), based on the averaged matched invariant, mitigates several of the limitations associated with the switching criterion in generalised structure tensor frameworks, its non-integral structure restricts its ability to accurately reproduce both shear and normal stress responses under general in-plane biaxial loading. To overcome these shortcomings, we introduce <em>VanAngI</em>, an angular–integration–based, Heaviside-free model developed within the framework of vanishing matched invariants. VanAngI (1) achieves a 42% reduction in the uniaxial fitting error compared with the AngIx model while correctly capturing the sign of the experimental out-of-plane Poisson’s ratio, (2) accurately resolves the simple shear response, and (3) delivers consistently superior biaxial predictions—all while using at most two fibre families and a minimal set of material parameters.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104477"},"PeriodicalIF":5.7,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.ijengsci.2026.104473
Francesco Paolo Pinnola , Francesco Scudieri , Gioacchino Alotta , Francesco Marotti de Sciarra
The bending vibrations of nonlocal viscoelastic plates subjected to stochastic excitations are investigated within the framework of the axisymmetric Kirchhoff model. This study is particularly relevant to the design of mesoscale heterogeneous structures, biotissues, miniaturized two-dimensional structures and metamaterials, such as those employed in energy harvesters, sensors, actuators, wave energy converters, transistors, bioinspired devices, and microrobots, often fabricated from unconventional materials. For such systems, classical local continuum theories fail to accurately capture the underlying mechanics. To address this, the mechanical response is analyzed by accounting for two key features: viscoelasticity and nonlocality. The constitutive behavior is described through a stress-driven integral nonlocal model coupled with fractional-order viscoelastic stress–strain relation, allowing the formulation to incorporate both size-dependent and hereditary effects. Random excitation is introduced to account for the inherent variability of external dynamic environments, leading to a stochastic partial differential equation featuring fractional operators. Owing to the complexity of this equation, a semi-analytical solution procedure based on modal decomposition is developed in order to compute the time-dependent response and evaluate the power spectral densities. The results highlight the influence of nonlocal interactions and viscoelastic parameters on the dynamic response and natural frequencies of the system. These findings offer valuable insights for the design and optimization of advanced two-dimensional nano- and micro-scale devices and other devices where long-range interactions occur.
{"title":"On the stochastic dynamics of nonlocal viscoelastic plates","authors":"Francesco Paolo Pinnola , Francesco Scudieri , Gioacchino Alotta , Francesco Marotti de Sciarra","doi":"10.1016/j.ijengsci.2026.104473","DOIUrl":"10.1016/j.ijengsci.2026.104473","url":null,"abstract":"<div><div>The bending vibrations of nonlocal viscoelastic plates subjected to stochastic excitations are investigated within the framework of the axisymmetric Kirchhoff model. This study is particularly relevant to the design of mesoscale heterogeneous structures, biotissues, miniaturized two-dimensional structures and metamaterials, such as those employed in energy harvesters, sensors, actuators, wave energy converters, transistors, bioinspired devices, and microrobots, often fabricated from unconventional materials. For such systems, classical local continuum theories fail to accurately capture the underlying mechanics. To address this, the mechanical response is analyzed by accounting for two key features: viscoelasticity and nonlocality. The constitutive behavior is described through a stress-driven integral nonlocal model coupled with fractional-order viscoelastic stress–strain relation, allowing the formulation to incorporate both size-dependent and hereditary effects. Random excitation is introduced to account for the inherent variability of external dynamic environments, leading to a stochastic partial differential equation featuring fractional operators. Owing to the complexity of this equation, a semi-analytical solution procedure based on modal decomposition is developed in order to compute the time-dependent response and evaluate the power spectral densities. The results highlight the influence of nonlocal interactions and viscoelastic parameters on the dynamic response and natural frequencies of the system. These findings offer valuable insights for the design and optimization of advanced two-dimensional nano- and micro-scale devices and other devices where long-range interactions occur.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104473"},"PeriodicalIF":5.7,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-17DOI: 10.1016/j.ijengsci.2026.104470
Mojtaba Adaei-Khafri, Mohammad Javad Ashrafi, Fathollah Taheri-Behrooz
This research presents a three-dimensional, thermodynamically consistent phase-field model for nanoscale martensitic transformation in NiTi (B2 → B19′) implemented in a finite-element COMSOL framework. The novelty of this work lies in its physics-based approach to modeling the martensitic transformation and nano-twin evolution in NiTi alloys. We incorporate elastic anisotropy and surface stress using 2-3-4-5 polynomial energy functions characterized by physically meaningful parameters for energy contributions. Furthermore, to enhance computational efficiency in solving these complex equations, we employ a reduced-order parameter approach where three order parameters represent six martensitic variants in two-dimensional simulations. In contrast to models calibrated against macroscopic data, our physical parameters are derived directly from NiTi's strain-energy landscape. This approach ensures an accurate representation of the transformation energy barriers and stresses, thereby enabling a thermodynamically consistent analysis of fundamental mechanisms such as nucleation barrier and variant interactions. This study successfully reproduces both the banded and herringbone morphologies frequently observed in experimental studies. Elastic anisotropy is identified as the dominance driver of variant selection and the formation of banded and herringbone patterns. Furthermore, the results indicate that a higher associated driving force promotes the growth of dominant, preferentially oriented variants. Specifically, higher stress increases the phase concentration and promotes the formation of wider martensitic variant bands, while a lower cooling temperature increases the nucleation rate, thereby resulting in thinner bands. This thermodynamically consistent model accurately predicts nano-scale NiTi martensite evolution, which is critical for designing microstructures with enhanced functional stability and performance.
{"title":"A thermodynamically consistent phase-field model of martensitic nano-twin evolution in NiTi alloys: effects of stress, temperature, and elastic anisotropy","authors":"Mojtaba Adaei-Khafri, Mohammad Javad Ashrafi, Fathollah Taheri-Behrooz","doi":"10.1016/j.ijengsci.2026.104470","DOIUrl":"10.1016/j.ijengsci.2026.104470","url":null,"abstract":"<div><div>This research presents a three-dimensional, thermodynamically consistent phase-field model for nanoscale martensitic transformation in NiTi (B2 → B19′) implemented in a finite-element COMSOL framework. The novelty of this work lies in its physics-based approach to modeling the martensitic transformation and nano-twin evolution in NiTi alloys. We incorporate elastic anisotropy and surface stress using 2-3-4-5 polynomial energy functions characterized by physically meaningful parameters for energy contributions. Furthermore, to enhance computational efficiency in solving these complex equations, we employ a reduced-order parameter approach where three order parameters represent six martensitic variants in two-dimensional simulations. In contrast to models calibrated against macroscopic data, our physical parameters are derived directly from NiTi's strain-energy landscape. This approach ensures an accurate representation of the transformation energy barriers and stresses, thereby enabling a thermodynamically consistent analysis of fundamental mechanisms such as nucleation barrier and variant interactions. This study successfully reproduces both the banded and herringbone morphologies frequently observed in experimental studies. Elastic anisotropy is identified as the dominance driver of variant selection and the formation of banded and herringbone patterns. Furthermore, the results indicate that a higher associated driving force promotes the growth of dominant, preferentially oriented variants. Specifically, higher stress increases the phase concentration and promotes the formation of wider martensitic variant bands, while a lower cooling temperature increases the nucleation rate, thereby resulting in thinner bands. This thermodynamically consistent model accurately predicts nano-scale NiTi martensite evolution, which is critical for designing microstructures with enhanced functional stability and performance.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104470"},"PeriodicalIF":5.7,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-13DOI: 10.1016/j.ijengsci.2026.104472
J.D. Clayton, C.E. Hampton
The coupled mechanical, thermal, and active contractile responses of skeletal muscle tissue are described by a continuum framework. The tissue comprises a solid phase of muscle fibers aligned in a matrix of connective collagen and ground substance and an interstitial fluid phase. A constrained mixture theory is implemented for dynamic loading over time scales too brief for macroscopic diffusion, whereby free volume is saturated and locally occluded. Physics described by the model include the following: compressibility and thermoelastic coupling important for dynamic and shock loading, nonlinear anisotropic elasticity and viscoelasticity, degradation in fibers and matrix measured by order parameters, active cellular tension, and switching between active and passive states. The theory distinguishes among damage driven by tensile and shear mechanisms and injury that can have a lower threshold and also be affected by hydrostatic compression. Comparison of model results to existing 1-D tensile experiments describes effects of activation and over-stretching on stresses and damage. A 3-D implementation in finite-element software is exercised to study injuries resulting from high-rate dynamic loading by either distributed or concentrated forces to tissues in passive and active states. Different outcomes for damage and injury are possible depending on fiber orientation, isometric versus extendable active tension, degree of viscoelastic stiffening, and loading protocol. In some cases, fiber activation inhibits injury, while in others, activation exacerbates injury.
{"title":"Dynamic damage in active and passive skeletal muscle: A continuum mechanical model","authors":"J.D. Clayton, C.E. Hampton","doi":"10.1016/j.ijengsci.2026.104472","DOIUrl":"10.1016/j.ijengsci.2026.104472","url":null,"abstract":"<div><div>The coupled mechanical, thermal, and active contractile responses of skeletal muscle tissue are described by a continuum framework. The tissue comprises a solid phase of muscle fibers aligned in a matrix of connective collagen and ground substance and an interstitial fluid phase. A constrained mixture theory is implemented for dynamic loading over time scales too brief for macroscopic diffusion, whereby free volume is saturated and locally occluded. Physics described by the model include the following: compressibility and thermoelastic coupling important for dynamic and shock loading, nonlinear anisotropic elasticity and viscoelasticity, degradation in fibers and matrix measured by order parameters, active cellular tension, and switching between active and passive states. The theory distinguishes among damage driven by tensile and shear mechanisms and injury that can have a lower threshold and also be affected by hydrostatic compression. Comparison of model results to existing 1-D tensile experiments describes effects of activation and over-stretching on stresses and damage. A 3-D implementation in finite-element software is exercised to study injuries resulting from high-rate dynamic loading by either distributed or concentrated forces to tissues in passive and active states. Different outcomes for damage and injury are possible depending on fiber orientation, isometric versus extendable active tension, degree of viscoelastic stiffening, and loading protocol. In some cases, fiber activation inhibits injury, while in others, activation exacerbates injury.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104472"},"PeriodicalIF":5.7,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-12DOI: 10.1016/j.ijengsci.2025.104453
A. Chauhan, C. Sasmal
This study presents extensive three-dimensional numerical simulations to investigate the hemodynamics within a stenosed artery under both steady and pulsatile inflow conditions. Two different blood rheology models are employed, namely, the conventional Newtonian model and the more physiologically accurate multimode simplified Phan–Thien–Tanner (sPTT) viscoelastic model. The parameters for the sPTT model are calibrated using experimental rheological data of real whole blood, obtained from standard viscometric flows such as steady simple shear and small-amplitude oscillatory shear (SAOS). This enables the model to capture both the shear-thinning and viscoelastic nature of blood, thus offering a more realistic representation of blood flow dynamics in a physiologically relevant arterial geometry. Under steady inflow conditions, a high-velocity jet is formed as blood flows through the stenosed region, which subsequently extends downstream into the post-stenotic area. This jet is found to be shorter in length but more turbulent and unsteady when simulated with the sPTT model compared to the Newtonian model. The sPTT model simulations reveal more concentrated small-scale vortical structures within and immediately downstream of the stenosis, indicating increased flow complexity due to viscoelastic and shear-thinning effects of blood. The same trend is also observed in the case of pulsatile flow conditions. Clinically significant hemodynamic parameters such as the pressure drop across the stenosis and wall shear stress (WSS) were also analyzed. The pressure drop is observed to decrease with increasing Reynolds number but increase with the degree of stenosis. WSS, a critical indicator in vascular health assessment, increases with stenosis severity and attains its maximum during the systolic (peak) phase of the pulsatile cycle, where blood velocity is at its highest. Throughout the simulations, the Newtonian model consistently overestimates both the pressure drop and WSS compared to the sPTT model. Therefore, reliance on Newtonian assumptions may lead to misinterpretation or overestimation of key hemodynamic metrics in both diagnostic and therapeutic contexts. Overall, this study provides in-depth insights into the complex flow behavior in stenosed arteries, with emphasis on the rheological fidelity of the blood model. The findings of this study have potential implications for improving clinical diagnosis, treatment planning, and the design of medical devices targeting vascular diseases in the context of atherosclerosis, a progressively prevalent cardiovascular condition.
{"title":"A comparative study of Newtonian and multi-mode viscoelastic models for blood flow in stenosed arteries at high physiologic Reynolds and Womersley numbers","authors":"A. Chauhan, C. Sasmal","doi":"10.1016/j.ijengsci.2025.104453","DOIUrl":"10.1016/j.ijengsci.2025.104453","url":null,"abstract":"<div><div>This study presents extensive three-dimensional numerical simulations to investigate the hemodynamics within a stenosed artery under both steady and pulsatile inflow conditions. Two different blood rheology models are employed, namely, the conventional Newtonian model and the more physiologically accurate multimode simplified Phan–Thien–Tanner (sPTT) viscoelastic model. The parameters for the sPTT model are calibrated using experimental rheological data of real whole blood, obtained from standard viscometric flows such as steady simple shear and small-amplitude oscillatory shear (SAOS). This enables the model to capture both the shear-thinning and viscoelastic nature of blood, thus offering a more realistic representation of blood flow dynamics in a physiologically relevant arterial geometry. Under steady inflow conditions, a high-velocity jet is formed as blood flows through the stenosed region, which subsequently extends downstream into the post-stenotic area. This jet is found to be shorter in length but more turbulent and unsteady when simulated with the sPTT model compared to the Newtonian model. The sPTT model simulations reveal more concentrated small-scale vortical structures within and immediately downstream of the stenosis, indicating increased flow complexity due to viscoelastic and shear-thinning effects of blood. The same trend is also observed in the case of pulsatile flow conditions. Clinically significant hemodynamic parameters such as the pressure drop across the stenosis and wall shear stress (WSS) were also analyzed. The pressure drop is observed to decrease with increasing Reynolds number but increase with the degree of stenosis. WSS, a critical indicator in vascular health assessment, increases with stenosis severity and attains its maximum during the systolic (peak) phase of the pulsatile cycle, where blood velocity is at its highest. Throughout the simulations, the Newtonian model consistently overestimates both the pressure drop and WSS compared to the sPTT model. Therefore, reliance on Newtonian assumptions may lead to misinterpretation or overestimation of key hemodynamic metrics in both diagnostic and therapeutic contexts. Overall, this study provides in-depth insights into the complex flow behavior in stenosed arteries, with emphasis on the rheological fidelity of the blood model. The findings of this study have potential implications for improving clinical diagnosis, treatment planning, and the design of medical devices targeting vascular diseases in the context of atherosclerosis, a progressively prevalent cardiovascular condition.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104453"},"PeriodicalIF":5.7,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-10DOI: 10.1016/j.ijengsci.2026.104471
Youcef Amirat , Vladimir Shelukhin , Konstantin Trusov
To describe two-phase flows in porous media, a two-scale mathematical model is developed using the homogenization method applied to the coupled system of Navier–Stokes and Cahn–Hilliard equations. This system is based on the assumption that the fluid phases are separated by a diffusion layer. We prove that the macro-equations represent a generalized Darcy law with cross-coupling permeabilities. It implies that the seepage velocity of each phase depends on pressure gradients of both the phases. Micro-equations serve for determination both of the permeability tensors and the capillary diffusion energy. It is established that a formal sharp-interface limit justifies the empirical concept of relative phase permeabilities. To illustrate the capabilities of the new two-scale model, the problem of counter-current capillary imbibition is solved. We show that the imbibition rate is lower compared to that predicted by traditional equations based on the empirical concept of relative phase permeability.
{"title":"Cross-coupling permeabilities in two-phase flows through porous media: Spontaneous counter-current capillary imbibition","authors":"Youcef Amirat , Vladimir Shelukhin , Konstantin Trusov","doi":"10.1016/j.ijengsci.2026.104471","DOIUrl":"10.1016/j.ijengsci.2026.104471","url":null,"abstract":"<div><div>To describe two-phase flows in porous media, a two-scale mathematical model is developed using the homogenization method applied to the coupled system of Navier–Stokes and Cahn–Hilliard equations. This system is based on the assumption that the fluid phases are separated by a diffusion layer. We prove that the macro-equations represent a generalized Darcy law with cross-coupling permeabilities. It implies that the seepage velocity of each phase depends on pressure gradients of both the phases. Micro-equations serve for determination both of the permeability tensors and the capillary diffusion energy. It is established that a formal sharp-interface limit justifies the empirical concept of relative phase permeabilities. To illustrate the capabilities of the new two-scale model, the problem of counter-current capillary imbibition is solved. We show that the imbibition rate is lower compared to that predicted by traditional equations based on the empirical concept of relative phase permeability.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"221 ","pages":"Article 104471"},"PeriodicalIF":5.7,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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