Article
Mechanics
Jun Hong, Shaopeng Wang, Gongye Zhang, Changwen Mi
Summary: A new functionally graded non-classical Timoshenko microbeam model has been developed, incorporating strain gradient, couple stress, and velocity gradient effects to explain power-law variation in two-phase materials. The model demonstrates significant differences from classic models when the FGM beam thickness is very small, but these differences diminish as thickness increases.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2021)
Article
Materials Science, Multidisciplinary
Yishuang Huang, Peijun Wei, Yuqian Xu, Yueqiu Li
Summary: The study investigates flexural wave propagation in a microbeam using a nonlocal strain gradient model with fractional order derivatives, demonstrating the model's flexibility in capturing dispersive properties. Numerical comparisons with integer order models and molecular dynamic simulations validate the effectiveness of the fractional order nonlocal strain gradient model.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Acoustics
Sina Massoumi, Noel Challamel, Jean Lerbet
Summary: This study theoretically investigates the free vibration problem of a discrete granular system and analyzes the effects of microstructure on the dynamic behavior of the equivalent continuum structural model. Natural frequencies are calculated for both the discrete and continuous models, showing the dependency of beam dynamic responses on the beam length ratio.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Mathematics, Applied
Kalyan Boyina, Raghu Piska
Summary: This work investigates wave propagation in a viscoelastic Timoshenko nanobeam under the influence of surface stress and magnetic field effects. The study provides a mathematical model and closed-form solutions for such scenarios. The results indicate that the introduction of surface stress values increases the damping ratio of flexural and shear waves.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Multidisciplinary
Sergei Khakalo, Anssi Laukkanen
Summary: This study combines Mindlin's strain gradient elasticity theory and Gudmundson-Gurtin-Anand strain gradient plasticity theory to form a unified framework, enriching the modeling capabilities by including the gradient of elastic strains. Numerical results show that the elastic length scale parameter controls the slope of the elastic part and causes additional hardening in the plastic part of the material response curves.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Crystallography
Shuohui Yin, Zhibing Xiao, Jingang Liu, Zixu Xia, Shuitao Gu
Summary: This paper presents a novel non-classical Timoshenko-Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The model includes the strain gradient effect, couple stress effect, and velocity gradient effect by using a single material length scale parameter. The performance and accuracy of the model are verified through convergence studies and comparisons to analytical solutions. Different boundary conditions, material length scale parameters, and beam thicknesses are also investigated to certify the applicability of the proposed approach.
Article
Engineering, Multidisciplinary
Baotong Li, Yuqi Duan, Hua Yang, Yanshan Lou, Wolfgang H. Muiller
Summary: In this paper, optimal topologies of isotropic linear elastic strain gradient materials are investigated using isogeometric topology optimization. Strain gradient theory is applied to capture the microstructural effects of materials and regulate stress/strain concentration phenomena.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
S. Ali Faghidian
Summary: The nonlocal modified gradient theory combines the frameworks of nonlocal integral elasticity and modified strain gradient theory, applied to a beam model. Nanoscopic effects are accommodated, and well-posedness of problems on bounded structural domains is confirmed. Analytical solutions and numerical illustrations are provided for flexural wave behavior in nano-sized beams, and wave propagation in carbon nanotubes is validated through molecular dynamics simulations.
JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING
(2021)
Article
Materials Science, Multidisciplinary
Victor A. Eremeyev
Summary: This study analyzes the constitutive equations of strain gradient fluids based on a unified approach using a local material symmetry group. The strain energy density for the strain gradient medium is dependent on higher-order gradients of placement vector, while for fluids it depends on current mass density and its gradients. Both models found applications in modeling materials with complex inner structures, such as beam-lattice metamaterials, and were introduced independently on general strain gradient continua.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Mathematics, Applied
Andi Lai, Bing Zhao, Xulong Peng, Chengyun Long
Summary: In this study, a buckling model of Timoshenko micro-beam with local thickness defects was established based on a modified gradient elasticity. By using the variational principle, the variable coefficient differential equations of the buckling problem were obtained by introducing the local thickness defects function. The critical load and buckling modes of the micro-beam with defects were obtained by combining the eigensolution series of the complete micro-beam with the Galerkin method. The results showed that the depth and location of the defect were the main factors affecting the critical load, and the combined effect of boundary conditions and defects could significantly change the buckling mode of the micro-beam.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2022)
Article
Mechanics
Run Zhang, Jiahao Cheng, Tingrui Chen, Hongzhi Zhong
Summary: This article presents a numerical scheme for analyzing geometrically nonlinear elastic strain gradient beams using weak form quadrature element formulation and the geometrically exact beam model. The formulation incorporates the derivatives of displacements and rotations as additional degrees of freedom at element boundary nodes to meet the C1 continuity requirements brought about by the introduction of strain gradients. A generalized differential quadrature scheme based on Hermite interpolation functions is employed to approximate the derivatives of displacements and rotations. The quaternion-based scheme for spatial rotations and rotation derivatives is introduced to realize a total Lagrange formulation without singularities. The feasibility and validity of the formulation are demonstrated through six typical examples.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Mathematics, Applied
Pham Toan Thang, T. Nguyen-Thoi, Jaehong Lee
Summary: The main goal of this research paper is to model and analyze bidirectional functionally graded nanobeams using the Timoshenko beam theory and nonlocal strain gradient theory. The study focuses on understanding mechanical behavior, calculating important parameters, and formulating equilibrium and stability equations for a detailed investigation. Specific examples are presented to verify the proposed solution, and the influences of material properties and nonlocal parameter on critical buckling load and transverse deflection are examined.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Civil
Guangyang Fu, Zhenjie Zhang, Chunmei Dong, Yanfei Sun, Jianjun Wang, Hongyu Zheng
Summary: A extended piezomagnetic elasticity theory is developed to describe the size effects phenomenon by incorporating strain gradient elasticity and flexomagneticity. The influence mechanism of strain gradient elasticity on magneto-mechanical response is clarified through analysis of Terfenol-D/Silicon bilayer microbeam. Results show that strain gradient effects and flexomagnetic effects significantly affect the magnetic potential and bending deflection when the beam thickness is comparable to the material length-scale parameters. The extended piezomagnetic elasticity theory with general strain gradient elasticity predicts the magneto-mechanical behavior more appropriately compared to that with reduced strain gradient elasticity.
THIN-WALLED STRUCTURES
(2023)
Article
Mathematics, Applied
Mohammad Arhami, Hamid Moeenfard
Summary: The objective of this paper is to develop a modified strain gradient beam constraint model (MSGBCM) to improve the modeling accuracy of small-scale compliant mechanisms. By considering nano/micro flexure beams and P-flexures, closed-form expressions for the nonlinear load-displacement relationships and stiffness values are derived. The results show that the modified model provides a more accurate description of the behavior of small-scale compliant mechanisms.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
S. Ali Faghidian, Krzysztof Kamil Zur, Ernian Pan
Summary: The mixture unified gradient theory of elasticity integrates the stress gradient, strain gradient, and classical elasticity theory within a consistent variational framework. It incorporates all the governing equations into a single functional, making it a suitable counterpart for the two-phase local/nonlocal gradient theory. The theory can effectively examine various multi-dimensional structural problems in Engineering Science and has significant practical importance.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Engineering, Mechanical
Song Guo, Yuming He, Zhenkun Li, Jian Lei, Dabiao Liu
INTERNATIONAL JOURNAL OF PLASTICITY
(2019)
Article
Mechanics
Jian Lei, Yuming He, Zhenkun Li, Song Guo, Dabiao Liu
COMPOSITE STRUCTURES
(2019)
Article
Mechanics
Lei Liu, Shimin Zheng, Dabiao Liu
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2020)
Article
Instruments & Instrumentation
W. Ali, D. Liu, J. Li, A. D. Pery, N. Herrada, D. Mills, R. A. Owen, P. A. Burton, D. Dong, G. Gannaway, A. J. Bushby, D. J. Dunstan
REVIEW OF SCIENTIFIC INSTRUMENTS
(2020)
Article
Chemistry, Applied
Fuqiang Wan, Hang Ping, Wenxuan Wang, Zhaoyong Zou, Hao Xie, Bao-Lian Su, Dabiao Liu, Zhengyi Fu
Summary: Biological materials possess excellent mechanical properties due to their organized structures at different scales. This study introduces a stress-induced method to fabricate anisotropic alginate fibers by incorporating aligned hydroxyapatite nanowires. The detailed structural characterization reveals a bone-like structure of the reinforced alginate fibers, showing promising mechanical properties.
CARBOHYDRATE POLYMERS
(2021)
Article
Engineering, Mechanical
Fenfei Hua, Dabiao Liu, Yuan Li, Yuming He, D. J. Dunstan
Summary: This study investigates the mechanical properties of thin foils in bending, tension, and constrained layers through experiments and simulations. The passivated layer significantly increases the flow stress of the foil, while the dissipative gradient terms contribute to the increased yield strength and the energetic gradient terms lead to increased strain hardening and an anomalous Bauschinger effect.
INTERNATIONAL JOURNAL OF PLASTICITY
(2021)
Article
Mechanics
Lei Liu, Dabiao Liu, Xinxin Wu, Yuming He
Summary: A quantitative approach for guiding the optimal structural design of multi-strand ropes with hierarchical helical structures has been developed, focusing on optimizing the structural pattern to maximize load-bearing capacity and minimize global torque. The study identifies favorable structural patterns and emphasizes the beneficial effect of crisscross arrangement of strands or wires within the multi-strand ropes for achieving torque-balanced state. Structural parameters have a significant impact on the global mechanical behavior of ropes, with the initial helix angle of the outer strands playing a crucial role in the axial stiffness of wire ropes.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2021)
Article
Materials Science, Multidisciplinary
Tong Luo, Fenfei Hua, Dabiao Liu
Summary: This study investigates the plastic behaviors of thin metallic foils, such as size effect, Bauschinger effect, and passivation effect, under cyclic bending using the strain gradient visco-plasticity theory. Finite element simulations are conducted to analyze the cyclic bending of elasto-viscoplastic thin foils with passivated and unpassivated surfaces, as well as the transition from a passivated surface to an unpassivated one. The results show that the dissipative and energetic gradient terms play crucial roles in influencing the yield strength and strain hardening of the foils, while the surface passivation effect increases both the normalized bending moment at initial yielding and strain hardening.
ACTA MECHANICA SOLIDA SINICA
(2022)
Article
Mechanics
Jianhui Hu, Lei Liu, Liang Zeng, Yuming He, Dabiao Liu
Summary: Twist insertion is an efficient method for producing twisted and coiled polymer muscles. A novel in situ torsion tester is developed to measure the torsional behavior of filaments under axial forces. The critical torques for different instabilities are obtained and compared with the predictions of different models. The results show good agreement between experimental data and model predictions, providing valuable insights into the mechanics of filament-based artificial muscles.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2022)
Article
Instruments & Instrumentation
Jianhui Hu, Liang Zeng, Peng Hu, Yuming He, Dabiao Liu
Summary: The torsional properties of single fibers have significant effects on fabric performance. A new high-resolution torsion tester has been developed to accurately measure these properties, demonstrating high anisotropy in the mechanical properties of various fibers.
REVIEW OF SCIENTIFIC INSTRUMENTS
(2021)
Article
Engineering, Mechanical
Jianfeng Zhao, Bo Zhang, Dabiao Liu, Avraam A. Konstantinidis, Guozheng Kang, Xu Zhang
Summary: This study has reformulated Aifantis' SGP model by incorporating a power-law relation for strain-dependent ILS and considering the grain size effect. The results show that the ILS depends on both the sample size and grain size and can be described by the strain hardening exponent.
ACTA MECHANICA SINICA
(2022)
Article
Materials Science, Multidisciplinary
Ruyan Sun, Dabiao Liu, Zhi Yan
Summary: This work presents a finite element approach for analyzing flexoelectric beam energy harvesters with nonuniform cross-sections. A two-node finite element model with 10 degrees of freedom is proposed, using Hermite polynomials to satisfy the higher order continuity requirement. The proposed method is validated using analytical solutions for a flexoelectric actuator. Results show that energy harvesters with nonuniform cross-sections outperform rectangular ones.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
Song Guo, Yuyang Xie, Jian Lei, Shihao Han, Dabiao Liu, Yuming He
Summary: This study experimentally investigates the coupled effect of specimen size and grain size on the stress relaxation of micron-sized copper wires. It is found that the specimen and grain size decrease leading to an increase in the relaxation process and a decrease in activation volume. The yield strength is affected by the ratio of specimen diameter to grain size, with a critical value of 3.
JOURNAL OF MATERIALS SCIENCE
(2022)
Article
Physics, Applied
Hao Liu, Lei Liu, Zhi Yan, Yuming He, David J. Dunstan, Dabiao Liu
Summary: The morphological transitions of slender ribbons under tension and torsion are studied using a combination of experiment and theory. A unified phase diagram is constructed, and two types of shape evolutions are identified. The mechanical behavior of the stretched and twisted ribbon is described based on an energy method, and the study reveals the dependence of morphology transitions on aspect ratio and tension.
APPLIED PHYSICS LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Lei Liu, Hao Liu, Yuming He, Dabiao Liu
Summary: This study investigates the mechanics and topologically complex morphologies of twisted rubber filaments using a combination of experiment and finite strain theory. A finite strain theory for hyperelastic filaments under combined tension, bending, and torsion has been established, and an experimental and theoretical morphological phase diagram has been constructed. The results accurately determine the configuration and critical points of phase transitions, and the theoretical predictions agree closely with the measurements.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2024)
Article
Mathematics, Applied
Guo Zheng, Zengqiang Cao, Yuehaoxuan Wang, Reza Talemi
Summary: This study introduces two novel methods for predicting the fatigue response of Dynamic Cold Expansion (DCE) and Static Cold Expansion (SCE) open-hole plates. The accuracy of the prediction is enhanced by considering stress distributions and improving existing methods. The study also discusses the mechanisms behind fatigue life enhancement and fatigue crack propagation modes in cold expansion specimens.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Eric Heppner, Tomohiro Sasaki, Frank Trommer, Elmar Woschke
Summary: This paper presents a modeling approach for estimating the bonding strength of friction-welded lightweight structures. Through experiments and simulations, a method for evaluating the bonding strength of friction-welded lightweight structures is developed, and the plausibility and applicability of the model are discussed.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Summary: Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. Traditional projection based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Chanh Dinh Vuong, Xiaofei Hu, Tinh Quoc Bui
Summary: In this paper, we present a dynamic description of the smoothing gradient-enhanced damage model for the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of the dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F. M. Andrade Pires
Summary: This study focuses on analyzing various deformation mechanisms that affect the behavior of PC/ABS blends using computational homogenization. By establishing a representative microstructural volume element, defining the constitutive description of the material phases, and modeling the interfaces and matrix damage, accurate predictions can be achieved. The findings have important implications for broader applications beyond PC/ABS blends.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
David Hoffmeyer, A. R. Damanpack
Summary: This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. The efficacy of the method is validated by numerical examples and a benchmark example, and the analysis on a real sawn timber cross-section reveals significant disparities in the maximum stresses compared to conventional engineering approaches.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Vladimir Stojanovic, Jian Deng, Dunja Milic, Marko D. Petkovic
Summary: The present paper investigates the dynamic analysis of a coupled Timoshenko beam-beam or beam-arch mechanical system with geometric nonlinearities. A modified p-version finite element method is developed for the vibrations of a shear deformable coupled beam system with a discontinuity in an elastic layer. The main contribution of this work is the discovery of coupled effects and phenomena in the simultaneous vibration analysis of varying discontinuity and varying curvature of the newly modelled coupled mechanical system. The analysis results are valuable and have broader applications in the field of solids and structures.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Gihwan Kim, Phill-Seung Lee
Summary: The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. By recovering the fine mesh in the crack path domain into a coarse mesh, this method significantly reduces the number of degrees of freedom involved in the computation.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Souhail Chaouch, Julien Yvonnet
Summary: In this study, an unsupervised machine learning-based clustering approach is developed to reduce the computational cost of nonlinear multiscale methods. The approach clusters macro Gauss points based on their mechanical states, reducing the problem from macro scale to micro scale. A single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster, using a linear approximation of the macro stress. Anelastic macro strains are used to handle internal variables. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Hoang-Giang Bui, Jelena Ninic, Christian Koch, Klaus Hackl, Guenther Meschke
Summary: With the increasing demand for underground transport infrastructures, it is crucial to develop methods and tools that efficiently explore design options and minimize risks to the environment. This study proposes a BIM-based approach that connects user-friendly software with effective simulation tools to analyze complex tunnel structures. The results show that modeling efforts and computational time can be significantly reduced while maintaining high accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Aslan Nasirov, Xiaoyu Zhang, David Wagner, Saikumar R. Yeratapally, Caglar Oskay
Summary: This manuscript presents an efficient model construction strategy for the eigenstrain homogenization method (EHM) for the reduced order models of the nonlinear response of heterogeneous microstructures. The strategy relies on a parallel, element-by-element, conjugate gradient solver, achieving near linear scaling with respect to the number of degrees of freedom used to resolve the microstructure. The linear scaling in the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. The developed framework has been verified using an additively manufactured polycrystalline microstructure of Inconel 625.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Atticus Beachy, Harok Bae, Jose A. Camberos, Ramana V. Grandhi
Summary: Emulator embedded neural networks leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. However, training the ensemble models can be costly and pose computational challenges. This work presents a new type of emulator embedded neural network using the rapid neural network paradigm, which trains near-instantaneously without loss of prediction accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Arash Hajisharifi, Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: This paper introduces three reduced order models for reducing computational time in atmospheric flow simulation while preserving accuracy. Among them, the PODI method, which uses interpolation with radial basis functions, maintains accuracy at any time interval.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
D. Munoz, S. Torregrosa, O. Allix, F. Chinesta
Summary: The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework used for parametric analysis of physical problems. It allows for offline computation and real-time simulation in various situations. However, its efficiency may decrease when the domain itself is considered as a parameter. Optimal transport techniques have shown exceptional performance in interpolating fields over geometric domains with varying shapes. Therefore, combining these two techniques is a natural choice. PGD handles the parametric solution while the optimal transport-based methodology transports the solution for a family of domains defined by geometric parameters.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Jothi Mani Thondiraj, Akhshaya Paranikumar, Devesh Tiwari, Daniel Paquet, Pritam Chakraborty
Summary: This study develops a diffused interface CPFEM framework, which reduces computational cost by using biased mesh and provides accurate results using non-conformal elements in the mesh size transiting regions. The accuracy of the framework is confirmed through comparisons with sharp and stepped interface results.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
