Theory and Formulation: This talk introduces a basic theory for unified formulation of a wide class of compatible and incompatible methods based on FEM and meshfree settings for solid mechanics problems. Important properties and inequalities for G spaces are proven, leading to the so-called weakened weak (W2) formulation that guarantees stable and convergent solutions. We then present some W2 models that are: 1) linearly conformability ensuring the stability and convergence; 2) softening effects leading to certified solutions and real-time computational models; 3) insensitivity to the quality of mesh allowing effective uses of triangular/tetrahedral meshes best suited for adaptive analyses.

Applications: Examples will be presented for simulating material behavior at various extreme situations, crack propagation in materials, fatigue lift prediction, dynamic behavior and interactions of red blood cells, blood flow over heart valve, inverse identification of material properties and cracks in engineering structural systems, and integrity assessment of dental implant systems via inverse analysis with real-time computation.

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Dr. Liu received PhD from Tohoku University, Japan in 1991. He was a Postdoctoral Fellow at Northwestern University, USA from 1991-1993. He is currently a Professor, Ohio Eminent Scholar and School Faculty Chair at the School of Aerospace Systems, University of Cincinnati. He served as a Deputy Head of the Department of Mechanical Engineering, the Director of the Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, and the President of the Association for Computational Mechanics. He is the President of the Asia-Pacific Association for Computational Methods, and an Executive Council member of the International Association for Computational Mechanics. He authored a large number of international journal papers and books including two bestsellers: “Mesh Free Method: moving beyond the finite element method” and “Smoothed Particle Hydrodynamics: a Meshfree Particle Methods.” He is the Editor-in-Chief of the International Journal of Computational Methods, Associate Editor of the international technical journal Inverse Problems in Science and Engineering (IPSE), and served as an editorial member of five other journals including the IJNME.