Barna Szabó
Center for Computational Mechanics
Washington University in St. Louis, USA
szabo@me.wustl.edu
Singularities and boundary layers are of considerable interest in mathematical analysis because they characterize the regularity of the solution. The solutions in the neighborhoods of singular points and generally at steep stress gradients are of great engineering interest also because failure events typically originate in those neighborhoods. Most of the development work to date has been concerned with linear models.
The question of why and under what conditions is it possible to employ linear models for the prediction of failure in solid bodies, an essentially nonlinear phenomenon, is addressed. Engineering computations are usually performed with one of three objectives in mind: (a) Establishment of criteria for design; (b) design, and (c) certification of design.
Establishment of design criteria is a continuously evolving process. It involves the formulation of a hypothesis and experimental testing to determine whether to accept or reject the hypothesis. The ultimate goal is to validate a hypothesis for a widest possible range of conditions. Since the parameters postulated by the hypothesis are not observable directly, they must be determined by computation. The asymptotic expansions in linear models have been used very successfully for metallic bodies subjected to cyclic loading. The investigation of design criteria for composite materials and metals at elevated temperatures is much more complicated and typically requires that non-linear behavior be taken into account. This suggests the need for extending the investigation of critical regions to nonlinear models. Examples will be presented.