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Applied Mathematics and mechanics(English Edition) 2023年第7期44卷 1039-1068页

作者： W.WU M.DANEKER M.A.JOLLEY K.T.TURNER L.LU Department of Anesthesiology and Critical Care Medicine Children's Hospital of PhiladelphiaPhiladelphiaPA 19104U.S.A. Division of Pediatric Cardiology Children's Hospital of PhiladelphiaPhiladelphiaPA 19104U.S.A. Department of Chemical and Biomolecular Engineering University of PennsylvaniaPhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied mechanics University of PennsylvaniaPhiladelphiaPA 19104U.S.A.

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

关键词： solid mechanics material identification physics-informed neural network(PINN) data sampling boundary condition(BC)constraint

光滑粒子流体力学方法在流体、固体和生物力学中的应用

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Acta Mechanica Sinica 2023年第2期39卷 3-38页

作者：徐绯王佳怡杨扬王璐代震汉芮岐 School of Aeronautics Northwestern Polytechnical UniversityXi’an710072China Institute for Computational mechanics and Its Applications Northwestern Polytechnical UniversityXi’an710072China School of Architecture and Engineering Chang’an UniversityXi’an710064China

光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)作为最早发展的无网格粒子方法之一,对于模拟爆炸、冲击等涉及大变形问题,具有广阔的发展前景.本文对SPH方法在流体、固体和生物力学领域的改进算法和工程应用进行了全面介绍.... 详细信息

光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)作为最早发展的无网格粒子方法之一,对于模拟爆炸、冲击等涉及大变形问题,具有广阔的发展前景.本文对SPH方法在流体、固体和生物力学领域的改进算法和工程应用进行了全面介绍.阐述了SPH的基本理论和高精度SPH改进算法,分析了流体、固体和生物力学领域的改进技术.在模拟流体问题时,采用δ-SPH和GSPH方法解决了流体不稳定性的问题,并且讨论了流固耦合中的界面接触方法.针对固体的数值模拟,总结了三种传统改进方法(如应力点法、守恒光滑法、人工应力法)和Total Lagrangian SPH方法,改善了拉伸不稳定性问题;在生物力学方面,阐述了SPH控制方程和相互作用力的计算方法.本文综述了近年来SPH方法的应用进展,包括复杂海洋工程中的流固耦合问题,固体领域的天体、岩土力学、爆炸冲击以及增材制造等工程应用和生物力学中血流动力学、肠道健康和植物生长等典型应用;并分析了国内外SPH软件的发展,介绍了多尺度自适应分辨率方法、并行计算方法和网格自动生成技术来克服数值模拟方法在计算效率和计算规模上的限制.最后对目前存在的问题进行总结与展望,包括提高SPH算法的数值精度、如何精确描述固体的损伤与断裂问题和计算精度与效率之间的平衡等.在未来研究中,建立多尺度耦合SPH模型和深度学习将是进一步拓宽SPH方法应用的重要方向.

关键词： Smoothed particle hydrodynamics High-accuracy algorithms solid mechanics Biomechanics Computational efficiency

Dynamic tensile and failure behavior of bi-directional reinforced GFRP materials

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Acta Mechanica Sinica 2020年第2期36卷 460-471页

作者： Zishang Liu Zhe Yang Yuchao Chen Yangyang Yu Yanpeng Wei Maohui Li Chenguang Huang Institute of mechanics Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China CRRC Qingdao Sifang Co. LTDQingdao 266111China The Quartermaster Research Institute of Engineering and Technology Beijing 100010China

In this paper,a series of static/dynamic tensile tests are performed for glass fiber reinforced plastic(GFRP)composites.Using the combination of high-speed photography and digital image correlation(DIC)technology,true stress-strain curves in different directions and strain rates are obtained.We also obtained the dynamic failure strain of the material in different directions,which are used to accurately describe the dynamic tensile and failure behavior of the material.The experimental results show that there is a stiffness change point N in three directions under different strain rate(10-3 s-1,10 s-1,100 s-1)tensile conditions.The stiffness before and after N point is recorded as Einitial and Echanged respectively.The values of Echanged in weft direction and warp direction are about 30%to 50%of Einitial,while Echanged in tilt direction is only about 10%of Einitial.The fiber has the highest strength in the weft direction and the tilt direction has the lowest strength.With the combination of high-speed photography and DIC technology,the dynamic failure parameters of different directions under the strain rate of 100 s-1 are obtained.The dynamic failure strains in three directions are 0.245,0.373 and 0.341,respectively.The parameters are verified by impact three-point bending test.These works can more accurately describe the dynamic mechanical behavior of glass fiber reinforced plastic(GFRP)composites and provide reference for the design of GFRP structures.

关键词： solid mechanics Dynamic failure strain Digital image correlation Strain rate effect Stiffness

Algorithm design and the development of a discrete element method for simulating particulate flow and heat transfer

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Clean Energy 2021年第2期5卷 141-166页

作者： Bing Liu National Institute of Clean-and-Low-Carbon Energy CHN Energy InvestmentBeijing 102211P.R.China

An algorithm using the discrete element method(DEM)for simulating the particulate behaviour of flow and heat transfer is developed and described,the reasonable hypothesis and the ingenious design of which have been presented in detail.The organizational structure of the developed algorithm contains an efficient method for determining particle collisions,the status analysis for each particle and the particulate-kinematics analysis during the time step.The reasonability and correctness of the developed DEM algorithm are validated by laboratory experiments:the discharge process of glass beads from a silo;and heating of metal alloy particles in a calciner.Afterwards,a group of validated mechanics parameter values for coal and sand have been tested and verified in the article,preparing for the simulation of the pyrolysis process in a downer or screw reactor in subsequent research projects.

关键词： DEM algorithm particulate flow solid mechanics heat-transfer model

Dynamic crack propagation in plates weakened by nclined cracks:an investigation based on peridynamics

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Frontiers of Structural and Civil Engineering 2018年第4期12卷 527-535页

作者： A.SHAFIEI Department of Mechanical Engineering Yazd UniversityIran Institute of Structural mechanics Bauhaus UniversityWeimarGermany

Peridynamics is a theory in solid mechanics that uses integral equations instead of partial differential equations as governing equations. It can be applied to fracture problems in contrast to the approach of fracture mechanics. In this paper by using peridynamics, the crack path for inclined crack under dynamic loading were investigated. The peridynamics solution for this problem represents the main features of dynamic crack propagation such as crack bifurcation. The problem is solved for various angles and different stress values. In addition, the influence of geometry on inclined crack growth is studied. The results are compared with molecular dynamic solutions that seem to show reasonable agreement in branching position and time.

关键词： peridynamics inclined crack dynamic fracture crack branching Inclined cracks Plates Crack propagation PLATES solid mechanics

Static analysis of elastic cable structures under mechanical load using discrete catenary theory

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Fundamental Research 2023年第6期3卷 967-973页

作者： Weicheng Huang Dongze He Dezhong Tong Yuzhen Chen Xiaonan Huang Longhui Qin Qingguo Fei School of Mechanical Engineering Southeast UniversityNanjing 211189China Jiangsu Engineering Research Center of Aerospace Machinery Southeast UniversityNanjing 211189China Department of Mechanical and Aerospace Engineering University of CaliforniaLos AngelesCA 90095USA Department of Mechanical Engineering and Materials Science Yale UniversityNew HavenCT 06511USA

In this paper,the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory.A cable net is discretized into multiple nodes and edges in our numerical approach,which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation.A fully implicit framework is proposed based on the discrete differential geometry(DDG)theory.The equilibrium configuration of a target object is derived by adding damping force into the system,known as the dynamic relaxation method.The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation.A more intricate scenario is further discussed in detail,where a structure consisting of multiple slender cables is connected through joints.Utilizing the robustness and efficiency of our discrete numerical framework,a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers.Finally,an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties,material characteristics,component numbers,and cable orientations.Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures,and could motivate innovative designs in both mechanical and civil engineered equipment.

关键词： Cable structures Rigidity solid mechanics Computational mechanics Numerical simulation Nonlinearity

Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

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Applied Mathematics and mechanics(English Edition) 2013年第10期34卷 1201-1224页

作者：泮世东周振功吴林志 Center for Composite Materials and Structures Harbin Institute of Technology

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.

关键词： functionally graded piezoelectric/piezomagnetic material multiple parallel symmetric crack crack shielding effect solid mechanics

On Computational Modelling of Strain-Hardening Material Dynamics

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Communications in Computational Physics 2012年第5期11卷 1525-1546页

作者： Philip Barton Evgeniy Romenski Graduate Aerospace Laboratories California Institute of TechnologyCalifornia 91125USA Sobolev Institute of Mathematics Russian Academy of SciencesNovosibirsk 630090Russia

In this paper we show that entropy can be used within a functional forthe stress relaxation time of solid materials to parametrise finite viscoplastic strainhardeningdeformations. Through doing so the classical empirical recovery of a suitableirreversible scalar measure of work-hardening from the three-dimensional stateparameters is avoided. The success of the proposed approach centres on determinationof a rate-independent relation between plastic strain and entropy, which is foundto be suitably simplistic such to not add any significant complexity to the final model.The result is sufficiently general to be used in combination with existing constitutivemodels for inelastic deformations parametrised by one-dimensional plastic strain providedthe constitutive models are thermodynamically consistent. Here a model for thetangential stress relaxation time based upon established dislocation mechanics theoryis calibrated for OFHC copper and subsequently integrated within a two-dimensionalmoving-mesh scheme. We address some of the numerical challenges that are faced inorder to ensure successful implementation of the proposedmodel within a hydrocode.The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

关键词： Entropy viscoplasticity solid mechanics relaxation time Maxwell solid Eulerian

A STUDY ON THE COUNTER-INTUITIVE BEHAVIORS OF PIN-ENDED BEAMS UNDER PROJECTILE IMPACT

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Acta Mechanica solida Sinica 2006年第2期19卷 135-140页

作者： Li Haiwang Qin Dongqi Department of Civil Engineering Taiyuan University of Technology Taiyuan 030024 China

The counter-intuitive behaviors of pin-ended beams under the projectile impact axe investigated with ANSYS/LS-DYNA in this paper. It studies in detail their displacement-time history curves, final deformed shapes, energy relationships and projectile impact velocity ranges related to their counter-intuitive behaviors. The influences of the impact positions on their counterintuitive behaviors are also discussed. The results show that no matter where the impact position on the beam is, the counter-intuitive behaviors of pinned beams will occur as long as the impacting velocity lies within a proper range. Corresponding to the occurring of the counter-intuitive behaviors, the rebounding number in the displacement history curves of the beams decreases from a few times to zero with an increase of the impact velocity. The final deformation modes of the beam corresponding to the counter-intuitive behaviors will appear in symmetrical and unsymmetrical forms no matter where the impact position is; the impact velocity of the first-occurring of the counter-intuitive behaviors of the beam increases slowly with the deviation of the impact position away from the mid-span.

关键词： solid mechanics counter-intuitive behaviors numerical analysis pin-ended beam,projectile impact impact velocity

Damage mechanics with Finite Elements 1

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