Computational Continuum Mechanics

Computational Continuum Mechanics


  • Course code

    ME 616

  • L-T-P-C

    3-0-0-6

  • Syllabus

    Download

  • Eligible Programmes

    Masters



  • Computational Continuum Mechanics

    Review of mathematical preliminaries; Kinematics; Stress and Equilibrium equations; Work conjugacy; Concept of stress rates; Constitutive relations for hyperelastic, incompressible and nearly incompressible materials; Rate-independent plasticity: Multiplicative decomposition of finite deformation, rate kinematics, constitutive relations; Variational/weak Formulation for hyperelasticity, incompressibility and rate independent plasticity; Total Lagrangian formulation; Updated Lagrangian formulation; Linearization of equilibrium equations; Integration of constitutive relations and algorithmic tangent modulus; Discretization and solution: discretized kinematics, discretized equilibrium equations, Newton’s method, line search method, arc-length method; Computational contact mechanics: general formulation, numerical solution procedures.

    Texts/References

    1. J. Bonet and R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, 2008.
    2. K-J. Bathe, Finite Element Procedures, Premtice-Hall India, New Delhi, 1996.
    3. J. C. Simo and T. J. R. Hughes, Computational Inelasticity, Springer-Verlag, New York, 1998.
    4. A. F. Bower, Applied Mechanics of Solids, CRC Press, Boca Raton, 2010. (Also accessible through authors website: http://solidmechanics.org/).
    5. Z. H. Zhong, Finite Element Procedures for Contact-Impact Problems, Oxford University Press, 1993.
    6. J. Besson, G. Cailletaud, J.-L. Chaboche and S. Forest, Non-Linear Mechanics of Materials, Springer, 2010.
    7. P. M. Dixit and U. S. Dixit, Plasticity: Fundamentals and Applications, CRC Press, 2014.
    8. F. Dunne and N. Petrinic, Introduction to Computational Plasticity, Oxford University Press, 2005.
    9. G. A. Holzapfel, Nonlinear Solid Mechanics - A Continuum Approach for Engineering, John Wiley and Sons Ltd., 2000.
    10. T. Belytschko, W. K. Liu, B. Moran and K. Elkhodary, Nonlinear Finite Elements for Continua and Structures, Wiley, 2013.
    11. R. De Borst, M. A. Crisfield, J. J. C. Remmers and C. V. Verhoosel, Nonlinear Finite Element Analysis of Solids and Structures, John Wiley and Sons Ltd., 2012.