FUNDAMENTAL ISSUES IN FINITE ELEMENT ANALYSES OF LOCALIZATION OF DEFORMATION

TLDR

Classical continuum models lacking an internal length scale exhibit excessive mesh dependence with strain‑softening and fail to capture the size effect seen in quasi‑brittle failure. The study evaluates three enrichment strategies—higher‑order deformation gradients, micropolar continuum models, and rate dependence—to remedy these deficiencies, and examines the role of dispersion in wave propagation for dynamic problems. Numerical simulations will determine the conditions under which these enriched theories permit deformation localization while maintaining ellipticity for static problems and hyperbolicity for dynamic problems.

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi‐brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher‐order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain‐softening media will also be highlighted.