Numerical Methods for Nonlinear Mechanics

University of Grenoble Alpes
EE - Earthquake Engineering
Fall 2015
Date (from - to):
01/09/2015 – 29/01/2016
  • From physics to numerical models: continuum mechanics problems, variational formulations, Rayleigh Ritz methods, Finite element one dimensional example
  • Introduction to solid mechanics problems : elastostatics virtual work theorem : finite element discretization, the example of simple finite elements (constant strain triangle), Comments about Stiffness matrices
  • Variational formulation of an initial boundary value problem: change of configuration, introduction to different stress and deformation tensors, the so called small strain approximation
  • Time discretization and incremental problem: Newton method, residual computations, auxiliary linear system computations, boundary condition issues
  • Space discretization : finite element method, projection on to a finite dimensional space, isoparametric finite element numerical integration Gauss method
  • Constitutive equations integrations : consistent tangent stiffness matrix: numerical approach, Hardening plasticity,  integration algorithms, consistent tangent stiffness matrix : analytical approach, Locking ant related topics
  • Miscellaneous : coupling problems, the rate problem and uniqueness issues

Suggested readings:

  • Zienkiewicz an Taylor. – The finite element method. Butterworth Heinemann, Oxford, 2000
  • Belytschko Liu and Moran – Nonlinear finite elements for continua and strutures. JohnWiley, New‐York, 2001
  • Simo Hughes. ‐ The Computational inelasticity. Springer, New‐York, 1998
  • Crisfield. – Non linear finite element analysis of solids and structures (Volume 2). JohnWiley, New‐York, 2000
  • Bonet Wood – Non linear continuum mechanics for finite element analysis, Cambridge University Press, 1997