Finite-Element-Formulierung

Theoretical and numerical contributions for the description of localization phenomena in structural mechanics

In the field of material research, the term 'localization' represents processes which are characterized by a concentration of inelastic deformations in narrow zones within solids; beyond these zones, pure elastic behaviour can normally be observed. The appearance of this phenomenon depends primarily on the specific characteristics of the material. Under experimental conditions, the following kinds of localizations can be observed: shear bands in ductile materials, slip surfaces in granular materials and cracks in brittle materials.

A continuum mechanical description based on standard stress-strain constitutive equations including strain-softening is not suitable to describe localization phenomena, since the type of the partial differential equations governing the problem changes when the localization appears; this finally leads to an ill-posed boundary value problem. In this case a finite-element calculation reveals that there is a pathological dependency of the results on the spatial discretization.

In this research project different models for the regularization of this problem are presented. In addition to extended continuum theories, which are primarily based on the consideration of a characteristic length in the material model, discontinuous models have also been investigated. They interpret the localization zone as a singular surface inside the body which contains certain kinematic discontinuities. With the help of numerical tests, a regularizing effect of the models which were tested could be demonstrated. The results did not reveal the presence of any pathological dependency on the chosen spatial discretization.

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