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A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows

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Acta Mechanica Sinica 2012年第5期28卷 1309-1322页

作者： Jian-Hui Liao zhuo zhuang School of Aerospace Tsinghua University

In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.

关键词： Two-phase flow XFEM SUPG/PSPG algorithm Consistency Discontinuous projection

Development of X-FEM methodology and study on mixed-mode crack propagation

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Acta Mechanica Sinica 2011年第3期27卷 406-415页

作者： zhuo zhuang Bin-Bin Cheng School of Aerospace Tsinghua University 100084 Beijing China

The extended finite element method（X-FEM） is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effiect on fracture made by interface and loading condition.

关键词： X-FEM - Mixed-mode fracture . Bi-material Sub-interfacial crack

A Lagrange-multiplier-based XFEM to solve pressure Poisson equations in problems with quasi-static interfaces

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Science China(Physics,Mechanics & Astronomy) 2012年第4期55卷 693-705页

作者： LIAO JianHui zhuang zhuo School of Aerospace Tsinghua UniversityBeijing 100084China

The XFEM(extended finite element method) has a lot of advantages over other numerical methods to resolve discontinuities across quasi-static interfaces due to the jump in fluidic parameters or surface ***,singularities corresponding to enriched degrees of freedom(DOFs) embedded in XFEM arise in the discrete pressure Poisson *** this paper,constraints on these DOFs are derived from the interfacial equilibrium condition and introduced in terms of stabilized Lagrange multipliers designed for non-boundary-fitted meshes to address this *** results show that the weak and strong discontinuities in pressure with straight and circular interfaces are accurately reproduced by the *** with the SUPG/PSPG(streamline upwind/pressure stabilizing Petrov-Galerkin) method without Lagrange multipliers validate the applicability and flexibility of the proposed constrained algorithm to model problems with quasi-static interfaces.

关键词： XFEM pressure Poisson equation singularity Lagrange multiplier quasi-static flows

A novel enriched CB shell element method for simulating arbitrary crack growth in pipes

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Science China(Physics,Mechanics & Astronomy) 2011年第8期54卷 1520-1531页

作者： zhuang zhuo CHENG BinBin School of Aerospace Tsinghua University Beijing 100084 China

In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.

关键词： CB shell element enriched shape functions extended finite element 3D arbitrary crack propagation energy release rate

Finite element analysis for wellbore stability of transversely isotropic rock with hydraulic-mechanical-damage coupling

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Science China(Technological Sciences) 2017年第1期60卷 133-145页

作者： WANG YongLiang LIUZhanLi YANG HengLin zhuang zhuo Drilling Research Institute China National Petroleum Corporation Beijing 100195 China

The finite element analysis （FEA） technology by hydraulic-mechanical-damage （HMD） coupling is proposed in this paper for wellbore stability analysis of transversely isotropic rock, developed basing on the recently established FEA technology for iso- tropic rock. The finite element （FE） solutions of numerical wellbore model, damage tensor calculation and Pariseau strength criterion for transversely isotropic rock are developed for researching the wellbore failure characteristics and computing the collapse and fracture pressure of laminated rock as shale reservoirs. The classic Blot constitutive for rock as porous medium is introduced to establish a set of FE equations coupling with elastic solid deformation and seepage flow. To be in accord with the inclined wellbore situation, the coordinate transformation for global, wellbore, in-situ stress and transversely isotropic for- mation coordinate systems is established for describing the in-situ stress field and the results in laminated rock. To be in accord with the practical situation, a three-dimensional FIE model is developed, in which several other auxiliary technologies are com- prehensively utilized, e.g., the typical Weibull distribution function for heterogeneous material description and adaptive tech- nology for mesh refinement. The damage tensor calculation technology for transversely isotropic rock are realized from the well-developed continuum damage variable of isotropic rock. The rock is subsequently developed into a novel conceptual and practical model considering the stress and permeability with the damage. The proposed method utilizing Parisean strength cri- terion fully reflects the strength parameters parallel or perpendicular to bedding of the transversely isotropic rock. To this end, an effective and reliable numerically three-step FEA strategy is well established. Numerical examples are given to show that the proposed method can establish efficient and applicable FE model and be suitable for analyz

关键词： finite element analysis wellbore stability transversely isotropic rock damage tensor hydraulic-mechanical-damagecoupling

Recent research progress in computational solid mechanics

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Chinese Science Bulletin 2012年第36期57卷 4683-4688页

作者： zhuang zhuo MAITIREYIMU Maigefeireti School of Aerospace Tsinghua University

Computational mechanics has had a profound impact on science and technology over the past five *** has numerically transformed much of the classical theory models into practical tools for predicting and understanding the complex engineering and science system.A short review is given in this paper on some recent progress in computational solid mechanics at multi-scales.

关键词：计算固体力学力学科学实用工具科学系统经典理论数字转换多尺度

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

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

Tensile properties of individual multicellular Bacillus subtilis fibers

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Science China(Physics,Mechanics & Astronomy) 2019年第9期62卷 70-78页

作者： Xuan Ye Tao Wang zhuo zhuang XiDe Li Applied Mechanics Laboratory Department of Engineering MechanicsTsinghua UniversityBeijing 100084China Center for Nano and Micro Mechanics Tsinghua UniversityBeijing 100084China

Microfibers formed by Bacillus subtilis(B. subtilis) have attracted interest because of their potential for use as biodegradable fibers. In this work, an efficient method based on the micro-liquid bridge method(LBM) is proposed to investigate the mechanical properties and the deformation evolution in individual fibers. For the first time, tensile testing of fibers of this type containing several cells is conducted in a scanning electron microscope(SEM) chamber and the in situ deformation evolution of the fibers and the septa is observed. Experimental results show that these fibers are almost broken at the positions of the septa at low humidity, but also show that their fracture morphologies are different. At high humidity, local necking deformation occurs at the septum position. To explore the deformation mechanism of an individual bacterial fiber with a diameter of several hundred nanometers under different humidity conditions, we use the finite element method(FEM) to analyze the tensile deformation behavior of these fibers when their septa are at various separation levels. The numerical results indicate that weak interactions among the septa lead to the dispersion of both the fibrous tensile strength and the modulus. These results may be helpful in understanding the deformation mechanism, thus leading to further improvements in the mechanical performance of these fibers.

关键词： Bacillus subtilis mechanical properties micro-liquid bridge method finite element method