Progress in Computational Analysis of Inelastic Structures

In recent years it has been observed active research work in the field of the instability phenomena of plastic flow processes. Particularly the localization of plastic deformation along a shear band treated as a prelude to failure initation has been a matter of a great interest.

Proper design of the computational algorithm is absolutely essential in order to account for the failure mechanisms that are responsible for the development of a strongly localized mode of deformation. In this paper we discuss how to simulate numerically localized behavior of the deformation due to incorporation of non-associated plastic flow and/or softening behavior in the elasto-plastic material model. The development of a localization zone of a slope stability problem is captured by the use of a FE-mesh adaptation strategy, which aims at realigning the inter-element boundaries so that the most critical kinematical failure mode is obtained. Based on the spectral properties of the characteristic material operator we define a criterion for discontinuous bifurcation. As a by-product from this criterion, we obtain critical bifurcation directions which are used to realign the element mesh in order to enhance the ability of the model to describe properly the failure kinematics. Moreover, a successful algorithm also includes consideration of stability properties of the elasto-plastic solution.

The goal of this lectures is to survey some recent developments in the numerical analysis of classical plasticity and viscoplasticity. For the infinitesimal theory, the continuum mechanics aspects of the subject are currently well understood and firmly established. Classical expositions of the basic theory can be found in the work of HILL [1950], KOITER [1960] and others. On the mathematical side, classical plasticity experienced a significant development in the 70’s and early 80’s, starting with the pioneering work of DUVAUT & LIONS [1972]. The subsequent improvement of JOHNSON [1978], MATTHIES [1979], SUQUET [1979], TEMAM & STRANG [1980] and others produced at the beginning of the 80’s a fairly complete mathematical picture of the theory.

This course will give an introduction to theoretical and numerical shake-down analysis of perfectly plastic and kinematic hardening materials in the framework of geometrical linear theory.

This three lectures course will give a modern concept of finite-element- analysis in nonlinear solid mechanics using material (Lagrangian) and spatial (Eulerian) coordinates. Elastic response of solids is treated as an essential example for the geometrically and material nonlinear behavior. Furthermore a brief introduction in stability analysis and the associated numerical algorithms will be given.

A main feature of these lectures is the derivation of consistent linearizations of the weak form of equilibrium within the same order of magnitude, taking also into account the material laws in order to get Newton-type iterative algorithms with quadratic convergence.

The lectures are intended to introduce into effective discretizations and algorithms based on a well founded mechanical and mathematical analysis.