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Documenta Geonica   1 / 1998

The theory of plasticity is used for the solution of many engineering problems. It serves for calculation of permanent deformation of structures, for prediction of plastic collapse structures, for investigation of stability in the soil mechanics, for calculation of forces in metal forming operations, ets. Another aspect of plasticity consists in its coupling with damage which is important for modelling concrete, rocks, etc. This range of applications shows the importance of the theory of plasticity which includes finding the accurate models which fit the behaviour of various materials under various types of loading, development of testing procedures for the determination of the material parameters for the plasticity models as well as development and analysis of the mathematical formulation and numerical methods for the solution of the plasticity problems.

Contents

  • Elasto – plasticity
    • Elasticity
    • Elasto – plasticity
  • Incremental finite element method
    • Basic discretization scheme
    • Explicit Euler scheme
    • Modified explicit Euler scheme
    • Explicit Euler method for regularized plasticity
    • Implicit Euler methods
    • Return mapping concept
    • Adaptive discretization
    • Concluding remarks
  • Inexact Newton –type solvers
    • Algebraic nonlinear systems
    • Newton – type methods
  • Programming the incremental FE methods
    • Basic data for problem description
    • Program plasticity
  • Convergence analysis of Newton – type solvers in the case of regularized plasticity
    • Approximation condition
    • Convergence analysis
    • Concluding remarks
  • Convergence analysis of Newton–type solvers for return mapping incremental method
    • Properties of the constitutive operator
    • Properties of the nonlinear operators
    • Inexact initial stiffness method
    • Inexact Newton method
  • Bibliography