Welcome to Luyu's academic page. 

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I am now working on the field is computational mechanics and its applications in geosciences and civil engineering. I focus on both numerical methods and analytical approaches. The underlying physicses include the poroelastic theory, hydrology and fracture mechanics in the deformable porous media, in which solid mechanics and fluid dynamics are two basic pillars. The main essential pursues a unified formulation in continuum mechanics and thermodynamics. 

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I am now a postdoctoral fellow at GeoRessources Lab., Université de Lorraine, French National Centre for Scientific Research (CNRS). I obtained the PhD degree at Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (CAS). During PhD career, I spent almost two years for studying at Department of Applied Math, Delft Uniersity of Technology (TUDelft) and Civil Engineering and Geosciences, Delft University of Technology (TUDelft). I am a member of Society for Industrial and Applied Mathematics (SIAM) of TU Delft Student Chapter and student member of Chinese Society of Theoretical and Applied Mechanics (CSTAM). I have been served as a reviewer of several peer-review journals, to name but a few, Acta Geotechnica; SPE Reservoir Evaluation and Engineering; GeoFluids; Mar. Georesour. Geotechnol.; ZAMM; Comp. Math. Meth.; Advan. Civil. Eng. ; Bull. Eng. Geol. Environ. In the past years, I have joined several projects related geosciences and geotechnical engineering, for instance, nuclear waste disposal, subsurface engineering, coal mining, slope engineering, reservoir engineering, etc. 

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In the past years, I developed my own simulators from scratch. Finite element method (FEM) and finite volume method (FVM) were implemented by C++, where they are used to simulate solid deformation and fluid flow and transport. For fluid dynamics, my works mainly include two topics of fluid flow, flow problem and transport problem. They can be treated as one of the basic PDEs in the view of mathematics, elliptic and  hyperbolic  PDEs, respectively. My devised algorithms are unstructured grid-based scheme, where the discontinuous surfaces (fractures) can be considered as special boundary inside the domain. Actually, when the fractures can be ignored, the code reduces to numerical methods of porous media. Besides, the well-known coupled problem of flow-deformation is an important and hot topic in the research field. The sequential methods are implemented to calculate the field of pressure and displacement in the studied domain. 

 

A mixed-finite element scheme (mixed-FEM) is proposed based on the constrained variational principle, to model the frictional contact and shear failure in deformable fractured media. I built my own simulator for contact mechanics, then the interaction on the intersecting fractures can be handled. Especially, a novel treatment is devised to guarantee physical solution on crossing fractures, therefore the frictional contact, slippage and opening of crossing fractures can be modelled. 

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Theoretical analysis to derive physical models also plays essential role in my research. Especially in the problems of instability of solid structures, I considered the complicated domain that containing fractures/cracks, and provide the analytical solutions during crack propagation around the crack tip using the complex variable theory and fracture mechanics. Moreover, I developed a kind of model based on the statistical physics and thermodynamics to obtain the evolution laws during crack propagation. In the problems of structural mechanics, I also proposed a structural mechanics-based model to study the instability responses regarding the subsurface engineering, where the model was used to predict the behaviours of structures. 

 

My interests also include the mesoscopic simulation, using Lattice Boltzmann Method (LBM). Morefurther, the spring model is coupled with LBM to achieve the coupled geomechanics-flow. Recently my interests are 3D modelling approach of fractured porous media, concerning the complex structures, typically the discrete fractures and the inclusions inside the medium. 

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Recently, I am interested in the Peridynamics (PD) theory. It is a powerful and exciting approach to analyse failure and dynamic damage of solids. Some researchers believe that it endows the properties of molecular dynamics, even view it as a continuum version of the atomic modeling technique. For sure it is an exciting field! 

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Go to other sections of my website: 

• Gallery

• Quotes

• Repository

• Research

• Contact

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