力学进展

2022 Vol. 52, No. 3

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Weight function theory and applications for crack analysis: A review and outlook

WU Xueren, XU Wu

2022, 52(3): 415-507. doi: 10.6052/1000-0992-21-060

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Abstract:
Fracture mechanics is the theoretical foundation for fatigue and fracture analyses of engineering materials and structures, damage tolerance design, and structural integrity assessment. Being the single characterizing parameter of the linear elastic crack tip singular stress/strain field and the crack deriving force, the stress intensity factor (SIF) plays a vital role in fracture mechanics analysis. The weight function method (WFM) is a powerful method for the determination of SIFs for cracks under complex load conditions, with remarkable computational efficiency and reliable solution accuracy, and is easy to use. Combined with the authors’ teamwork on WFM research in the past several decades, this article presents a comprehensive review of the historical developments of various WFMs over the past 50 years and also a brief outlook. The main topics include: a brief introduction of three types of analytical weight function approaches for 2D crack problems and accuracy verification based on Green’s functions; the slice synthesis weight function method and the point weight function method for 3D crack problems; various practical applications of WFMs, including determination of the key fracture mechanics parameters of SIFs and crack opening displacements under complex loadings, cohesive/bridging model analyses, WFM for multiple collinear cracks and residual strength prediction of panels containing multiple site damage, engineering weight function approaches to complex crack configurations, and inverse application of WFM for the determination of stress distributions in un-cracked bodies.

Review on research progress of mechanical metamaterials and their applications in vibration and noise control

YIN Jianfei, CAI Li, FANG Xin, XIAO Yong, YANG Haibin, ZHANG Hongjia, ZHONG Jie, ZHAO Honggang, YU Dianlong, WEN Jihong

2022, 52(3): 508-586. doi: 10.6052/1000-0992-22-005

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Mechanical metamaterials are man-made composite structures or materials constructed from artificial microstructural units with extraordinary static/dynamic properties not found in natural materials. Since these properties mainly depend on the microstructural units rather than the material components, this provides new design schemes for functional materials that allow us to manipulate mechanical properties to a larger extent. This paper first gives a brief introduction to the history, development, and main categories of mechanical materials, followed by their extraordinary mechanical properties. Then we mainly review the research progress and future trends on applications of mechanical metamaterials in underwater sound control, air-borne sound absorption/insulation, structural vibration, and impact control. Last but not least, several types of novel mechanical metamaterials are introduced to provide some reference for scientific researchers and engineers in related fields.

Neurological disease and cognitive dynamics (II): Neural oscillations and cognitive dynamics

HAN Fang, FAN Denggui, ZHANG Liyuan, WANG Qingyun, GU Xiaochun, WANG Zhijie

2022, 52(3): 587-622. doi: 10.6052/1000-0992-21-065

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The brain nervous system has various oscillatory rhythms, from slow to fast. These rhythmic oscillations are believed to be involved in the realization of various brain functions. The high-frequency Gamma synchronous oscillations are considered to be most related to the cognitive functions of the brain. In this review paper, the research progress of Gamma oscillations and their functions in biological experiments is expounded. Then, concerning the biological observation that the frequency of Gamma oscillations sensitively depends on the characteristics of external stimuli, the dynamical modeling work on the variable-frequency Gamma oscillations and the cognitive functions based on neural network models is also expounded. In this paper, the generation mechanisms of variable-frequency Gamma oscillation dynamics regulated by visual stimuli are explained, and a neurocognitive mechanism of global enhancement of firing rate contrast based on synchronous inhibition is proposed. The research results are helpful to understand the generation mechanisms of synchronous oscillations of nervous system and the cognitive functions and lay a foundation for the study of brain working mechanisms of cognitive activities and brain-like intelligence.

Numerical study of non-spherical particle-laden flows

CUI Zhiwen, WANG Ze, JIANG Xinyu, ZHAO Lihao

2022, 52(3): 623-672. doi: 10.6052/1000-0992-22-006

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Non-spherical particle-laden flows are commonly seen and important in nature and industrial processes. The particle's rotational and orientational behaviors could affect the forces and torques acting on the particle from ambient fluid flow. To accurately capture the motion of non-spherical particles, especially for angular particle dynamics, most numerical studies of non-spherical particle-laden flows are carried out in the Euler-Lagrange frame. There are two most popular numerical approaches: the point-particle method and the particle-resolved method. This paper comprehensively and systematically summarizes these methods and significant recent findings about non-spherical particles in simple and turbulent flows. The mechanism of particle orientation and rotation by suspended non-spherical particles, as well as the modulation effect of particles on turbulent drag reduction, are discussed. Furthermore, the key and unsolved problems of non-spherical particle-laden flows for future study are proposed at the end of the paper.

Design of lightweight lattice meta-structures and approaches to manipulate their multi-functional mechanical properties

WU Wenwang, XIA Re

2022, 52(3): 673-718. doi: 10.6052/1000-0992-22-002

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With the rapid development of advanced manufacturing technology, multidisciplinary integration, and artificial intelligence technology, high-end equipment demonstrates the development trends of lightweight, integrated, composited, multi-functional, intelligent, flexible, and biomimetic features. Traditional structural research has encountered many intrinsic problems that constrain devices, and instruments performances, such as structural design and manufacturing are separated from each other, relative low manufacturing efficiency of complex structures, practical structural performances, and reliability of manufactured structures are significantly lower than theoretical predictions, insufficient multi-functional integration of structures, and high costs. In addition, materials and structures for constructing advanced industrial equipments are required to maintain reliable performances and endure extremely crucial service environments. It is urgent to carry out research on the synergy effects of design, manufacture, function, and applications of structures, thus providing theoretical foundations and technical support for solving the key technical problems of advanced manufacturing strategic plans. Lightweight multi-functional lattice meta-structures exhibit extraordinary mechanical performance advantages of lightweight, specific strength, impact energy absorption, shock absorption, and noise reduction advantages, and demonstrate great industrial application potentials in aerospace, transportation, national defense, biomedical, energy, machinery, equipment, and other industrial fields. Considering the above-mentioned status-quo, inspired by the multi-scale microstructures of the polycrystalline, the mechanical design of lightweight multi-functional lattice meta-structures is reviewed in this paper, and is elaborated from the perspectives of typical design methods, such as nodes, strut components, unit cell types, dual-phase structures, gradient structures and hierarchical structures of lattice structures. Afterward, physical foundations for design innovations based on multi-scale microstructures of polycrystalline are explained, rational regulations of multi-functional mechanical properties, and the underlying deformation and failure mechanisms are demonstrated.

Interfacial electrohydrodynamic waves under horizontal electric fields: Hamilton’s principle and multi-scale modeling

WANG Zhan

2022, 52(3): 719-729. doi: 10.6052/1000-0992-22-035

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This paper is concerned with the multi-scale modeling of interfacial waves between two dielectric fluids under a horizontal electric field. First, we give a detailed proof of the Hamilton principle for this system. Next, based on the Hamiltonian structure and the analytical property of the Dirichlet-Neumann operator, the kinetic energy and electric potential energy in the Hamiltonian are expanded into the form of convergent series, and the order of truncation is determined. Finally, the reduced model is obtained by calculating the variational derivatives of the approximate total energy after truncation. The above process provides a systematic method for establishing nonlinear multi-scale models. Taking the case of “deep upper layer and shallow lower layer” as an example, we describe the whole modeling process in detail. Furthermore, the nonlinear coherent structure in the newly proposed model is computed using the modified Petviashvili iterative method. The asymptotic technique developed in this paper differs from previous work. Its advantage is that the derived reduced models naturally retain the energy conservation property; at the same time, this paper also extends the previous results to the three-dimensional situation.

2022 Vol. 52, No. 3

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