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Revealing and predicting the long-term biomechanical response of orthokeratology by developing a patient-specific computational model

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Science China(Physics,mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 156-168页

作者： Yifeng Li Zhuoran Yang Ziming Yan Huibin Shi Zhanli Liu Kaijie Wang Department of Engineering mechanics School of Aerospace Engineering Tsinghua University Beijing Tongren Eye Center Beijing Tongren Hospital Capital Medical University Beijing Ophthalmology & Visual Sciences Key Lab

Orthokeratology(OK) is widely used for effective myopia correction and control. However, the incomplete understanding of its biomechanical mechanisms makes OK lens fitting rely heavily on clinician judgment, complicating accurate predictions of treatment outcomes. In this paper, we performed clinical experiments and numerical analysis to study corneal deformation modes and long-term changes in central corneal thickness. Clinical experiments were conducted on 194 Chinese myopic patients under OK treatment for 3 months. Based on the experimental data, a patient-specific computational biomechanical model for OK was established and validated. Specifically, the anisotropic mechanical properties of the cornea were incorporated into the model to describe the significant difference between its shear modulus(29.5 kPa) and tensile modulus(768.4 kPa). Additionally, a viscohyperelastic material model with a prolonged corneal relaxation time of 5.6 h was developed to capture the long-term deformation response. The results show that corneal thickness reduction in OK is primarily due to out-of-plane shear deformation,influenced by the cornea's low shear resistance. Modeling the extended corneal relaxation time is crucial for predicting long-term biomechanical responses. The computational model effectively captures long-term changes in central corneal thickness, potentially improving OK lens fitting accuracy.

关键词： orthokeratology computational biomechanical model long-term viscoelasticity myopia correction

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Fundamental problem in optimizing the biaxial testing specimen

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Science China(Technological Sciences) 2019年第5期62卷 773-780页

作者： IMTIAZ Haroon FANG YaoPeng DU JianBin LIU Bin Department of Engineering mechanics Applied Mechanics Lab Tsinghua University

Most of the elements in structural design are subjected to the complex loading conditions that need to be predicted in advance for a reliable design. The failure prediction of these structural elements is based on the failure theories that employ the experimental data of the uniaxial, the biaxial and the shear tests. Among these tests, the biaxial testing is used to model the behavior of the structure loaded in more than one direction. In this study, we discover an interesting fact for the biaxial tension specimen that the thickness reduction of the measuring region cannot increase the stress to a high level. This behavior of the biaxial testing is different from the uniaxial testing where the thickness reduction of the measuring region always increases its stress to a higher level. Therefore, we further investigate the biaxial testing specimen via related fundamental problem, i.e., an axisymmetric plate with varying thickness under axisymmetric tension. We perform the shape optimization based on our analytical solution and the FEM results. For an infinite axisymmetric disk, the optimized design should include a low slope diverging section connecting the inner to outer region. On the contrary, the larger inner measuring region for finite axisymmetric disk would result in higher corresponding stress. These conclusions can be used as a guideline for the design of a biaxial testing specimen.

关键词： uniaxial testing biaxial testing axisymmetric disk problem optimization

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Damage evaluation of reinforced concrete frame based on a combined fiber beam model

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Science China(Physics,mechanics & Astronomy) 2014年第4期57卷 723-730页

作者： SHANG Bing LIU ZhanLi ZHUANG Zhuo applied mechanics lab School of Aerospace Tsinghua University

In order to analyze and simulate the impact collapse or seismic response of the reinforced concrete(RC)structures,a combined fiber beam model is proposed by dividing the cross section of RC beam into concrete fiber and steel *** stress-strain relationship of concrete fiber is based on a model proposed by concrete codes for concrete *** stress-strain behavior of steel fiber is based on a model suggested by *** constitutive models are implemented into a general finite element program ABAQUS through the user defined subroutines to provide effective computational tools for the inelastic analysis of RC frame *** fiber model proposed in this paper is validated by comparing with experiment data of the RC column under cyclical lateral *** damage evolution of a three-dimension frame subjected to impact loading is also investigated.

关键词： RC frame structure fiber model beam-column element dynamic response impact

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On determination of the damping factor of linear viscoelastic materials using dynamic indentation:a theoretical study

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Science China(Physics,mechanics & Astronomy) 2011年第4期54卷 598-605页

作者： CAO YanPing JI XiangYing FENG XiQiao applied mechanics lab Department of Engineering Mechanics Tsinghua University Beijing 100084 China

In this study,we theoretically investigate the dynamic indentation for measuring the loss (damping) factor of a linear viscoelastic material from its indentation response.A rigid indenter with arbitrary tip profile is assumed to indent into a viscoelastic substrate with arbitrary *** perform a theoretical analysis and identify the conditions under which the loss factor of the material can be determined from the phase angle between the applied harmonic indentation load and the corresponding harmonic displacement,a directly measurable quantity in a dynamic indentation *** validate the conclusion drawn from our theoretical analysis,a series of numerical experiments are performed,including the spherical indentation of a soft layer with irregular surface morphology bonded to a rigid substrate,a conical indenter with tip defects indenting into a half-spherical particle,and the indentation of porous *** study may facilitate the use of the dynamic indentation technique to evaluate the damping properties of linear viscoelastic materials,including some advanced polymers and biological soft tissues.

关键词： dynamic indentation damping properties viscoelastic materials f'mite element simulation

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XFEM modeling of hydraulic fracture in porous rocks with natural fractures

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Science China(Physics,mechanics & Astronomy) 2017年第8期60卷 45-59页

作者： Tao Wang ZhanLi Liu QingLei Zeng Yue Gao Zhuo Zhuang applied mechanics lab. School of Aerospace Engineering Tsinghua University

Hydraulic fracture （HF） in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method （XFEM） coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures （NFs）. In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex frac^xre network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk （KGD） model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.

关键词： hydraulic fracture XFEM porous media fluid flow multi-physics coupling

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INTERFACIAL BEHAVIOR OF PIPE JOINTS UNDER TORSION LOADS

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Acta Mechanica Solida Sinica 2015年第5期28卷 521-535页

作者： Jun Han Hong Yuan Jiayu Wu MOE Key lab of Disaster and Control in Engineering Institute of Applied Mechanics Jinan University

The interfacial behavior of pipe joints is studied in this paper. Firstly, through nonlinear fracture mechanics, the analytical expressions of interfacial shear stress and the load- displacement relationship at loaded end of pipe joints under torsion loads are obtained. Thus the shear stress propagation and the debonding process of the whole interface for different bond lengths can be predicted. Secondly, through the analytical solutions, the influences of different bond lengths on the load-displacement curve and the ultimate load are studied. The stress trans- fer mechanism, the interface crack propagation and the ductility behavior of the joints can be explained.

关键词： interface failure mechanism softening debonding torsion pipe joints

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A hierarchical dislocation-grain boundary interaction model based on 3D discrete dislocation dynamics and molecular dynamics

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Science China(Physics,mechanics & Astronomy) 2011年第4期54卷 625-632页

作者： GAO Yuan ZHUANG Zhuo YOU XiaoChuan applied mechanics lab School of Aerospace Tsinghua University Beijing 100084 China

We develop a new hierarchical dislocation-grain boundary （GB） interaction model to predict the mechanical behavior of poly- crystalline metals at micro and submicro scales by coupling 3D Discrete Dislocation Dynamics （DDD） simulation with the Molecular Dynamics （MD） simulation. At the microscales, the DDD simulations are responsible for capturing the evolution of dislocation structures; at the nanoscales, the MD simulations are responsible for obtaining the GB energy and ISF energy which are then transferred hierarchically to the DDD level. In the present model, four kinds of dislocafion-GB interactions, i.e. transmission, absorption, re-emission and reflection, are all considered. By this methodology, the compression of a Cu mi- cro-sized bi-crystal pillar is studied. We investigate the characteristic mechanical behavior of the bi-crystal compared with that of the single-crystal. Moreover, the comparison between the present penetrable model of GB and the conventional impenetrable model also shows the accuracy and efficiency of the present model.

关键词： Grain boundary Multiscale simulation Discrete dislocation dynamics Bi-crystal compression

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Deformable micro-continua in which quantum mysteries reside

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applied Mathematics and mechanics(English Edition) 2019年第12期40卷 1805-1830页

作者： Heng XIAO Shanghai Institute of applied Mathematics & mechanics College of Mechanics and Engineering Science Shanghai University College of mechanics and Construction Engineering MOE Lab of Disaster Forecast and Control in Engineering Jinan University

Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic *** every instant,the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass,the velocity,the internal stress,and the intrinsic angular *** deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density *** is shown that these microcontinua are endowed with the following unique response features:(i)the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable;(ii)this fundamental dynamic equation and this complex field variable are just the Schrodinger equation and the complex wave function in quantum theory;and,accordingly,(iii)the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered,thus following objective and deterministic response patterns for quantum entities,in which the physical origins and meanings of the wave function and the Schrodinger equation become self-evident and,in particular,any probabilistic indeterminacy becomes irrelevant.

关键词： quantum entity micro-continuum Hencky strain-energy density nonlinear dynamic equation exact linearization Schrodinger equation deterministic pattern

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ENRICHED GOAL-ORIENTED ERROR ESTIMATION applied TO FRACTURE mechanics PROBLEMS SOLVED BY XFEM

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Acta Mechanica Solida Sinica 2012年第4期25卷 393-403页

作者： Zhijia Lin Zhuo Zhuang Xiaochuan You Heng Wang Dandan Xu applied mechanics lab. School of AerospaceTsinghua UniversityBeijing 100084China

Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method （XFEM）, which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.

关键词： goal-oriented error estimation extended finite element method fracture mechanics error bounds

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Hierarchical model for strain generalized streaming potential induced by the canalicular fluid flow of an osteon

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Acta Mechanica Sinica 2015年第1期31卷 112-121页

作者： Xiao-Gang Wu Wei-Lun Yu Hai-Peng Cen Yan-Qin Wang Yuan Guo Wei-Yi Chen College of mechanics Shanxi Key Lab. of Material Strength & Structural Impact Taiyuan University of Technology Institute of applied mechanics and Biomedical Engineering Taiyuan University of Technology

A hierarchical model is developed to predict the streaming potential （SP） in the canaliculi of a loaded os teon. Canaliculi are assumed to run straight across the os teon annular cylinder wall, while disregarding the effect of lacuna. SP is generalized by the canalicular fluid flow. Ana lytical solutions are obtained for the canalicular fluid veloc ity, pressure, and SP. Results demonstrate that SP amplitude （SPA） is proportional to the pressure difference, strain am plitude, frequency, and strain rate amplitude. However, the key loading factor governing SP is the strain rate, which is a representative loading parameter under the specific phys iological state. Moreover, SPA is independent of canalicu lar length. This model links external loads to the canalicu lar fluid pressure, velocity, and SP, which can facilitate fur ther understanding of the mechanotransduction and electro mechanotransduction mechanisms of bones.

关键词： Canaliculi Streaming potential (SP) - Poroe-laticity Fluid flow

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